Wave Function Interpretation and Quantum Mechanics Equations

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inter-item agreement 指数 -回复

inter-item agreement 指数-回复[Interitem Agreement Index]Interitem agreement refers to the level of agreement among multiple items, statements, or questions in a given measurement tool or survey instrument. This index is used to assess the consistency and reliability of the measurements produced by the instrument. In this article, we will delve deeper into the concept of interitem agreement, discuss its calculation and interpretation, and explore its importance in research and data analysis.To begin with, interitem agreement is a statistical measure that quantifies the extent to which items in a measurement tool are correlated with each other. It is commonly used in the fields of psychology, sociology, and marketing research to evaluate the internal consistency of a scale or survey. Internal consistency refers to the degree to which the items in a measurement tool measure the same underlying construct or concept.The interitem agreement index is calculated using various methods, with Cronbach's alpha being the most widely used. Cronbach's alpha is a coefficient that ranges from 0 to 1, where a higher value indicates stronger interitem agreement. A value of 1 represents perfect agreement, while a value close to 0 indicates poor agreement among the items.To calculate Cronbach's alpha, researchers use the formula:α= (n / (n-1)) * [1 - (Σσ²i / σ²x)]In this formula, 'n' represents the number of items in the measurement tool, σ²i denotes the variance of each item, and σ²x is the variance of the total score. The sum of the variances of each item is divided by the variance of the total score, and the resulting value is subtracted from 1. Lastly, the equation is multiplied by the adjustment factor (n / (n-1)) to correct for bias.Once Cronbach's alpha is calculated, the interpretation of the interitem agreement index depends on its value. Generally, a value above 0.7 is considered acceptable for research purposes, while values above 0.8 are desirable. However, it is important to note that the acceptable threshold may vary based on the specific context and research field.A high interitem agreement index indicates that the items in the measurement tool are measuring the same construct consistently. This suggests that the items are reliable and can be used to accurately measure the targeted concept. On the other hand, a low interitem agreement index suggests that the items are assessing different aspects or dimensions of the construct, leading to inconsistent results.Why is interitem agreement important? Firstly, it ensures thereliability and validity of measurement tools. By assessing the consistency among items, researchers can identify problematic questions or statements that may need refining or removal from the instrument. This helps to minimize measurement error and increase the accuracy of the collected data.Furthermore, interitem agreement provides insights into the underlying structure of the measured construct. High agreement indicates that the items are unidimensional and reflect a single factor or trait. However, if the interitem agreement is low, it suggests that the construct may be multidimensional, and further exploration is needed to understand its complex nature.In conclusion, the interitem agreement index plays a crucial role in research and data analysis. It quantifies the consistency and reliability of measurement tools, provides insights into the structure of the measured construct, and helps researchers assess the quality of their instruments. By understanding and calculating the interitem agreement index, researchers can enhance the robustness and reliability of their findings, as well as contribute to the advancement of knowledge in their respective fields.。

色彩还原度英语

色彩还原度英语Color Restoration DegreeThe world we live in is a vibrant tapestry of hues, each color possessing the power to evoke emotions, influence perceptions, and shape our experiences. From the serene azure of a clear sky to the fiery crimson of a sunset, the interplay of colors is a fundamental aspect of our visual landscape. However, in our modern era, where technology has become an integral part of our daily lives, the true essence of color can often become distorted or diminished.The concept of color restoration degree is a crucial consideration in the digital age. As we increasingly rely on electronic devices to capture, display, and share visual information, it is essential to ensure that the colors we perceive accurately reflect the original scene or object. This is where the color restoration degree comes into play, serving as a measure of how faithfully the digital representation of color matches the physical reality.One of the primary challenges in achieving accurate color restoration lies in the inherent limitations of digital imaging and display technologies. Digital cameras, for instance, use sensors that aredesigned to capture light in specific wavelength ranges, which may not always align perfectly with the human visual system. Similarly, computer monitors and other display devices have their own color gamuts, or the range of colors they can reproduce, which may not encompass the full spectrum of colors perceivable by the human eye.To address these challenges, color management systems have been developed to optimize the color reproduction process. These systems employ various algorithms and calibration techniques to ensure that the colors displayed on our screens, printed on our documents, or captured by our cameras closely match the original colors in the physical world.The color restoration degree is a metric that quantifies the success of these color management efforts. It is typically expressed as a percentage, with 100% representing a perfect match between the digital and physical colors. The higher the color restoration degree, the more accurate and true-to-life the color representation will be.Achieving a high color restoration degree is particularly crucial in industries where color accuracy is of paramount importance, such as photography, graphic design, and fine art reproduction. In these fields, even minor deviations in color can have significant consequences, affecting the overall aesthetic, emotional impact, or even the commercial value of the final product.However, the importance of color restoration degree extends beyond professional applications. In our everyday lives, the ability to accurately perceive and reproduce colors can have a profound impact on our experiences and our understanding of the world around us.Consider the case of medical imaging, where accurate color representation can be crucial for the accurate diagnosis and treatment of various conditions. Doctors and healthcare professionals rely on digital imaging technologies, such as X-rays, MRI scans, and endoscopic procedures, to visualize the internal structures of the human body. If the color restoration degree in these images is not high enough, it can lead to misinterpretations or missed diagnoses, with potentially serious consequences for the patient.Similarly, in the realm of education and research, the ability to accurately reproduce color can be essential for the effective communication of scientific concepts, the analysis of data visualizations, and the accurate representation of natural phenomena. Inaccurate color reproduction can hinder the understanding and interpretation of crucial information, ultimately impacting the quality of learning and the advancement of knowledge.Beyond these professional and academic applications, the color restoration degree also plays a role in our everyday aesthetic experiences. The way we perceive and interact with the digital world, from the vibrant hues of our social media posts to the subtle nuances of our favorite films and television shows, can be greatly influenced by the quality of color reproduction.When the color restoration degree is high, we are able to fully immerse ourselves in the visual experiences presented to us, allowing us to appreciate the true essence of the colors and the emotional resonance they evoke. Conversely, when the color restoration degree is low, the disconnect between the digital representation and the physical reality can be jarring, disrupting our sense of engagement and undermining the overall aesthetic impact.In conclusion, the color restoration degree is a critical consideration in the digital age, with far-reaching implications across a wide range of industries and aspects of our lives. By ensuring accurate and faithful color reproduction, we can unlock the full potential of digital technologies, enhance our understanding of the world around us, and enrich our aesthetic experiences. As we continue to navigate the ever-evolving landscape of digital media, the importance of color restoration degree will only continue to grow, serving as a vital bridge between the virtual and the physical realms.。

threshold and

Effective wavelet-based compression method with adaptive quantizationthreshold and zerotree codingArtur Przelaskowski, Marian Kazubek, Tomasz JamrógiewiczInstitute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa,PolandABSTRACTEfficient image compression technique especially for medical applications is presented. Dyadic wavelet decomposition by use of Antonini and Villasenor bank filters is followed by adaptive space-frequency quantization and zerotree-based entropy coding of wavelet coefficients. Threshold selection and uniform quantization is made on a base of spatial variance estimate built on the lowest frequency subband data set. Threshold value for each coefficient is evaluated as linear function of 9-order binary context. After quantization zerotree construction, pruning and arithmetic coding is applied for efficient lossless data coding. Presented compression method is less complex than the most effective EZW-based techniques but allows to achieve comparable compression efficiency. Specifically our method has similar to SPIHT efficiency in MR image compression, slightly better for CT image and significantly better in US image compression. Thus the compression efficiency of presented method is competitive with the best published algorithms in the literature across diverse classes of medical images. Keywords: wavelet transform, image compression, medical image archiving, adaptive quantization1. INTRODUCTIONLossy image compression techniques allow significantly diminish the length of original image representation at the cost of certain original data changes. At range of lower bit rates these changes are mostly observed as distortion but sometimes improved image quality is visible. Compression of the concrete image with its all important features preserving and the noise and all redundancy of original representation removing is do required. The choice of proper compression method depends on many factors, especially on statistical image characteristics (global and local) and application. Medical applications seem to be challenged because of restricted demands on image quality (in the meaning of diagnostic accuracy) preserving. Perfect reconstruction of very small structures which are often very important for diagnosis even at low bit rates is possible by increasing adaptability of the algorithm. Fitting data processing method to changeable data behaviour within an image and taking into account a priori data knowledge allow to achieve sufficient compression efficiency. Recent achievements clearly show that nowadays wavelet-based techniques can realise these ideas in the best way.Wavelet transform features are useful for better representation of the actual nonstationary signals and allow to use a priori and a posteriori data knowledge for diagnostically important image elements preserving. Wavelets are very efficient for image compression as entire transformation basis function set. This transformation gives similar level of data decorrelation in comparison to very popular discrete cosine transform and has additional very important features. It often provides a more natural basis set than the sinusoids of the Fourier analysis, enables widen set of solution to construct effective adaptive scalar or vector quantization in time-frequency domain and correlated entropy coding techniques, does not create blocking artefacts and is well suited for hardware implementation. Wavelet-based compression is naturally multiresolution and scalable in different applications so that a single decomposition provides reconstruction at a variety of sizes and resolutions (limited by compressed representation) and progressive coding and transmission in multiuser environments.Wavelet decomposition can be implemented in terms of filters and realised as subband coding approach. The fundamental issue in construction of efficient subband coding techniques is to select, design or modify the analysis and synthesis filters.1Wavelets are good tool to create wide class of new filters which occur very effective in compression schemes. The choice of suitable wavelet family, with such criteria as regularity, linearity, symmetry, orthogonality or impulse and step response of corresponding filter bank, can significantly improve compression efficiency. For compactly supported wavelets corresponding filter length is proportional to the degree of smoothness and regularity of the wavelet. Butwhen the wavelets are orthogonal (the greatest data decorrelation) they also have non-linear phase in the associated FIR filters. The symmetry, compact support and linear phase of filters may be achieved by biorthogonal wavelet bases application. Then quadrature mirror and perfect reconstruction subband filters are used to compute the wavelet transform. Biorthogonal wavelet-based filters occurred very efficient in compression algorithms. A construction of wavelet transformation by fitting local defined basis transformation function (or finite length filters) into image data characteristics is possible but very difficult. Because of nonstationary of image data, miscellaneous image futures which could be important for good reconstruction, significant various image quality (signal to noise level, spatial resolution etc.) from different imaging systems it is very difficult to elaborate the construction method of the optimal-for-compression filters. Many issues relating to the choice of the most efficient filter bank for image compression remain still unresolved.2The demands of preserving the diagnostic accuracy in reconstructed medical images are exacting. Important high frequency coefficients which appear at the place of small structure edges in CT and MR images should be saved. Accurate global organ shapes reconstruction in US images and strong noise reduction in MN images is also required. It is rather difficult to imagine that one filter bank can do it in the best way. Rather choosing the best wavelet families for each modality is expected.Our aim is to increase the image compression efficiency, especially for medical applications, by applying suitable wavelet transformation, adaptive quantization scheme and corresponding processed decomposition tree entropy coding. We want to achieve higher acceptable compression ratios for medical images by better preserving the diagnostic accuracy of images. Many bit allocation techniques applied in quantization scheme are based on data distribution assumptions, quantiser distortion function etc. All statistical assumptions built on global data characteristics do not cover exactly local data behaviour and important detail of original image, e.g., different texture small area may be lost. Thus we decided to build quantization scheme on the base of local data characteristics such a direct data context in two dimensions mentioned earlier. We do data variance estimation on the base of real data set as spatial estimate for corresponding coefficient positions in successive subbands. The details of quantization process and correlated coding technique as a part of effective simple wavelet-based compression method which allows to achieve high reconstructed image quality at low bit rates are presented.2. THE COMPRESSION TECHNIQUEScheme of our algorithm is very simple: dyadic, 3 levels decomposition of original image (256×256 images were used) done by selected filters. For symmetrical filters symmetry boundary extension at the image borders was used and for asymmetrical filters - a periodic (or circular) boundary extension.Figure 1. Dyadic wavelet image decomposition scheme. - horizontal relations, - parent - children relations. LL - the lowest frequency subband.Our approach to filters is utilitarian one, making use of the literature to select the proper filters rather than to design them. We conducted an experiment using different kinds of wavelet transformation in presented algorithm. Long list of wavelet families and corresponding filters were tested: Daubechies, Adelson, Brislawn, Odegard, Villasenor, Spline, Antonini, Coiflet, Symmlet, Beylkin, Vaid etc.3 Generally Antonini 4 filters occurred to be the most efficient. Villasenor, Odegard and Brislawn filters allow to achieve similar compression efficiency. Finally: Antonini 7/9 tap filters are used for MR and US image compression and Villasenor 18/10 tap filters for CT image compression.2.1 Adaptive space-frequency quantizationPresented space-frequency quantization technique is realised as entire data pre-selection, threshold selection and scalar uniform quantization with step size conditioned by chosen compression ratio. For adaptive estimation of threshold and quantization step values two extra data structure are build. Entire data pre-selection allows to evaluate zero-quantized data set and predict the spatial context of each coefficient. Next simple quantization of the lowest frequency subband (LL) allows to estimate quantized coefficient variance prediction as a space function across sequential subbands. Next the value of quantization step is slightly modified by a model build on variance estimate. Additionally, a set of coefficients is reduced by threshold selection. The threshold value is increased in the areas with the dominant zero-valued coefficients and the level of growth depends on coefficient spatial position according variance estimation function.Firstly zero-quantized data prediction is performed. The step size w is assumed to be constant for all coefficients at each decomposition level. For such quantization model the threshold value is equal to w /2. Each coefficient whose value is less than threshold is predicted to be zero-valued after quantization (insignificant). In opposite case coefficient is predicted to be not equal to zero (significant). It allows to create predictive zero-quantized coefficients P map for threshold evaluation in the next step. The process of P map creation is as follows:if c w then p else p i i i <==/201, (1)where i m n m n =⋅−12,,...,;, horizontal and vertical image size , c i - wavelet coefficient value. The coefficient variance estimation is made on the base of LL data for coefficients from next subbands in corresponding spatial positions. The quantization with mentioned step size w is performed in LL and the most often occurring coefficient value is estimated. This value is named MHC (mode of histogram coefficient). The areas of MHC appearance are strongly correlated with zero-valued data areas in the successive subbands. The absolute difference of the LL quantized data and MHC is used as variance estimate for next subband coefficients in corresponding spatial positions. We tested many different schemes but this model allows to achieve the best results in the final meaning of compression efficiency. The variance estimation is rather coarse but this simple adaptive model built on real data does not need additional information for reconstruction process and increases the compression efficiency. Let lc i , i =1,2,...,lm , be a set ofLL quantized coefficient values, lm - size of this set . Furthermore let mode of histogram coefficient MHC value be estimated as follows:f MHC f lc MHC Al lc Al i i ()max ()=∈∈ and , (2)where Al - alphabet of data source which describes the values of the coefficient set and f lc n lmi lc i ()=, n lc i - number of lc i -valued coefficients. The normalised values of variance estimate ve si for next subband coefficients in corresponding to i spatial positions (parent - children relations from the top to the bottom of zerotree - see fig. 1) are simply expressed by the following equation: ve lc MHC ve si i =−max . (3)These set of ve si data is treated as top parent estimation and is applied to all corresponding child nodes in wavelet hierarchical decomposition tree.9-th order context model is applied for coarser data reduction in ‘unimportant' areas (usually with low diagnostic importance). The unimportance means that in these areas the majority of the data are equal to zero and significant values are separated. If single significant values appear in these areas it most often suggests that these high frequency coefficients are caused by noise. Thus the coarser data reduction by higher threshold allows to increase signal to noise ratio by removing the noise. At the edges of diagnostically important structures significant values are grouped together and the threshold value is lower at this fields. P map is used for each coefficient context estimation. Noncausal prediction of the coefficient importance is made as linear function of the binary surrounding data excluding considered coefficient significance. The other polynomial, exponential or hyperbolic function were tested but linear function occurred the most efficient. The data context shown on fig. 2 is formed for each coefficient. This context is modified in the previous data points of processing stream by the results of the selection with the actual threshold values at these points instead of w /2 (causal modification). Values of the coefficient importance - cim are evaluated for each c i coefficient from the following equation:cim coeff p i i j j =⋅−=∑1199(),, where i m n =⋅12,,...,. (4)Next the threshold value is evaluated for each c i coefficient: th w cim w ve i i si =⋅+⋅⋅−/(())211, (5)where i m n =⋅12,,...,, si - corresponding to LL parent spatial location in lower decomposition levels.The modified quantization step model uses the LL-based variance estimate to slightly increase the step size for less variance coefficients. Threshold data selection and uniform quantization is made as follows: each coefficient value is firstly compared to its threshold value and then quantized using w step for LL and modified step value mw si for next subbands . Threshold selection and quantization for each c i coefficient can be clearly described by the following equations:LLif c then c c welse if c th then c else c c mw i i i i i i i i si∈=<==//0, (6)where mw w coeff ve si si =⋅+⋅−(())112. (7)The coeff 1 and coeff 2 values are fitted to actual data characteristic by using a priori image knowledge and performingentire tests on groups of similar characteristic images.a) b)Figure 2. a) 9-order coefficient context for evaluating the coefficient importance value in procedure of adaptive threshold P map context of single edge coefficient.2.2 Zerotrees construction and codingSophisticated entropy coding methods which can significantly improve compression efficiency should retain progressive way of data reconstruction. Progressive reconstruction is simple and natural after wavelet-based decomposition. Thus the wavelet coefficient values are coded subband-sequentially and spectral selection is made typically for wavelet methods. The same scale subbands are coded as follows: firstly the lowest frequency subband, then right side coefficient block, down-left and down-right block at the end. After that next larger scale data blocks are coded in the same order. To reduce a redundancy of such data representation zerotree structure is built. Zerotree describes well the correlation between data values in horizontal and vertical directions, especially between large areas with zero-valued data. These correlated fragments of zerotree are removed and final data streams for entropy coding are significantly diminish. Also zerotree structure allows to create different characteristics data streams to increase the coding efficiency. We used simple arithmetic coders for these data streams coding instead of applied in many techniques bit map (from MSB to LSB) coding with necessity of applying the efficient context model construction. Because of refusing the successive approximation we lost full progression. But the simplicity of the algorithm and sometimes even higher coding efficiency was achieved. Two slightly different arithmetic coders for producing ending data stream were used.2.2.1 Construction and pruning of zerotreeThe dyadic hierarchical image data decomposition is presented on fig. 1. Decomposition tree structure reflects this hierarchical data processing and strictly corresponds to created in transformation process data streams. The four lowest frequency subbands which belong to the coarsest scale level are located at the top of the tree. These data have not got parent values but they are the parents for the coefficients in lower tree level of greater scale in corresponding spatial positions. These correspondence is shown on the fig. 1 as parent-children relations. Each parent coefficient has got four direct children and each child is under one direct parent. Additionally, horizontal relations at top tree level are introduced to describe the data correlation in better way.The decomposition tree becomes zerotree when node values of quantized coefficients are signed by symbols of binary alphabet. Each tree node is checked to be significant (not equal to zero) or insignificant (equal to zero) - binary tree is built. For LL nodes way of significance estimation is slightly different. The MHC value is used again because of the LL areas of MHC appearance strong correlation with zero-valued data areas in the next subbands. Node is signed to be significant if its value is not equal to MHC value or insignificant if its value is equal to MHC. The value of MHC must be sent to a decoder for correct tree reconstruction.Next step of algorithm is a pruning of this tree. Only the branches to insignificant nodes can be pruned and the procedure is slightly other at different levels of the zerotree. Procedure of zerotree pruning starts at the bottom of wavelet zerotree. Sequential values of four children data and their parent from higher level are tested. If the parent and the children are insignificant - the tree branch with child nodes is removed and the parent is signed as pruned branch node (PBN). Because of this the tree alphabet is widened to three symbols. At the middle levels the pruning of the tree is performed if the parent value is insignificant and all children are recognised as PBN. From conducted research we found out that adding extra symbols to the tree alphabet is not efficient for decreasing the code bit rate. The zerotree pruning at top level is different. The checking node values is made in horizontal tree directions by exploiting the spatial correlation of the quantized coefficients in the subbands of the coarsest scale - see fig. 1. Sequentially the four coefficients from the same spatial positions and different subbands are compared with one another. The tree is pruned if the LL node is insignificant and three corresponding coefficients are PBN. Thus three branches with nodes are removed and LL node is signed as PBN. It means that all its children across zerotree are insignificant. The spatial horizontal correlation between the data at other tree levels is not strong enough to increase the coding efficiency by its utilisation.2.2.2 Making three data streams and codingPruned zerotree structure is handy to create data streams for ending efficient entropy coding. Instead of PBN zero or MHC values (nodes of LL) additional code value is inserted into data set of coded values. Also bit maps of PBN spatial distribution at different tree levels can be applied. We used optionally only PBN bit map of LL data to slightly increase the coding efficiency. The zerotree coding is performed sequentially from the top to the bottom to support progressive reconstruction. Because of various quantized data characteristics and wider alphabet of data source model after zerotree pruning three separated different data streams and optionally fourth bit map stream are produced for efficient data coding. It is well known from information theory that if we deal with a data set with significant variability of data statistics anddifferent statistics (alphabet and estimate of conditional probabilities) data may be grouped together it is better to separate these data and encode each group independently to increase the coding efficiency. Especially is true when context-based arithmetic coder is used. The data separation is made on the base of zerotree and than the following data are coded independently:- the LL data set which has usually smaller number of insignificant (MHC-valued) coefficients, less PBN and less spatial data correlation than next subband data (word- or charwise arithmetic coder is less efficient then bitwise coder);optionally this data stream is divided on PBN distribution bit map and word or char data set without PBNs,- the rest of top level (three next subbands) and middle level subband data set with a considerable number of zero-valued (insignificant) coefficients and PBN code values; level of data correlation is greater, thus word- or charwise arithmetic coder is efficient enough,- the lowest level data set with usually great number of insignificant coefficients and without PBN code value; data correlation is very high.Urban Koistinen arithmetic coder (DDJ Compression Contest public domain code accessible by internet) with simple bitwise algorithm is used for first data stream coding. For the second and third data stream coding 1-st order arithmetic coder built on the base of code presented in Nelson book 5 is applied. Urban coder occurred up to 10% more efficient than Nelson coder for first data stream coding. Combining a rest of top level data and the similar statistics middle level data allows to increase the coding efficiency approximately up to 3%.The procedure of the zerotree construction, pruning and coding is presented on fig. 3.Construction ofbinary zerotreeBitwise arithmetic codingFinal compressed data representationFigure 3. Quantized wavelet coefficients coding scheme with using zerotree structure. PBN - pruned branch node.3. TESTS, RESULTS AND DISCUSSIONIn our tests many different medical modality images were used. For chosen results presentation we applied three 256×256×8-bit images from various medical imaging systems: CT (computed tomography), MR (magnetic resonance) and US(ultrasound) images. These images are shown on fig. 4. Mean square error - MSE and peak signal to noise ratio - PSNR were assumed to be reconstructed image quality evaluation criteria. Subjective quality appreciation was conducted in very simple way - only by psychovisual impression of the non-professional observer.Application of adaptive quantization scheme based on modified threshold value and quantization step size is more efficient than simple uniform scalar quantization up to 10% in a sense of better compression of all algorithm. Generally applying zerotree structure and its processing improved coding efficiency up to 10% in comparison to direct arithmetic coding of quantized data set.The comparison of the compression efficiency of three methods: DCT-based algorithm,6,7 SPIHT 8 and presented compression technique, called MBWT (modified basic wavelet-based technique) were performed for efficiency evaluation of MBWT. The results of MSE and PSNR-based evaluation are presented in table 1. Two wavelet-based compression techniques are clearly more efficient than DCT-based compression in terms of MSE/PSNR and also in our subjective evaluation for all cases. MBWT overcomes SPIHT method for US images and slightly for CT test image at lower bit rate range.The concept of adaptive threshold and modified quantization step size is effective for strong reduction of noise but it occurs sometimes too coarse at lower bit rate range and very small details of the image structures are put out of shape. US images contain significant noise level and diagnostically important small structures do not appear (image resolution is poor). Thus these images can be efficiently compressed by MBWT with image quality preserved. It is clearly shown on fig.5. An improvement of compression efficiency in relatio to SPIHT is almost constant at wide range of bit rates (0.3 - 0.6 dB of PSNR).a) b)c)Figure 4. Examples of images used in the tests of compression efficiency evaluation. The results presented in table 1 and on fig. 5 were achieved for those images. The images are as follows: a ) echocardiography image, b) CT head image, c) MR head image.Table 1. Comparison of the three techniques compression efficiency: DCT-based, SPIHT and MBWT. The bit rates are chosen in diagnostically interesting range (near the borders of acceptance).Modality - bit rateDCT-based SPIHT MBWTMSE PSNR[dB] MSE PSNR[dB] MSE PSNR[db] MRI - 0.70 bpp8.93 38.62 4.65 41.45 4.75 41.36 MRI - 0.50 bpp13.8 36.72 8.00 39.10 7.96 39.12 CT - 0.50 bpp6.41 40.06 3.17 43.12 3.1843.11 CT - 0.30 bpp18.5 35.46 8.30 38.94 8.0639.07 US - 0.40 bpp54.5 30.08 31.3 33.18 28.3 33.61 US - 0.25 bpp 91.5 28.61 51.5 31.01 46.8 31.43The level of noise in CT and MR images is lower and small structures are often important in image analysis. That is the reason why the benefits of MBWT in this case are smaller. Generally compression efficiency of MBWT is comparable to SPIHT for these images. Presented method lost its effectiveness for higher bit rates (see PSNR of 0.7 bpp MR representation) but for lower bit rates both MR and CT images are compressed significantly better. Maybe the reason is that the coefficients are reduced relatively stronger because of its importance reduction in MBWT threshold selection at lower bits rate range.0,20,30,40,50,60,70,8Rate in bits/pixel PSNR in dBFigure 5. Comparison of SPIHT and presented in this paper technique (MBWT) compression efficiency at range of low bit rates. US test image was compressed.4. CONCLUSIONSAdaptive space-frequency quantization scheme and zerotree-based entropy coding are not time-consuming and allow to achieve significant compression efficiency. Generally our algorithm is simpler than EZW-based algorithms 9 and other algorithms with extended subband classification or space -frequency quantization models 10 but compression efficiency of presented method is competitive with the best published algorithms in the literature across diverse classes of medical images. The MBWT-based compression gives slightly better results than SPIHT for high quality images: CT and MR and significantly better efficiency for US images. Presented compression technique occurred very useful and promising for medical applications. Appropriate reconstructed image quality evaluation is desirable to delimit the acceptable lossy compression ratios for each medical modality. We intend to improve the efficiency of this method by: the design a construction method of adaptive filter banks and correlated more sufficient quantization scheme. It seems to be possible byapplying proper a priori model of image features which determine diagnostic accuracy. Also more efficient context-based arithmetic coders should be applied and more sophisticated zerotree structures should be tested.REFERENCES1.Hui, C. W. Kok, T. Q. Nguyen, …Image Compression Using Shift-Invariant Dydiadic Wavelet Transform”, subbmited toIEEE Trans. Image Proc., April 3nd, 1996.2.J. D. Villasenor, B. Belzer and J. Liao, …Wavelet Filter Evaluation for Image Compression”, IEEE Trans. Image Proc.,August 1995.3. A. Przelaskowski, M.Kazubek, T. Jamrógiewicz, …Optimalization of the Wavelet-Based Algorithm for Increasing theMedical Image Compression Efficiency”, submitted and accepted to TFTS'97 2nd IEEE UK Symposium on Applications of Time-Frequency and Time-Scale Methods, Coventry, UK 27-29 August 1997.4.M. Antonini, M. Barlaud, P. Mathieu and I. Daubechies, …Image coding using wavelet transform”, IEEE Trans. ImageProc., vol. IP-1, pp.205-220, April 1992.5.M. Nelson, The Data Compression Book, chapter 6, M&T Books, 1991.6.M. Kazubek, A. Przelaskowski and T. Jamrógiewicz, …Using A Priori Information for Improving the Compression ofMedical Images”, Analysis of Biomedical Signals and Images, vol. 13,pp. 32-34, 1996.7. A. Przelaskowski, M. Kazubek and T. Jamrógiewicz, …Application of Medical Image Data Characteristics forConstructing DCT-based Compression Algorithm”, Medical & Biological Engineering & Computing,vol. 34, Supplement I, part I, pp.243-244, 1996.8. A. Said and W. A. Pearlman, …A New Fast and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees”,submitted to IEEE Trans. Circ. & Syst. Video Tech., 1996.9.J. M. Shapiro, …Embedded Image Coding Using Zerotrees of Wavelet Coefficients”, IEEE Trans. Signal Proces., vol.41, no.12, pp. 3445-3462, December 1993.10.Z. Xiong, K. Ramchandran and M. T. Orchard, …Space-Frequency Quantization for Wavelet Image Coding”, IEEETrans. Image Proc., to appear in 1997.。

A Quantum Delayed-Choice Experiment

A quantum delayed choice experimentAlberto Peruzzo,1Peter Shadbolt,1Nicolas Brunner,2Sandu Popescu,2and Jeremy L.O’Brien 1,∗1Centre for Quantum Photonics,H.H.Wills Physics Laboratory &Department of Electrical and Electronic Engineering,University of Bristol,Bristol BS81UB,UK2H.H.Wills Physics Laboratory,University of Bristol,Tyndall Avenue,Bristol,BS81TL,United KingdomQuantum systems exhibit particle-like or wave-like behaviour depending on the experimental apparatus they are confronted by.This wave-particle duality is at the heart of quantum mechanics,and is fully captured in Wheeler’s famous delayed choice gedanken experiment.In this variant of the double slit experiment,the observer chooses to test either the particle or wave nature of a photon after it has passed through the slits.Here we report on a quantum delayed choice experiment,based on a quantum controlled beam-splitter,in which both particle and wave behaviours can be investigated simultaneously.The genuinely quantum nature of the photon’s behaviour is tested via a Bell inequality,which here replaces the delayed choice of the observer.We observe strong Bell inequality violations,thus showing that no model in which the photon knows in advance what type of experiment it will be confronted by,hence behaving either as a particle or as wave,can account for the experimental data.Quantum mechanics predicts with remarkable accu-racy the result of experiments involving small objects,such as atoms and photons.However,when looking more closely at these predictions,we are forced to admit that they defy our intuition.Indeed,quantum mechanics tells us that a single particle can be in several places at the same time,and that distant entangled particles behave as a single physical object no matter how far apart they are [1].In trying to grasp the basic principles of the theory,in particular to understand more intuitively the behaviour of quantum particles,some of its pioneers introduced the notion of wave-particle duality [2].A quantum system,for instance a photon,may behave either as a particle or a wave.However,the way in which it behaves de-pends on the kind of experimental apparatus with which it is measured.Hence,both aspects,particle and wave,which appear to be incompatible,are never observed si-multaneously [3].This is the notion of complementarity in quantum mechanics [4,5],which is central in the stan-dard Copenhagen interpretation,and has been intensely debated in the past.In an eﬀort to reconcile quantum predictions and com-mon sense,it was suggested that quantum particles may in fact know in advance to which experiment they will be confronted,via a hidden variable,and could thus de-cide which behaviour to exhibit.This simplistic argu-ment was however challenged by Wheeler in his elegant ‘delayed choice’arrangement [6–8].In this gedanken ex-periment,sketched in Fig.1(a),a quantum particle is sent towards a Mach-Zender interferometer.The relative phase ϕbetween the two arms of the interferometer can be adjusted such that the particle will emerge in output D 0with certainty.That is,the interference is fully con-structive in output D 0,and fully destructive in output D 1.This measurement thus clearly highlights the wave aspect of the quantum particle.However,the observerperforming the experiment has the choice of modifying the above experiment,in particular by removing the sec-ond beam-splitter of the interferometer.In this case,he will perform a which-path measurement.The photon will be detected in each mode with probability one half,thus exhibiting particle-like behaviour.The main point is that the experimentalist is free to choose which experiment to perform (i.e.interference or which-path,thus testing the wave or the particle aspect),once the particle is al-ready inside the interferometer.Thus,the particle could not have known in advance (for instance via a hidden variable)the kind of experiment it will be confronted,since this choice was simply not made when the parti-cle entered the interferometer.Wheeler’s experiment has been implemented experimentally using various systems,all conﬁrming quantum predictions [9–12].In a recent experiment with single photons,a space-like separation between the choice of measurement and the moment the photon enters the interferometer was achieved [13].Here we explore a conceptually diﬀerent take on Wheeler’s experiment.Our starting point is a recent theoretical proposal [14]of a delayed choice experiment based on a quantum-controlled beamsplitter,which can be in a superposition of present and absent.Hence,the interferometer can be simultaneously closed and open,thus testing both the wave and the particle behaviour of the photon at the same time.Here,using a recon-ﬁgurable integrated quantum photonic circuit [15],we implement an interferometer featuring such a quantum beam-splitter,observing continuous morphing between wave and particle behaviour [14].We point out however that this morphing behaviour can be reproduced by a simple classical model,and note that this loophole also plagues both the theoretical proposal of [14]as well as two of its recent NMR implementations [16,17].In or-der to overcome this issue,we then present and experi-mentally demonstrate a quantum delayed choice schemea r X i v :1205.4926v 2 [q u a n t -p h ] 28 J u n 20122[18],which allows us to testmodel.The main conceptualthe temporal arrangementi.e.the delayed choiceis not necessary any-quantum nature of the pho-the violation of a Bell in-in a device-independent way,about the function-local hidden variable modelcan reproduce the quantum predictions.In other words,no model in which the photon decided in advance whichbehaviour to exhibit—knowing in advance the measure-ment setup—can account for the observed statistics.Inour experiment,we achieve strong Bell inequality viola-tions,hence giving an experimental refutation to suchhidden variable models,up to a few additional assump-tions due to imperfections in our setup.The scheme is presented in Fig.1(b).A single photonis sent through an interferometer.At theﬁrst beamsplit-ter,the photon evolves into a superposition of the twospatial modes,represented by two orthogonal quantumstates|0 and|1 .Formally,thisﬁrst BS is represented bya Hadamard operation[19],which transforms the initialphoton state|0 into the superposition(|0 +|1 )/√2.Aphase shifter then modiﬁes the relative phase between thetwo modes,resulting in the state|ψ =(|0 +e iϕ|1 )/√2.Both modes are then recombined on a second BS before aﬁnal measurement in the logical({|0 ,|1 })basis.In thestandard delayed-choice experiment,the presence of thissecond BS is controlled by the observer(see Fig.1(a)).Here,on the contrary,the presence of the second beam-splitter depends on the state of an ancillary photon.Ifthe ancilla photon is prepared in the state|0 ,no BS ispresent,hence the interferometer is left open.Formallythis corresponds to the identity operator acting on|ψ ,hence resulting in the state|ψp =1√2(|0 +e iϕ|1 ).(1)Theﬁnal measurement(in the{|0 ,|1 }basis)indicateswhich path the photon took,in other words revealing theparticle nature of the photon.The measured intensitiesin both output modes are equal and phase-independent,i.e I0=I1=1/2.If,however,the ancilla photon is prepared in the state|1 ,the BS is present and the interferometer is there-fore closed.Formally this corresponds to applying theHadamard operation to|ψ resulting in the state|ψw =cosϕ2|0 −i sinϕ2|1 .(2)Theﬁnal measurement gives information about the phaseϕthat was applied in the interferometer,but indeed notabout which path the photon took.The measured inten-sities are I0=cos2ϕ2and I1=sin2ϕ2.The main feature of this quantum controlled BS isthat it can be put in a superposition of being present(a)(b)FIG.1.Quantum delayed choice experiment.(a)Schematicof Wheeler’s original delayed choice experiment.A photon issent into a Mach-Zehnder interferometer.At theﬁrst beam-splitter(solid blue line),the photon is split into a superposi-tion across both paths.Once the photon is inside the interfer-ometer,the observer decides to close(or not)the interferom-eter by inserting(or not)the second beam-splitter(dashedblue line).For a closed interferometer,the statistics of themeasurements at detectors D0and D1will depend on thephaseϕhence revealing the wave nature of the photon.Foran open interferometer,both detectors will click with equalprobability,revealing the particle nature of the photon.(b)Schematic of the quantum delayed choice experiment.Thesecond beam-splitter is now a quantum beam-splitter(rep-resented by a controlled-Hadamard operation),which can beset in a superposition of present and absent,by controllingthe state of an ancilla photon|ψa .This allows intermediatequantum behaviour to be observed,with continuous transfor-mation between particle and wave behaviour.and absent.Indeed,if the ancilla photon is initiallyin a superposition,for instance in the state|ψα =cosα|0 +sinα|1 ,the global state of the system evolvesinto|Ψf(α,ϕ) =cosα|ψps|0a+sinα|ψws|1a(3)where the subscripts s and a refer to the state of thesystem and ancilla photons respectively.Importantly thesystem and ancilla photons now become entangled,when0<α<π/2.The measured intensity at detector D0is then givenbyI0(ϕ,α)=I p(ϕ)cos2α+I w(ϕ)sin2α=12cos2α+cos2(ϕ2)sin2α(4)while intensity at D1is I1(ϕ,α)=1−I0(ϕ,α).We fabricated the quantum circuit shown in Fig.2in a silica-on-silicon photonic chip[15].The Hadamardoperation is implemented by a directional coupler ofreﬂectivity1/2,equivalent to a50/50beam-splitter.The controlled-Hadamard(CH)is based on a non-deterministic control-phase gate[20,21].The system and3A S’0’1011dc 1dc 2dc 3dc 9dc 6dc 7dc 8dc dc 11dc 12dc dc 4dc 52345678U BobCHHϕαU AliceFIG.2.Implementation of the quantum delayed choice experiment on a reconﬁgurable integrated photonic device.Non-entangled photon pairs are generated using type I parametric downconversion and injected into the chip using polarization maintaining ﬁbres (not shown).The system photon (S),in the lower part of the circuit,enters the interferometer at the Hadamard gate (H ).A relative phase ϕis applied between the two modes of the interferometer.Then the controlled-Hadamard (CH)is implemented by a nondeterministic CZ gate with two additional MZ interferometers.The ancilla photon (A),in the upper part of the circuit,is controlled by the phase shifter α,which determines the quantum state of the second beam-splitter,i.e a superposition of present and absent.Finally the local measurements for the Bell test are performed through single qubit rotations (U A and U B )followed by APD’s.The circuit is composed of directional couplers of reﬂectivity 1/2(dc 1−5and dc 9−13),and 1/3(dc 6−8)and resistive heaters (orange rectangles)that implement the phase shifters.See Methods section for more details.ancilla photon pairs are generated at 808nm via para-metric down conversion and detected with silicon APDs at the circuit’s output.We ﬁrst characterized the behaviour of our setup,for various quantum states of the ancilla photon.We mea-sured the output intensities I 0,1(ϕ,α)for α∈[0,π/2],and ϕ∈[−π/2,3π/2].In particular,by increasing the value of α,we observe the morphing between a par-ticle measurement (α=0)and a wave measurement (α=π/2).For α=0,i.e.no BS,the measured intensi-ties are independent of ϕ.For α=π/2the BS is present,and the data shows interference fringes.Our results are in excellent agreement with theoretical predictions (see Fig.3).To achieve our main goal —that is,to refute models in which the photon knows in advance with which setup it will be confronted —we must go one step further.In-deed,it is important to realize that the result of Fig.3does not refute such models.The main point is that,although we have inserted the ancilla photon in a super-position,hence testing both wave and particle aspects at the same time,we have in fact not checked the quantum nature of this superposition.This is because the ﬁnal measurement of the ancilla photon was made in the log-ical ({|0 ,|1 })basis.Therefore,we cannot exclude the fact that the ancilla may have been in a statistical mix-ture of the form cos 2α|0 0|+sin 2α|1 1|,which would lead to the same measured statistics.Hence the data can be explained by a classical model,in which the state of the ancilla represents a classical variable (a classical bit)indicating which measurement,particle or wave,will be performed.Since the state of the ancilla may have been known to the system photon in advance—indeed here nodelayed choice is performed by the observer—no conclu-sion can be drawn from this experiment.Note that this loophole also plagues the recent theoretical proposal of Ref.[14],as well as two of its NMR implementations [16,17].In order to show that the measurement choice could not have been known in advance,we must ensure that our quantum controlled beam-splitter behaves in a gen-uine quantum way.In particular,we will ensure that it creates entanglement between the system and ancilla photons,which is the clear signature of a quantum pro-cess.The global state of the system and ancilla pho-tons,given in equation (3),is entangled for all values 0<α<π/2.Note that ψp |ψw ∼cos ϕ,hence the de-gree of entanglement depends on ϕand α;in particular for α=π/4and ϕ=π/2,the state (3)is maximally entangled.In order to certify the presence of this entanglement,we will test the Clauser-Horne-Shimony-Holt (CHSH)Bell inequality [22],the violation of which will imply in a device-independent way that the measured data could not have been produced by a classical model.In the CHSH Bell scenario,each party (here Alice holds the system photon while Bob holds the ancilla photon)chooses among two possible measurement settings,de-noted x =0,1for Alice and y =0,1for Bob.Each measurement is dichotomic,i.e.giving a binary result A x =±1and B y =±1.The CHSH inequality then readsS = A 0B 0 + A 0B 1 + A 1B 0 − A 1B 1 ≤2(5)This represents a Bell inequality in the sense that any local model must satisfy it.FIG.3.Characterization of the continuous transition between wave and particle behaviour.Measured (a)and simulated (b)intensity at detector D 0when continuously tuning the state of the ancilla photon |ψa .The experimental data (white dots)were ﬁtted using equation (4).The data shows excellent agreement with theoretical predictions.Indeed,this inequality can be violated by making judi-ciously chosen local measurements on certain entangled states.We measured S for the output state |Ψf (α,ϕ) ,for α∈[0,π/2],and ϕ∈[−π/2,3π/2].We tailored the local measurement operators of Alice and Bob (adjusting phase shifters 5,6and 8,see Appendix for details)for the maximally entangled state |Ψf (α=π/4,ϕ=π/2) .Hence,for this state,we expect the maximal possible vi-olation of the CHSH inequality in quantum mechanics,namely S =2√2[23].It is interesting to note that the choice of apparatus in Wheeler’s original setup,is here,in some sense,replaced by the choice of measurement set-tings for the Bell test.The latter choice is nevertheless conceptually diﬀerent from the former in that it can be performed after the photon left the interferometer.Experimentally we observe a maximal violation of S =2.45±0.03,for α=π/4and ϕ=π/2,which is in good agreement with theoretical predictions (see Fig.4).Therefore,our data could not been accounted for by any model in which the system photon would have known in advance whether to behave as a particle or as a wave.However,for this claim to hold without mak-ing further assumptions,a loophole-free Bell inequality violation is required.Indeed this is not the case in our experiment,as in all optical Bell tests performed so far,which forces us to make a few additional assumptions.We make the standard fair-sampling assumption (allow-ing us to discard inconclusive results,and post-select only coincidence events),which must here be slightly strength-ened because of the nondeterministic implementation of the controlled Hadamard operation.We must also as-sume independence between the photon source and the choice of measurement setting used in the Bell inequal-ity test.As usual,if the photons could know in advancethe choice of measurement setting in the Bell test,then a local model can mimic Bell inequality violations.In the future it would be interesting to perform a more reﬁned experiment in which these assumptions could be relaxed.In conclusion we have reported on a quantum delayed choice experiment,giving a novel demonstration of wave-particle duality,Feynman’s ’one real mystery’in quan-tum mechanics.In our experiment,the delayed choice of Wheeler’s proposal is replaced by a quantum controlled beam-splitter followed by a Bell inequality test.In this way we demonstrate genuine quantum behaviour of sin-gle photons.The demonstration of a quantum controlled beam-splitter shows that a single measurement device can continuously tune between particle and wave mea-surements,hence pointing towards a more reﬁned notion of complementarity in quantum mechanics [14,24,25].Acknowledgements.We thank R.Ionicioiu,S.Pironio,T.Rudolph,N.Sangouard,and D.R.Terno for useful discussions,and acknowledge ﬁnancial support from the UK EPSRC,ERC,QUANTIP,PHORBITECH,Nokia,NSQI,the Templeton Foundation,and the EU DIQIP.J.L.OB.acknowledges a Royal Society Wolfson Merit Award.Note added.We note a related work of Kaiser et al.[26]who performed a similar quantum delayed choice ex-periment.∗Electronic email:Jeremy.OBrien@[1]J.S.Bell,Speakable and Unspeakable in Quantum Me-chanics (Cambridge University Press,Cambridge,2004).[2]R.P.Feynman,R.B.Leighton,and M.L.Sands,LectureFIG.4.Experimental Bell-CHSH inequality test.Measured(a)and simulated(b)Bell-CHSH parameter S(equation(5)). When the CHSH inequality is violated,i.e.S>2(yellow dots in(a)and yellow circle in(b)),no local hidden variable model can explain the observed data,hence demonstrating genuine quantum behaviour.The maximal experimental violation (S=2.45±0.03)is achieved forα=π/4andϕ=π/2,as expected.The data is in excellent agreement with theoretical predictions.notes on Physics(Addison-Wesley,Reading,MA,1965).[3]N.Bohr,in Quantum Theory and Measurement,J.A.Wheeler,W.H.Zurek,Eds.(Princeton Univ.Press, Princeton,NJ),pages949,1984.[4]M.O.Scully,B.-G.Englert,and H.Walther,Quantumoptical tests of complementarity,Nature351,111(1991).[5]B.-G.Englert,Fringe Visibility and Which-Way Infor-mation:An Inequality,Phys.Rev.Lett.77,2154(1996).[6]J.A.Wheeler,pp.9-48in Mathematical Foundations ofQuantum Mechanics,edited by A.R.Marlow(Academic, New-York,1978).[7]J.A.Wheeler,pp.182-213in Quantum Theory and Mea-surement,J.A.Wheeler and W.H.Zurek eds(Princeton University Press,1984).[8]A.J.Leggett,pp.161-166in Compendium of QuantumPhysics,D.Greenberger,K.Hentschel and F.Weinert eds(Springer,Berlin,2009).[9]T.Hellmut,H.Walther,A.G.Zajonc,and W.Schle-ich,Delayed-choice experiments in quantum interference, Phys.Rev.A35,2532(1987).[10]wson-Daku,R.Asimov,O.Gorceix,Ch.Miniatura,J.Robert,and J.Baudon,Delayed choices in atom Stern-Gerlach interferometry,Phys.Rev.A54, 5042(1996).[11]Y.-H.Kim,R.Yu,S.P.Kulik,Y.Shih,and M.O.Scully,Delayed choice quantum eraser,Phys.Rev.Lett.84,1 (2000).[12]A.Zeilinger,G.Weihs,T.Jennewein,M.Aspelmeyer,Happy centenary,photon,Nature433,230(2005). [13]V.Jacques,E.Wu,F.Grosshans,F.Treussart,P.Grang-ier,A.Aspect,and J.-F.Roch,Experimental realization of Wheeler’s delayed choice experiment,Science315,966 (2007).[14]R.Ionicioiu and D.R.Terno,Proposal for a quantumdelayed-choice experiment,Phys.Rev.Lett.107,230406 (2011).[15]P.J.Shadbolt,M.R.Verde, A.Peruzzo, A.Politi, A.Laing,M.Lobino,J.C.F.Matthews,J.L.O’Brien, Generating,manipulating and measuring entanglement and mixture with a reconﬁgurable photonic circuit,Na-ture Photonics6,45(2012).[16]S.S.Roy,A.Shukla,and T.S.Mahesh,NMR implementa-tion of a quantum delayed-choice experiment,Phys.Rev.A85,022109(2012).[17]R.Auccaise,R.M.Serra,J.G.Filgueiras,R.S.Sarthour,I.S.Oliveira,and L.C.Cleri,Experimental analysis ofthe quantum complementarity principle,Phys.Rev.A85, 032121(2012).[18]J.S.Bell,Physics(Long Island City,N.Y.)1,195(1964).[19]M.A.Nielsen and I.L.Chuang,Quantum computationand quantum information,Cambridge University Press (2000).[20]T.C.Ralph,ngford,T.B.Bell,and A.G.White,Linear optical controlled-NOT gate in the coincidence ba-sis,Phys.Rev.A65,062324(2002).[21]H.F.Hofmann and S.Takeuchi,Quantum phase gate forphotonic qubits using only beam splitters and postselec-tion,Phys.Rev.A66,024308(2002).[22]J.F.Clauser,M.Horne, A.Shimony,R.A.Holt,Pro-posed Experiment to Test Local Hidden-Variable Theo-ries,Phys.Rev.Lett.23,880(1969).[23]B.S.Cirelson,Quantum generalizations of Bell’s inequal-ity,Lett.Math.Phys.4,93(1980).[24]J.-S.Tang,Y.-L.Li, C.-F.Li,G.-C.Guo,RevisitingBohr’s principle of complementarity using a quantum de-vice,arXiv:1204.5304.[25]T.Qureshi,Quantum version of complementarity:a du-ality relation,arXiv:1205.2207.[26]F.Kaiser,T.Coudreau,man,D.B.Ostrowsky,and S.Tanzilli,Entanglement-enabled delayed choice ex-periment,arXiv:1206.4348.6CZ gate and 5(a).The W ,(6)is equivalent to the operation of a beamsplitter with re-ﬂectivity η=cos 2(π8).This was achieved,up to a non measurable global phase,by setting phase shifters 4and 7—in the Mach-Zehnder interferometers indicated withW in Fig.5(b)—to 5π4and 3π4respectively.Measurements for the Bell testAlice and Bob’s local measurement operators on the max-imally entangled state (3)(with α=π/4and ϕ=π/2)were performed through single qubit rotations and single photon detection.For this state,the optimal measure-ment settings for the CHSH inequality are given byA 1=−Z ,A 2=−X −Y √2(7)andB 1=X −Z √2,B 2=−X −Z √2(8)for Alice and Bob respectively (where X ,Y ,Z arethe usual Pauli matrices).In the experiment,Alice and Bob’s measurements were implemented by setting (φ5=−π/2,φ6=0)for A 1,(φ5=π/4,φ6=π/2)for A 2,(φ8=π/4)for B 1,and (φ8=−π/4)for B 2.=(a)FIG.5.Integrated photonics implementation of the CH gate.(a)Block diagram of the CH decomposition,(b)implementa-tion using an integrated photonics device.。

常见物理专业名词

数学天地的英文

数学天地的英文Mathematical WorldMathematics, often referred to as the language of the universe, encompasses a vast and fascinating world. The study of numbers, shapes, patterns, and relationships not only helps us understand the world around us but also forms the foundation of many scientific and technological advancements. In this article, we will delve into the English vocabulary related to mathematics and explore the various branches and applications of this intriguing field.1. Numbers and OperationsNumbers are the building blocks of mathematics. From the basic integers to the complex realm of imaginary numbers, each numerical concept holds its own significance. Addition, subtraction, multiplication, and division are the fundamental operations that manipulate numbers and create mathematical expressions. Furthermore, concepts such as fractions, decimals, and percentages expand our understanding of numerical values and their representation in everyday life.2. Geometry and ShapesGeometry deals with the study of shapes and their properties. Euclidean geometry, named after the ancient Greek mathematician Euclid, is the most widely recognized branch. It explores the properties of lines, angles, curves, polygons, and three-dimensional figures. Geometric concepts, like symmetry and congruence, play essential roles in architectural design, art, and navigation systems.3. Algebra and EquationsAlgebra introduces variables and symbols into mathematical expressions and equations. By using algebraic techniques, we can solve equations, simplify expressions, and analyze patterns and relationships between variables. Algebraic concepts find applications in fields such as physics, engineering, and economics, providing tools to model and solve real-world problems.4. Calculus and AnalysisCalculus is a branch of mathematics that studies change and motion. It comprises differential calculus, which examines the rate of change, and integral calculus, which analyzes accumulation. Calculus has revolutionized the fields of physics and engineering, enabling the understanding of complex phenomena such as motion, acceleration, and rates of growth.5. Statistics and ProbabilityStatistics deals with data collection, analysis, interpretation, and presentation. It provides methods to make inferences, draw conclusions, and make informed decisions based on available information. Probability, a fundamental concept in statistics, quantifies the likelihood of events occurring. Statistics and probability are widely used in scientific research, social sciences, and business analytics.6. Applied MathematicsApplied mathematics bridges the gap between theory and real-world applications. This interdisciplinary field combines mathematical techniques with other areas like physics, computer science, and finance to solvepractical problems. Examples include mathematical modeling of climate patterns, optimization algorithms, cryptography, and financial forecasting.ConclusionMathematics is a universal language that transcends cultural and linguistic boundaries. Its concepts, vocabulary, and applications are valuable tools in many aspects of life. From counting and measuring to predicting and analyzing, mathematics permeates our everyday experiences. Embracing the beauty and power of mathematics opens doors to endless possibilities and deepens our understanding of the world we live in.Note: The word count of this article is 618 words. If you require additional content, please let me know.。

纹理物体缺陷的视觉检测算法研究--优秀毕业论文

摘要
在竞争激烈的工业自动化生产过程中，机器视觉对产品质量的把关起着举足轻重的作用，机器视觉在缺陷检测技术方面的应用也逐渐普遍起来。与常规的检测技术相比，自动化的视觉检测系统更加经济、快捷、高效与安全。纹理物体在工业生产中广泛存在，像用于半导体装配和封装底板和发光二极管，现代化电子系统中的印制电路板，以及纺织行业中的布匹和织物等都可认为是含有纹理特征的物体。本论文主要致力于纹理物体的缺陷检测技术研究，为纹理物体的自动化检测提供高效而可靠的检测算法。纹理是描述图像内容的重要特征，纹理分析也已经被成功的应用与纹理分割和纹理分类当中。本研究提出了一种基于纹理分析技术和参考比较方式的缺陷检测算法。这种算法能容忍物体变形引起的图像配准误差，对纹理的影响也具有鲁棒性。本算法旨在为检测出的缺陷区域提供丰富而重要的物理意义，如缺陷区域的大小、形状、亮度对比度及空间分布等。同时，在参考图像可行的情况下，本算法可用于同质纹理物体和非同质纹理物体的检测，对非纹理物体的检测也可取得不错的效果。在整个检测过程中，我们采用了可调控金字塔的纹理分析和重构技术。与传统的小波纹理分析技术不同，我们在小波域中加入处理物体变形和纹理影响的容忍度控制算法，来实现容忍物体变形和对纹理影响鲁棒的目的。最后可调控金字塔的重构保证了缺陷区域物理意义恢复的准确性。实验阶段，我们检测了一系列具有实际应用价值的图像。实验结果表明本文提出的纹理物体缺陷检测算法具有高效性和易于实现性。关键字: 缺陷检测；纹理；物体变形；可调控金字塔；重构
Keywords: defect detection, texture, object distortion, steerable pyramid, reconstruction
II

深入探究布朗运动的正确解读方案

深入探究布朗运动的正确解读方案Exploring the Correct Interpretation of Brownian MotionBrownian motion, named after the botanist Robert Brown who discovered it in 1827, refers to the random movement of microscopic particles in a fluid medium. It was one of the early pieces of evidence for the existence of atoms and molecules, and it has since become a crucial concept in various scientific fields, including physics, chemistry, and biology.The original interpretation of Brownian motion was provided by Albert Einstein in 1905, where he described it as the result of the random collisions of molecules with the particles, leading to their erratic movement. This explanation was later confirmed through experimental observations and became the standard model for understanding Brownian motion.However, recent advancements in technology and theoretical frameworks have led to a re-evaluation of the correct interpretation of Brownian motion. Quantum mechanics and statistical mechanics have provided new insights into the underlying mechanisms of Brownian motion, challenging theclassical view proposed by Einstein.Quantum mechanics suggests that the motion of particles in a fluid is not solely due to the physical collisions with the surrounding molecules but is also influenced by the probabilistic nature of quantum processes. This implies that the classical description of Brownian motion as purely a result of molecular collisions may not capture the complete picture.Moreover, statistical mechanics has introduced the concept of entropy and the role it plays in the behavior of systems. Entropy, which quantifies the disorder or randomness in a system, has been found to have a significant impact on the movement of particles in a fluid medium. This perspective highlights the importance of considering the statistical distribution of particle trajectories rather than focusing solely on individual collisions.In light of these developments, the correct interpretation of Brownian motion can be seen as a combination of classical mechanics, quantum mechanics, and statistical mechanics. While the classical model proposed by Einstein provides a goodapproximation for macroscopic observations, the underlying quantum and statistical principles offer a more comprehensive understanding of the phenomenon at the microscopic level.Furthermore, modern experimental techniques, such as single-particle tracking and super-resolution microscopy, have enabled scientists to directly observe and analyze the trajectories of individual particles in real time. These high-resolution measurements have provided valuable data that can be used to validate and refine theoretical models of Brownian motion.In conclusion, the correct interpretation of Brownian motion should take into account the interplay between classical, quantum, and statistical principles. By integrating these different perspectives, we can gain a deeper understanding of the underlying mechanisms governing the random movement of particles in a fluid medium, leading to new insights and applications across various scientific disciplines.深入探究布朗运动的正确解读方案布朗运动是指微观粒子在流体介质中的随机运动，得名于于1827年发现它的植物学家罗伯特·布朗。

A Theory for Multiresolution Signal Decomposition The Wavelet ...

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Manuscript received July 30. 1987: revised December 23. 1988. This work was supported under the following Contracts and Grants: NSF grant IODCR-84 1077 1. Air Force Grant AFOSR F49620-85-K-0018. Army DAAG-29-84-K-0061. NSF-CERiDC82-19196 Ao2. and DARPAiONR ARPA N0014-85-K-0807. The author is with the Department of Computer Science Courant Institute of Mathematical Sciences. New York University. New York, NY 10012. IEEE Log Number 8928052.
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IEEE TRANSACTIONS PATTERN ON ANALYSISAND MACHINE INTELLIGENCE.VOL. II, NO. 7. JULY 1%')
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
STEPHANE Gsolution representations are very effective for analyzing the information content of images. We study the properties of the operator which approximates a signal at a given resolution. We show that the difference of information between the approximation of a signal at the resolutions 2’ + ’ and 2jcan be extracted by decomposing this signal on a wavelet orthonormal basis of L*(R”). In LL(R ), a wavelet orthonormal basis is a family of functions ( @ w (2’ ~ n)) ,,,“jEZt, which is built by dilating and translating a unique function t+r(xl. This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror lilters. For images, the wavelet representation differentiates several spatial orientations. We study the application of this representation to data compression in image coding, texture discrimination and fractal analysis. Index Terms-Coding, fractals, multiresolution pyramids, ture mirror filters, texture discrimination, wavelet transform. quadra-

gwas r2公式

gwas r2公式GWAS (Genome-Wide Association Study) R2 FormulaIn the field of genetics and genomics, Genome-Wide Association Studies (GWAS) play a crucial role in the identification and understanding of the genetic variants associated with complex traits and diseases. One of the key statistical measures used in GWAS is the R2 value, which quantifies the proportion of variation in a trait that can be explained by genetic variants.The R2 value, also known as the coefficient of determination, ranges from 0 to 1 and provides an estimate of the proportion of genetic influence on a particular trait. A higher R2 value indicates a stronger association between the genetic variant and the trait of interest. In this article, we will explore the formula for calculating the R2 value in GWAS.Before discussing the R2 formula, it is essential to understand the terms used in the equation. In a typical GWAS, the genotypes of thousands or millions of single nucleotide polymorphisms (SNPs) across the genome are compared between individuals with and without a specific trait or disease. This comparison allows researchers to identify genetic variants that are associated with the trait.The R2 formula takes into account two key components: the variance of the trait, and the variance explained by the genetic variant or SNP. The variance of the trait, denoted as Var(trait), represents the total variability of the trait in the population being studied. It provides a measure of how much the trait values deviate from the mean.The variance explained by the genetic variant or SNP, denoted asVar(SNP), represents the proportion of the total variance in the trait that can be attributed to that particular variant. Var(SNP) is obtained by comparing the genotypes of individuals with different trait values and determining how much of the trait variability can be explained by the SNP.Using these components, the R2 formula can be expressed as:R2 = Var(SNP) / Var(trait)Now, let's break down the formula further to understand its implications. The Var(SNP) value is obtained by comparing the observed trait values between individuals with different genotypes for a specific SNP. This comparison allows us to determine how much of the trait variability is associated with that variant.On the other hand, Var(trait) represents the overall variability of the trait in the population being studied. It includes both genetic and environmental factors that contribute to the trait variation. By dividing Var(SNP) byVar(trait), we obtain the proportion of trait variance that can be attributed to the particular SNP, which is the R2 value.It is important to note that the R2 value is specific to a single genetic variant or SNP and does not account for other variants that may also be associated with the trait. Therefore, multiple SNPs need to be considered collectively to obtain a comprehensive understanding of the genetic architecture underlying the trait.In conclusion, the R2 value in GWAS provides a statistical measure of the genetic contribution to the variation in a trait. By comparing theobserved trait values and the genotypes of individuals, researchers can estimate the proportion of trait variance explained by a specific genetic variant. Understanding the R2 formula is crucial for accurate interpretation and analysis of GWAS findings, enhancing our understanding of the genetic basis of complex traits and diseases.。

成品油成分鉴定流程

成品油成分鉴定流程英文回答：Fuel Composition Characterization.Fuel composition characterization is a crucial process in the petroleum industry, providing valuable information about the chemical make-up of finished petroleum products. This information is utilized for various purposes,including quality control, fuel blending optimization, and regulatory compliance. The detailed process of fuel composition characterization involves several steps:1. Sample Collection and Preparation:Representative samples are collected from the finished fuel product.Sample preparation includes diluting the sample with appropriate solvents to achieve the desired concentrationand stabilize any volatile components.2. Analytical Techniques:Gas Chromatography (GC): GC separates volatile organic compounds (VOCs) based on their boiling points and chromatographic behavior. It provides information about the presence and concentration of individual hydrocarbons and other volatile components.High-Performance Liquid Chromatography (HPLC): HPLC separates polar and non-polar compounds based on their interactions with a stationary phase. It is used to determine the presence and concentration of specific components, such as oxygenates and additives.Mass Spectrometry (MS): MS identifies and quantifies molecules by their mass-to-charge ratio. It can provide detailed information about the molecular structure and composition of fuel components.3. Data Analysis and Interpretation:The data obtained from GC, HPLC, and MS is analyzed using specialized software to identify and quantify the various components present in the fuel sample.The results are then interpreted to determine the overall composition of the fuel, including its chemical composition, volatility profile, and presence of specific markers or additives.中文回答：成品油成分鉴定流程。

方差膨胀因子

⽅差膨胀因⼦ vif⽅差膨胀因⼦ VIF：Variance inflation factorVariance inflation factorIn statistics, the variance inflation factor (VIF) quantifies the severity of multicollinearity（多重共线性）in an ordinary least squares regression（普通最⼩⼆乘回归） analysis. It provides an index that measures how much the variance（⽅差）(the square of the estimate's standard deviation（标准差）) of an estimated regression coefficient is increased because of collinearity.A measure of the amount of multicollinearity in a set of multiple regression variables. The presence of multicollinearity within the set of independent variables can cause a number of problems in the understanding the significance of individual independent variables in the regression model. Using variance inflation factors helps to identify multicollinearity issues so that the model can be adjusted.Investopedia Says:The variance inflation factor allows a quick measure of how much a variable is contributing to the standard error （回归参数的标准差） in the regression.？？? When significant multicollinearity issues exist, the variance inflation factor will be very large for the variables involved. After these variables are identified, there are several approaches that can be used to eliminate or combine collinear variables, resolving the multicollinearity issue.DefinitionConsider the following linear model with k independent variables:Y = β0 + β1X1 + β2X2 + ... + βk X k + ε.The standard error of the estimate of βj is the square root of the j+1, j+1 element of s2(X′X)−1, where s is the standard error of the estimate (SEE) (note that SEE2 is an unbiased estimator of the true variance of the error term, σ2); X is the regression design matrix — a matrix such that X i, j+1 is the value of the j th independent variable for the i th case or observation, and such that X i, 1 equals 1 for all i. It turns out that the square of this standard error, the estimated variance of the estimate of βj, can be equivalently expressed aswhere R j2 is the multiple R2 for the regression of X j on the other covariates (a regression that does not involve the response variable Y). This identity separates the influences of several distinct factors on the variance of the coefficient estimate:·s2: greater scatter in the data around the regression surface leads to proportionately more variance in the coefficient estimates·n: greater sample size results in proportionately less variance in the coefficient estimates·: greater variability in a particular covariate leads to proportionately less variance in the corresponding coefficient estimateThe remaining term, 1 / (1 − R j2) is the VIF. It reflects all other factors that influence the uncertainty in the coefficient estimates. The VIF equals 1 when the vector X j is orthogonal to each column of the design matrix for the regression of X j on the other covariates. By contrast, the VIF is greater than 1 when the vector X j is not orthogonal to all columns of the design matrix for the regression of X j on the other covariates. Finally, note that the VIF is invariant to the scaling of the variables (that is, we could scale each variable X j by a constant c j without changing the VIF).Calculation and analysisThe VIF can be calculated and analyzed in three steps:Step oneCalculate k different VIFs, one for each X i by first running an ordinary least square regression that has X i as a function of all the other explanatory variables in the first equation.If i = 1, for example, the equation would bewhere c0 is a constant and e is the error term (误差项).Step twoThen, calculate the VIF factor for with the following formula:where R2i is the coefficient of determination（决定系数）of the regression equation in step one.Step threeAnalyze the magnitude of multicollinearity by considering the size of the . A common rule of thumb is that ifthen multicollinearity is high. Also 10 has been proposed (see Kutner book referenced below) as a cut offvalue.Some software calculates the tolerance which is just the reciprocal of the VIF. The choice of which to use is amatter of personal preference of the researcher.InterpretationThe square root of the variance inflation factor tells you how much larger the standard error is, compared withwhat it would be if that variable were uncorrelated with the other independent variables in the equation.ExampleIf the variance inflation factor of an independent variable were5.27 (√5.27 = 2.3) this means that the standard error for the coefficient of that independent variable is 2.3 timesas large as it would be if that independent variable were uncorrelated with the other independent variables.References· Longnecker, M.T & Ott, R.L :A First Course in Statistical Methods, page 615. Thomson Brooks/Cole, 2004.· Studenmund, A.H: Using Econometrics: A practical guide, 5th Edition, page 258–259. Pearson International Edition, 2006.· Hair JF, Anderson R, Tatham RL, Black WC: Multivariate Data Analysis. Prentice Hall: Upper Saddle River, N.J. 2006.· Marquardt, D.W. 1970 "Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation", Technometrics 12(3), 591, 605–07· Allison, P.D. Multiple Regression: a primer, page 142. Pine Forge Press: Thousand Oaks, C.A. 1999.· Kutner, Nachtsheim, Neter, Applied Linear Regression Models, 4th edition, McGraw-Hill Irwin, 2004.ps:PS:使⽤Eviews6不能直接计算VIF，可以分别⾸先计算出各个R k2，再计算VIF值ls LNINCOME LNPG LNPNC LNPUC Cgenr VIF1=1/(1-.870007)ls LNPG LNINCOME LNPNC LNPUC Cgenr VIF2=1/(1-.919054)ls LNPNC LNPG LNINCOME LNPUC Cgenr VIF3=1/(1-.986568)ls LNPUC LNPNC LNPG LNINCOME Cgenr vif4=1/(1-.988127)另⼀软件Stata提供了VIF的计算结果，所以尽量使⽤这种较容易的办法获得。

E_Van Bogaert

Vibration Conduct of Viaducts and Large Span Bridges due to the Crossing of High-speed TrainsPhilippe VANBOGAERTProfessorGhent University BelgiumPhilippe Van Bogaert born 1951 received his civil engineering degree and doctorate from Ghent university. He is currently working with the civil engineering department of Ghent univ and with Tuc Rail Ltd Henri DETANDTBridge Office ManagerTuc Rail Ltd, BrusselsBelgiumHenri Detandt born 1952received his civil engineeringdegree from Université Libre deBruxelles. He is currentlyworking with Tuc Rail LtdBrussels and at the civilengineering department ULBWim RAEMDONCKCivil Engineer, Tuc RailLtd, Brussels BelgiumWim Raemdonck, born 1976received his civil engineeringdegree from Ghent University in1999 and is currently working asa design engineer with Tuc RailLtd BrusselsSummaryVertical train car accelerations are the main cause for passenger discomfort. These accelerations have been widely measured and needed further statistical interpretation before comparing them to predicted values from calculation models. In particular a relevant galloping factor may be determined from measured values. Fourier-analysis and determining of the peak values of accelerations allow the definition of a resonance number. This number quantifies the accumulation of vibration energy. Comparing experimental values of accelerations with recommendations of Eurocode, shows that the latter may underestimate these effects for large bridges.Keywords: Bridges, viaducts, high-speed, measurements, vibration conduct.1. IntroductionRailway vehicles, crossing long span bridges or multi-span viaducts produce much higher displacements and accelerations of bridge superstructure as when these loads are acting statically. These effects increase rapidly with speed and have become well-known in the design of high-speed railway structures. The consequences of the increase of displacements and indeed those of accelerations are twofold. Force resultants, stresses and deformations of bridge superstructures are increasing rapidly with train speed and loading models may become inaccurate or underestimate the effects of real train vehicles. In addition, the bridge deck accelerations may exceed values at which track ballast looses its cohesion and behaves as a liquid. On the other hand, deformations and accelerations of the superstructures may on their turn be transmitted to the train cars. Interference of the train car movement with these time-dependent quantities causes increasing resulting train car accelerations and discomfort to passengers. As a consequence, passengers can feel nauseated. This effect has been examined widespread and is included in recommendations of Eurocode EN 1990 Annex 2 [1]. In addition the limiting values for bridge stiffness and conditions in general are more critical than other effects of high-speed.Prediction of passenger comfort conditions is carried out mostly by applying a time-dependent series of axle loads with a saw-tooth scheme, as was proposed since 1993 [2]. Modal analysis, followed by transient response calculation is then being carried out. As a result a time-dependent spectrum of bridge deformations or accelerations is found. These data are used as input for a multi-body system of train cars, with suspension system of springs, masses and dampers. The main results are the train car accelerations at the locations of the train car bogies. These accelerations are a consistent criterion for evaluating passenger comfort.The aim of the present research was to evaluate measured values of train car accelerations in different circumstances and for several bridges and viaducts. The results have been confronted with calculated values and with some recommendations of Eurocode EN 1990 Annex 2. Values of train car accelerations have been measured on the viaducts of Antoing, Arbre, Lembeek and Lot and on the steel tied arch bridge of Halle.2. Structures being considered in Measurements and evaluation Procedures2.1 AntoingviaductFig. 1 Antoing viaductLooking in the direction from Paris to Brussels, the structure consists of 5 concrete through-section spans of 50 m, a span steel-concrete span with steel arch of 116.8 m and a final 50 m long concrete span. The longest span allows the crossing of the river Scheldt and is shown from the inside in fig 1.Expressing the stiffness as the ratio of span to the vertical sag due to placing 2 loading schemes of LM 71 on the superstructure, the normal spans have L/y = 4200 whereas the longer span has L/y = 38502.2 ArbreviaductFig. 2 Arbre viaductThe Arbre viaduct is the longest structure on the Belgian high-speed network. Its concept is similar to the smaller spans of the Antoing viaduct. The structure allows crossing a valley of compressible soft soil and several roads as well as a small river. Looking again from Paris to Brussels, the spans of this viaduct are three times 50 m, one span of 60 m, followed by 3 x 50 m – 60 m – 2 x 50 m – 60 m – 7 x 50 m – 60 m – 4 x 50 m – 3 x 60 m – 50 m – 2 x 60 m and finally 7 x 50 m. The stiffness ratios, as defined in 2.1 are L/y = 4200 for the 50 m spans L/y = 2900 for the longer 60 m spans2.3 LembeekviaductFig 3 Lembeek Viaduct The Lembeek viaduct is located at the very beginning of the 300 km/h speed section, some 23 km to the South of Brussels. It consists of through section concrete single track elements. From South to North there are 4 19m spans, 6 31.5 m spans and again 14 19m spans. The larger spans consist of parallel girders. The stiffness ratio of all spans is identical and equals L/y = 1300. The viaduct is particular in this sense that it is the location where the rail, current and signalling changes to high-speed technology.2.4 LotviaductFig. 4 Viaduct Lot The completely prefabricated steel-concrete viaduct of Lot allows the crossing of the high-speed line Paris-Brussels with domestic tracks. Located 8 km to the South of Brussels, it consists of 16 identical spans of 41.5 m. The piers are alternatively straight and triangular elements, whereas each bridge deck has two lateral beams of HP-concrete C 80/95 with steel encased beams. Steel truss structures are bolted to the steel encased beams. Their principal function is to increase the bending stiffness. The stiffness ratio L/y equals 13002.5Tied arch bridge at HalleFig. 5 Halle tied arch steel bridges The steel tied arch bridges at Halle for the high-speed line and for domestic tracks, are located 20 km to the South of Brussels. The structures consist of 115 m single-span arch bridges and orthotropic plated steel deck, both being linked by triangular hangers.The stiffness factor for this structure equals L/y = 1520 3. Measurements and Results3.1 Acceleration samplingMost of the measured train car accelerations were recorded during test periods of the Lille-Brussels high-speed section from October 1997 to March 1998. More recent measurements are heavily influenced by track irregularities and do not show a clear image of the influence of bridges and viaducts, since the latter are really small. For the Lot viaduct 20 test samples could be used, whereas for the Halle bridge, the Lembeek, Arbre and Antoing viaducts 8 series of test samples were available.Train car accelerations were measured by a special train, generally used for track quality assessment. Apart from vertical car accelerations, the equipment of this train also records horizontal accelerations, track alignment and other parameters. The charts being produced are purely graphical and must be digitalised, by the process as described in [3]. Fig 6 shows the recording of accelerations by means of charts.All measured train car acceleration curves had to be re-assembled to eliminate vertical accelerations due to the vertical track alignment and to locate the structures exactly on the graphical data.Fig. 6 Recording of measurements In addition, the zero baselines must be determined exactly, requiring the use of statistical methods or double integration of the output signal. The relevancy of both these statistical methods has been verified by assessment of the maximum error. Comparing to the maximum accelerations, the inaccuracy of the method is limited to 1.8%.Additional calculations are concerned with deriving for each test graph the series of maximum and minimum train car accelerations. Fourier Transform of the graphical output enabled to assess clearly the main frequencies and accelerations. Finally, themost characteristic values of vertical accelerations are determined as 95% fractile values of the total sample population.3.2 Maximum acceleration valuesUnfortunately most trains cross the bridges being considered at usual speed. Therefore, it is not possible to make sufficiently correct assessments of the variation of maximum and minimumViaduct Antoing Arbre L = 50 m L=120m L = 50 m L=60m a max (m/s²) 0.789 0.489 0.566 0.713 Table 1 : maximum accelerations accelerations as a function of train speed. Both for the Antoing and Arbre viaducts, a relevant number of values is available todetermine 95% fractile values of the acceleration extremes at v= 300 km/h. These are shown in table 1For the viaducts of Lembeek (31,5m spans) and the Halle bridge, sufficient values are available to distinguish 2 speed classes, namely round 150 and 210 km/h. These results are shown in table 2. Halle bridge Lembeek viaduct Speed range 151-152 210-215 146-152 191-216 a 95% (m/s²) 0.526 0.573 0.341 0.492 Table 2 : 95% fracile acceleration values Since there are sufficient individual values, the 95% fractile value, below which only 5% of experimental results can occur, weretaken. For the Lot viaduct, there are sufficient data to establish a fitting curve as a function of train speed. This has been derived as :a = 4.4574*10-4 v² - 0.022287 v + 0.53777 (in m,s 100<v<220 km/h) (1) and corresponds to a second degree parabola, having horizontal tangent for v = 90 km/h.3.3 Galloping effectAs the train cars are crossing the structure, the vertical accelerations of the front and rear suspension bogies are unequal. Consequently, the train car rotates about a horizontal axis. This is the well-known galloping movement of high-speed trains. While interpreting the measurement results, galloping was found regularly. However, the galloping pattern may be difficult to find. It is expected that the galloping frequency corresponds to the structure’s span. The frequency then becomes f = v/L. To derive a relevant standard for the galloping effect, the accumulation of rotational energy has to be quantified. Looking at the measured accelerations, peak values may be identified easily. If 3 consecutive peak values are considered, and the third peak value C is larger than the values corresponding to peaks A and B, then the quantity p is defined as :p i = a peak C / a peak A (2) If the acceleration in C is lower than in A, p i is taken 0. This process is programmed for each series of measurements, and results in determining a resonance number as :Res = ∑i=3n p i + + ∑i=3n p i-2 n - 4(3) The newly defined quantity Res is an accurate standard to evaluate the accumulation of kinetic energy. During Fourier-analysis, the instantaneous accelerations and velocities can be expressed as : a (t) = ∑i A i cos (2πf i t)v (t) = ∑i A i 2π f i sin (2πf i t) (4a,b)Since kinetic energy is related to the square of velocity, by integration of the square values of eq 4(b) a standard for the energy of the several Fourier-terms can be found from :E ≈ A i ² / f i ²(5)0,20,40,60,811,21,41,61,800,511,522,5 Fig. 7 Resonance curve for galloping carsThis quantity is related to Fourier transform. The data related to all structures have been assembled to the graph of fig 7, showing the value of eq. (3) versus the main frequencies of the Fourier analyzed signal. As the main frequency is closer to the train car suspension frequency, the quantity from eq (3) exceeds 1. This shows that galloping energy is being accumulated. The graph of fig 7 allows determining for any combination of v and L, whether train cars will actually show the galloping movement, causing discomfort to passengers. Clearly, the data for this graph relate to the suspension system of Thalys-train cars, used during all measurements4. Comparing with calculated and recommended valuesAccording to EN 1990 – prAnn2 paragraph A.2.4.4.3 limiting values of bridge deck stiffness may be expressed as L/y , y being the vertical deflection of the bridge deck, caused by LM 71 multiplied with the appropriate dynamic factor Φ. The vertical acceleration then is inversely proportional to L/y. Two types of quantities can be determined to compare with the recommendations of EN 1990 prAnn2. The 95%-fractile value a 95 may be considered for a combination of L and train speed v. The value (L/y)EN corresponds to the recommended value to obtain maximum vertical acceleration of 1 m/s² . Since accelerations are inversely proportional to L/y, a predicted value of a EN may be found by the relationa EN = (L/y)EN 1m/s² / (L/y) (6)Another comparison is made by determining the relative stiffness factor, corresponding to the 95%-fractile acceleration(L/y) a95 = (L/y) EN 1m/s² / a 95 (7)For the Lot viaduct a wide variety of train speed is available. Both quantities are compared in fig 8. Obviously, the viaduct shows improved behaviour compared to the recommendations of prEN 1990 Ann 2, the difference becoming clearer as speed is increasing. The relative stiffness of this viaduct L/y = 1300 is certainly accurate. The value of the eq (3) quantity found for this viaduct is below 0.5. To reach vertical accelerations of 1 m/s², the actual train speed would need to be 240 km/h. Should the values of prEN 1990 have been adopted the required relative stiffness would be 2025, and the viaduct was to be more costly and more heavy.0,20,40,60,811,21,48010513015518020523005001000150020002500300090115140165190215240Fig. 8 Comparing Lot viaduct values to prEN 1990 recommendationsThe viaducts of Lembeek, Arbre and Antoing may be compared to the recommendations for singular train speed values only. In general, the recommendations of prEN 1990 overestimate the required stiffness of all of these structures.(km/h) measured 210 0,565 700 1238 Table 3 Compared values for Halle bridge The compared values for the Halle bridge are shown in table 3, for two representative classes of train speeds. As the stiffness factor equals 1520, the table shows that prEN 1990 Ann 2 requires the values of the last column to find the 95% value of the acceleration. Since the values from this column are much lower than 1520.The conclusion must be that prEN 1990 Ann 2 underestimates the required stiffness for larger bridges. This is probably because larger bridges were little considered in the recommended values. A more complete comparison for the Halle bridge is reported in [5].5. ConclusionsSeveral series of measurements of vertical train car accelerations while crossing bridges and viaducts have been interpreted statistically. A procedure for assessment of the galloping effect of train cars has been developed. Having compared measured accelerations with prEN 1990, the latter recommendations seem to require excessive bridge stiffness for medium span viaducts, especially those between 30 and 45 m span, underestimate the necessary stiffness for large span bridges.5.1 References[1] prEN 1991-2 EUROCODE 1 Actions on Structures Part 2 General Actions – Traffic loads on Bridges . European Committee for Standardisation, Brussels June 2001[2] V AN BOGAERT Ph. “Dynamic Response of Trains Crossing Large Span Double-Track Bridges”, Journal of Constructional Steel Research , V ol. 24, No. 1, 1993, pp. 57-74.[3] V AN BOGAERT Ph., “Drei stählerne Stabbogenbrücken zur Ueberquerung des Kanals Brüssel-Charleroi” Stahlbau , (in German), V ol 68, No 6 1999, pp 409-419.[4] RAEMDONCK W, Vervormbaarheidseisen van spoorviaducten voor hoge snelheid – confrontatie met meetresultaten van testritten , Graduation thesis, 1999, Ghent University, 160 pp[5] V AN BOGAERT Ph. “Behaviour of Train Cars Moving across Steel Tied Arch Bridges”, Proc Third Int Arch Bridges Conference Arch ’01. Paris – Sept 2001 pp 629-634. Ed C. Abdunur, Presses ENPC.。

短裙英语作文

短裙英语作文In the realm of fashion, the mini skirt stands as a symbol of youthful exuberance and style. This short garment, which typically extends to a length above the knees, has been a staple in the wardrobes of women across the globe. The following essay delves into the history, cultural impact, and the modern interpretation of the mini skirt.The mini skirt first gained popularity in the 1960s, a period marked by social and cultural revolution. It was seen as a bold departure from the longer skirts that were the norm, and it quickly became a symbol of the era's progressive spirit. Designers like Mary Quant are credited with popularizing the mini skirt, which was often paired with tights or boots to create a modish look.Culturally, the mini skirt has been a subject of debate. For some, it represents freedom and empowerment, allowing women to express their individuality and confidence. For others, it has been a point of contention, with discussions around modesty and appropriate attire in various social settings. Despite these debates, the mini skirt has endured as a fashion choice, reflecting the evolving nature of societal norms.In contemporary fashion, the mini skirt has taken on new forms and materials. From denim to leather, and from casual to formal occasions, the mini skirt is a versatile piece thatcan be styled in numerous ways. It is often seen paired with high heels to elongate the legs, or with sneakers for a more casual, sporty look.The mini skirt also serves as a canvas for designers to showcase their creativity. Embellishments, patterns, and unique cuts are common, making each mini skirt a potential statement piece. It is not just an article of clothing but a medium for artistic expression.In conclusion, the mini skirt is more than a fashion item; it is a cultural icon that has transcended time and continues to evolve with the changing tides of fashion. It is a testament to the dynamic nature of fashion and its ability to adapt to and reflect the spirit of the times. Whether worn as a symbol of rebellion, a nod to the past, or simply as a stylish choice, the mini skirt remains a beloved and enduring part of women's fashion.。

Donald Kiraly-Wolfgang Lorscher Translation performance, Translation Process and Translation strateg

Érudit est un consortium interuniversitaire sans but lucratif composé de l'Université de Montréal, l'Université Laval et l'Université du Québec à
Montréal. Il a pour mission la promotion et la valorisation de la recherche. Érudit offre des services d'édition numérique de documents scientifiques depuis 1998. Pour communiquer avec les responsables d'Érudit : erudit@umontreal.ca
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Wolfgang Lörscher. Translation Performance, Translation Process, and Translation Strategies. A Psycholinguistic Investigation. Tübingen, Gunter Narr, 1991, 307 p.
par Candace Séguinot
TTR : traduction, terminologie, rédaction, vol. 5, n° 1, 1992, p. 271-275.
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the translation process. For those of us whose knowledge of German is less than adequate, the fact that his 1987 professorial dissertation or Habilitationsschrift from the University of Essen, Überstzungsperformanz, Übersetzungs-prozeß und Übersetzungsstrategien. Eine psycholinguistische Untersuchung, has been published in English is very welcome news. In this book, as in his articles, Lörscher can be counted on to provide a thorough explanation of the current thinking in cognitive psychology and language learning relevant to the interpretation of data-driven research in translation. There is a section on thinking aloud as a way of collecting data (pp. 48-55), an interesting discussion of interpretive reconstruction (pp. 56-59) and a lengthy explanation of different concepts of strategy and text production models (pp. 67-81). This material provides the background for the experimental hypotheses underlying the psycholinguistic investigation of the subtitle. The strength of the actual data and the subsequent analysis lies in the theoretical and methodological issues that they raise. There is no escaping the fact that the grammar-translation method of language teaching which is alive and well and living in Germany is anathema to Canadians, and especially to Canadians who teach in schools of translation. If this point seems to be parochial, it is nevertheless central to the reader's willingness to accept generalizations about the translation process given the specifics of the experimental design. The subjects for the study were university students in English as a foreign language courses who had little experience translating, and very little translation training; they had varying degrees of competency in the foreign language itself. The task that they were asked to perform was an orally-produced translation of a written source text. Half the subjects translated one of six English texts toward German, their mother tongue, and the other half translated one of three German texts toward English. At the same time as they were producing their translations orally, the students were asked to think aloud about the process itself. "Whoa!" says the reader. Can you really call what the subjects are doing translating, and if so, does that imply that the strategies they use to problem solve are the same as those used by expert translators? And is it really possible to translate aloud and think aloud at the same time? To his credit, Lörscher anticipates these and other objections throughout the work. He begins (p. 3) by justifying the use of "nonprofessional translators" in two ways. First, his hypothesis is that "every

gap analysis 方差

gap analysis 方差英文版Gap Analysis: VarianceIn the field of statistics and data analysis, gap analysis and variance are two important concepts that are often used interchangeably. However, there are distinct differences between the two terms, and understanding these differences is crucial for accurate data interpretation.Gap analysis refers to the identification and measurement of differences between two or more groups or individuals. It involves comparing the performance, characteristics, or outcomes of different entities and determining the extent to which they differ from each other. Gap analysis can be used in various contexts, such as business performance, educational outcomes, or social disparities.Variance, on the other hand, is a measure of dispersion or spread in a dataset. It quantifies the amount of variation ordeviation from the mean value in a set of data points. Variance is typically used to describe the spread of numerical data and is calculated by summing the squared differences between each data point and the mean, then dividing by the number of data points.While gap analysis focuses on comparing and quantifying differences between groups, variance focuses on measuring the spread of data within a group. Gap analysis is concerned with identifying and explaining the gaps or differences between entities, while variance is concerned with understanding the variability or dispersion within a dataset.In summary, gap analysis and variance are distinct but related concepts in statistics and data analysis. Gap analysis is used to compare and quantify differences between groups, while variance is used to measure the spread of data within a group. Understanding the differences between these two terms is essential for accurate data interpretation and informed decision-making.中文版差距分析：方差在统计和数据分析领域，差距分析和方差是两个常被互换使用的重要概念。

(整理)石油词汇英语翻译(QR)

石油词汇英语翻译(QR)Q check 质量检查Q deconvolution Q反褶积Q value Q值；品质因数Q wave 勒夫波Q 第四纪q 公担Q 夸脱Q 量q 品质因数q 问题Q-band Q频带Q-joint Q 节理Q-law 品质因素定律Q-meter Q 表Q-mode cluster analysis Q型聚类分析Q-qualit 品质因数Q-RING 方形环Q. 夸德q.e. 这就是Q.I 质量指标Qa 二次淬火的QA 象限角QA 质量保证qb 速断；高速断路器Qc 快速检查QC 质量控制QD 俯角QED 证完QEF 这就是所要作的QEI 这就是所要找的qf 品质因数QFT 定量荧光分析法QISAM 队列索引顺序存取法ql. 公担；英制重量单位qlty 质Qp 更新世；更新统QPL 产品一览表qquasi-section 假剖面qr 四分之一；一刻钟QR 质量要求QRC 快速反应能力QRC 快速换装闸板型qt 夸脱QT 快速测试qt 数量QTC 鉴定试验试件QTR 检验合格报告qtr 四分之一qty 量qtz 石英qtze 石英岩quad word 四倍长字quad 四倍的；四重的；四个部分形成的quad 四边的quad 四角形quad 四路多工的；四倍的quad 象限quad. 四角形quadded cable 四线电缆quadr- 四Quadracypris 方星介属Quadraeculina 四字粉属quadrangle 四边形quadrangular 四边形的quadrant angle 象限角quadrant antenna 正方形天线quadrant depression 俯角quadrant elevation 仰角quadrant tooth 扇形轮齿quadrant valve 扇形阀quadrantal diagram 象限图quadrantal 象限的quadraphonics 四轨录音放音；四声道立体声quadrate 正方形；使成正方形；四等分quadratic approximation 二次逼近quadratic component 二次谐波quadratic criterion 二次准则quadratic curve 二次曲线quadratic damping 平方阻尼quadratic detection 平方律检波quadratic discriminant 二次方程判别式quadratic equation 二次方程quadratic expression 二次表达式quadratic form 二次型quadratic function 二次函数quadratic interpolation 二次插值quadratic mean deviation 中误差quadratic mean 均方值；有效值quadratic programming 二次规划quadratic root 平方根quadratic spline 二次样条quadratic sum 平方和quadratic surface 二次曲面quadratic transformation 二次变换quadratic variation 二次变分quadratic 二次方程式；二次项；二次的；平方的；象限的；方形的quadratin free number 无平方因子数quadratron 热阴极四极管quadrature analysis 正交分析quadrature component 正交分量quadrature filtering 90度相移滤波quadrature formula 求积公式quadrature network 无功电路quadrature spectrum 正交谱quadrature trace 正交道quadrature 求面积；求积分；正交；转象差；90度相位差quadrennial 连续四年的时间；每四年一次的事件；第四周年；连续四年的；每四年一次的quadri- 四quadric cone 二次锥面quadric stress 曲面应力quadric surface 二次曲面quadric 二次quadricorrelator 自动调节相位线路quadrilateral 四边形quadrille paper 方格纸quadrillion 1×1024quadrinomial 四项式quadripole 四极quadripolymer 四单体共聚物quadrivalence =quadrivalency 四价quadrntnt 四分之一圆；扇形体；象限仪；象限；扇形齿轮；四分仪quadrode 四极管quadru- 四quadruple block 四轮滑车quadruple board platform 二层台quadruple chain drive 四排链的传动quadruple coincidence set 四等分器quadruple completion 四层同时完成quadruple 四倍；四倍的；四重的；由四部分组成的；四路的；四工的；四倍地；成四倍；以四乘quadruple-action hand pump 四作用手摇泵quadrupler 四倍器；四频器；乘四装置；四倍乘数quadruplet 四件一套的东西quadruplex 四路多工系统；四倍的；四重的；四路多工的quadruplicate 一式四份的一份；一式四份；四倍的；四重的；四次方的；一式四份的quadruplication 放大四倍；反复四次quadrupole 四极quafric curve 二次曲线quafric of revolution 回转二次曲面quagmire 沼泽quake center 震中quake sheet 地震岩席quake 震动；颤抖qual. 定性的qual.anal. 定性分析qualia quale的复数qualification approval test 资格合格考试qualification certificate 资格证书qualification examination 资格审查qualification rate 合格率qualification test report 检验合格报告qualification test 资格考试qualification 资格qualificative 限定的qualified acceptance 有条件承兑qualified driller 合格司钻qualified part 合格零件qualified person 合格人员qualified product list 产品一览表qualified 合格的qualifier 合格的物；修饰词；限定词qualimeter X射线硬度测量仪qualitative analysis 定性分析qualitative assay 定性测定qualitative carbon steel 优质碳钢qualitative comparison 质量比较qualitative curve 定性曲线qualitative determination 定性测定qualitative examination 定性研究qualitative filter paper 定性滤纸qualitative formation evaluation 定性地层评价qualitative indication 定性指示qualitative interpretation 定性解释qualitative observation 定性观察qualitative respones data 定性响应数据qualitative scenarios 定性情景qualitative scheme 定性方法qualitative spectral scan 定性全谱扫描qualitative steel 优质钢qualitative stratigraphic corrrelation 定性地层对比qualitative tendency 特性趋势qualitative test 定性测试qualitative 定性的quality assessment 质量评价quality assurance provision 质量保证条例quality assurance 质量保证quality certificate 品质证书quality check 质量检查quality claim 品质索赔quality control by attributes 按固定指标控制quality control 质量控制quality determination 质量测定quality discrepancy record 质量不合规定的记录quality factor 品质因素quality grade 质量等级quality gravel 优质砾石quality index 质量指标quality inspection 质量检验quality leadership 质量领先quality level 质量水平quality loss 质量损耗quality management 质量管理quality matetrial 优质材料quality mind 质量意识quality monitoring 质量监测quality of balance 平衡度quality reduction 质量下降quality requirements 质量要求quality specification 质量标准quality standard 质量标准quality steel 优质钢quality supervision 质量监督quality 质量qualutative model 定性模型quan. 定量的quant. anal 定量分析quant. 定量的quant. 定量地quant. 数量quanta quantum的复数quantification 定时化；定量评价；量化quantifiter 量词；计量器quantifying risk 风险定量quantile 分位点数quantimeter 剂量计quantitative analysis 定量分析quantitative assay 定量测定quantitative assessment 定量评定quantitative change 量变quantitative check 定时检查quantitative classification 定量分类quantitative comparison 定量比较quantitative criterion 定量标准quantitative data 定量数据quantitative determination 定量测定quantitative evaluation 定量评价quantitative examination 定量研究quantitative filter paper 定量滤纸quantitative forecast 定量预报quantitative formation evaluation 定量地层评价quantitative geochemistry 定量地球化学quantitative geology 定量地质学quantitative index 数量指标quantitative interpretation 定量解释quantitative lithologic data 定量岩性资料quantitative measurement 定量测定quantitative paper chromatography 定量纸色谱法quantitative relation 数量关系quantitative reserve assessment 定时储量评定quantitative scenarios 定量情景quantitative seismic stratigraphy 定量地震地层学quantitative spectrograhic analysis 定量光谱分析quantitative spectrography 定量光谱学quantitative stratigraphy 定量地层学quantitative test 定量分析quantitative 定量的quantities uplifted 增加的数量quantity claim 数量索赔quantity control valve 油量控制阀quantity determination 数量确定法quantity discount 折扣量quantity estimate sheet 工作量估算表quantity loss 数量损耗quantity meter 总流量表quantity of heat 热量quantity of information 信息量quantity of injected water 注入水量quantity of precipitation 降水量quantity of remaining recoverable oil 剩余可采油量quantity production 大量生产quantity sheet 工程数量表quantity 量quantivalency 化合价quantivalent 多价的quantivative approach 定量方法quantization 量子化；数字化；分层quantometer 光量计quantum chemistry 量子化学quantum detector 量子探测器quantum effect 量子效应quantum efficiency 量子效率quantum energy 量子能quantum frequency standard 量子频率标准quantum mechanics 量子力学quantum of action 作用量子quantum optics 量子光学quantum theory 量子论quantum-mechanical theory 量子力学理论quanxtizer 数字转换器；量化器quaqavsal dome 圆形穹隆quaquaversal fold 穹状褶皱quaquaversal structure 穹状构造quaquaversal 穹状圆项；由中心向四方扩散的quaquavsal dip 穹倾斜quar 砂岩quarantine buoy 检疫浮标quarantine 检疫；隔离；隔离区；对…进行检疫quark 夸克学quarkonics 夸克学quarry stone 乱石；毛石quarry 石场；菱形的玻璃片；消息的来源；采；搜索；追求物quart 夸脱；一夸脱的容器quart- 四quart. 季度的；四分之一的；每季的；季刊quartation 析银法；；四分法quarter bend 90度弯管quarter deck 艉甲板quarter 四分之一；四分之一元；四等分；季度；一刻钟；方位；四个主要点中的一点；象限；方向；地区；方面；地区；住处；船的后部；相互垂直；弦；把…分为四部分；把…四等分；使与机器连接部quarter-life 四分之一寿命quarter-turn ball valve 直角回转球阀quarter-turn belt 直角回转皮带quarter-wave filter 四分之一波长滤波器quarter-wave 四分之一波长的quarterbost 宿营船quartering sea 船尾浪quartering 四等分；四分取样法；间柱；成直角的quarterline 四等分线quarterly account 季度报表quarterly report 季报quarterly 季刊；季度的；每季的；四分之一的；一季一次的；每季的quartermadter corps line 军用油管线quartern 四等分quarternary 四元的quartet 四人一组；四件一套；四重线quartic 四次的quartile 四分位数quartimax method 四次幂极大法quartimin method 四次幂极小法quarto 四开；四开本；四开的quartz anorthosite 石英斜长岩quartz crystal oscillator gauge 石英晶体振荡压力计quartz crystal 石英晶体quartz dioite 石英闪长岩quartz disoultion 石英辉长岩quartz fiber gravimeter 石英丝重力仪quartz fiber horizontal magnetometer 石英丝水平磁力仪quartz gabbro 石英辉长岩quartz gauge 石英压力计quartz knife edge 石英刀口quartz magnetometer 石英磁力仪quartz montzonite 石岩二长岩quartz monzobiorite 石英二长闪长岩quartz monzogabbro 石岩二长辉长岩quartz oscillator 石英晶体振荡器quartz sand 石英砂quartz sinter 硅华quartz spring gravimeter 石英弹簧式重力仪quartz syenite 石英正长岩quartz T variometer 石英T磁变仪quartz torsion fiber 石岩扭丝quartz 石英quartzarenite 石英砂屑岩quartzification 石英化quartzifous 石英质的quartzite 石英岩quartzitic grit 石英岩质粗砂岩quartzitic sandstone 石英岩质砂岩quartzmengwacke 石英蒙瓦克岩quartzo-feldspathic hornfels 石英长石质角岩quartzolite 硅英岩quartzose arkose 石英长石砂岩quartzose conglomerate 石英质砾岩quartzose laterite 石英质粗砂岩quartzose limestone 石英质灰岩quartzose sandstone 石英砂岩quartzose 石英质quartzwacke 石英瓦克岩quartzy sandstone 石英质砂岩quasi laminar flow 拟层状流quasi one-dimensional flow 准一维流动quasi particle 准粒子quasi shear-wave 准横波quasi steady state flow 准稳态流动quasi thixotropy 准触变性quasi- 似quasi-analog 拟quasi-analytical method 准解析法quasi-competent sands 半坚实砂层quasi-conductor 半导体quasi-coordinates 准坐标quasi-criterion 准评判准则quasi-cyclic code 准循环码quasi-dispersive wave group 准频散波群quasi-dry sample 低含水岩样quasi-elastic scattering 准弹性散射quasi-elastic 准弹性的quasi-equilibrium 准平衡quasi-ergodic principle 准各态遍历原理quasi-factor 拟因子quasi-flexural fold 拟挠曲褶皱quasi-fluid 似流体quasi-friction 准摩擦quasi-geologic joint 似地质节理quasi-gradiometer 准梯度仪quasi-gravity 准重力quasi-group 拟群quasi-homogeneous 准均质的quasi-instruction 拟指令quasi-isostatic displacement 准均衡位移quasi-linear 拟线性的quasi-linearization 拟线性化quasi-longitudinal wave 准纵波quasi-marine 准海成的quasi-Newton method 拟牛顿法quasi-optical 准光的quasi-optimal solution 准优解quasi-ordered system 拟序系统quasi-orthogonal 准正交的quasi-periodic 拟周期的quasi-periodicity 准周期quasi-plastic flow 半朵性流quasi-polynomials 准多项式quasi-random access memory 准随机存取存储器quasi-random 拟随机quasi-single phase flow 准单相流动quasi-sorted 半筛选的quasi-stability 准稳定性quasi-stagnant water 准停滞水quasi-static analysis 准静态分析quasi-static displacement 拟静态驱替quasi-static 似静定的quasi-stationary channel flow 准稳定槽流quasi-stationary oscillation 似稳振荡quasi-stationary 似稳定的quasi-steady state 准稳定态quasi-transverse wave 类横波quasi-variable 准变数quasi-viscous 准粘性的quasicraton 准克拉通quasicrystal 准晶体Quasiendothyra 似内卷虫属Quasifusulina 似纺锤NFDA3quasimoney 准货币quasiorthogonal code 准正交码quasiperfect network 准理想网络quasiseller 准卖主quatation 行情表quater- 四分之一quaterdenary 十四进制的quatermary 四；四个一组quaternary ammonium polymer 季铵聚合物quaternary ammonium 季铵quaternary carbon atom 季碳原子quaternary gain 四进制增益Quaternary geanticline 第四纪地背斜Quaternary glaciation 第四纪冰期Quaternary ice age 第四纪冰期Quaternary period 第四纪quaternary sediment 四组分沉积物Quaternary system 第四系quaternary system 四元系统Quaternary 第四纪第四系quaternion 四个一组；四人一组；四元数；四元法quaternity 四位一体；四人一组quaver 颤音；震动；颤抖；发颤音quay 码头qucidiao 缺次调queen 王后；女王；大石板quefrency domain 同态频率域quefrency 同态频率quench aging 淬火时效quench alloy steel 淬硬合金钢quench bath 淬火浴quench condensation 急冷凝quench duct 骤冷丝室quench hardening 粹火硬化quench oil 淬火油；急冷油quench tower 急冷塔quench zone 急冷段quench 淬火；急冷quenchant 淬火剂quenched and tempered steel 调质钢quenched combustion 急冷燃烧quenched water 急冷水quencher 扑灭者；熄灭器；淬灭剂；灭火器；灭弧器；减震器；阻尼器quenching agent 淬火剂quenching bath 淬化浴quenching crack 淬火裂纹quenching effect 骤冷效应quenching medium 淬火剂quenching oil column 急冷油塔quenching stack 骤冷甬道quenching strain 淬火应变quenching system 急冷系统quenching temperature 淬火温度quenching water column 骤冷水塔quenching 淬火quenchometer 冷却速度试验器querceta quercetum的复数Quercoidites 栎粉属quernstone 含铁砾质砂岩Querwellen wave 奎威林波query language 询问语言query 质问；疑问；询价；请问；疑问号；询问quest for oil 找油quest 探索；寻找；要求；追求question 问题；难题；议题；疑问句；可能性；询问questionable productive zone 可疑生产层questionable 可疑的questionary 询问的questionnaire 调查表queue anticline 背斜尾queue discipline 排队规则queue empty 队列空queue full 队列满queue priority 队列优先权queue 发辫；行列；梳成辫子；排队queued access method 队列存取法queued indexed sequential access method 排队索引按序存取法queued sequential access method 排队按序存取法queuing network 排队网络queuing theory 排队论queuing 排队quibinary code 五-二码quick access 快速存取quick acting 快动作的quick ash 烟道尘quick bleed 快排开关quick burning fuse 速燃引信quick cement 快凝水泥quick clay 过敏性粘土quick closing safety valve 快闭安全阀quick connector 快速连接器quick cooling 快速冷却quick coupler 快速连接器quick coupling 快速管箍quick current assets 速动资产quick depletion 速递减quick disconnection 速断开quick exhaust valve 快速放空阀quick freezing 速冻quick ground 流砂土quick hardening 快硬的quick lock 速关锁装置quick look scaler 快速直观解释比例尺quick open cover 快速开启盖quick opening shock valve 快开冲击阀quick ratio 速动比quick relealse 快松quick return motion 速回运动quick run 快速的quick setting cement 快凝水泥quick setting mortar 快凝灰浆quick solder 速熔焊料quick start 快启动quick talking cement 快凝水泥quick test 快速试验quick turn 急转弯quick union 快接接头quick 快的quick-acting coupling 快速接头quick-acting fuse 速燃引信quick-acting valve 快动作启闭阀quick-adjustsing 快速调整的quick-break switch 急断开关quick-break 速断quick-breaking emulsion 易破坏乳状液quick-change plug container 快卸式水泥头quick-change 快速调换的quick-closing lock 快关闭装置quick-closing valve 快关阀quick-detach 速拆卸quick-disconnect 速折卸的quick-drying lacquer 快干漆quick-drying oil 快干油quick-opening flow characteristic 快开流动特性quick-opening valve 快开阀quick-operating 快动的quick-reading flow sheet 简化流程quick-release coupling 快卸接头quick-release valve 快泄阀quick-replaceable 快速更换的quick-setting 快凝quick-speed 快速quick-stick test 快粘试验quick-wear part 易损零件quick-wearing 快磨损quicklime 生石灰quicklook interpretation 快速直观解释quicklook playback 快速直观回放quicklook 快速直观quicksand type formation 流砂型地层quicksand 流砂；动荡和捉摸不定的事物quicksilver 水银；汞；涂水银于QUICKTRAN 快速翻译程序quiddity 本质；遁辞quiescence 静止；沉寂quiescent condition 静止状态quiescent current 静态电流quiescent interval 间歇时间quiescent layer 静止层quiescent load 静负荷quiescent point 静态工作点quiescent tank 静水沉降池quiescent 静止的quiet day 无磁扰日quiet magnetic zone 地磁平静区quiet well 安静井quieter 消音装置quietus 偿清；解除；静止状态quilitative method 定性方法quill 羽毛；钻轴；衬套；导火线；做管状的褶子；卷在线轴上quilt 用垫料填塞；被；被状物；缝quin- 五quinary digit 五进制数字quinary notation 十五进制的quinary 五个一套；五的；五个的；五个一套的；第五位的；五进制的quindenary 奎宁；金鸡纳碱Quinguerhabdus 五角棒石quinine 奎诺酊quinoidine 喹啉quinoline 喹啉quinolinic acid 喹啉酸quinone 醌quinqu 五quint 五件一套；五度quintal 公担quintessence 精髓；典型；本位quintete 五人一组；五件一套；五重线quintic 五次的quintuple 五倍量；五个一套；成五倍；五的；五倍的quintupler 五倍器quintuplet 五人一组quintuplicate 五倍的数；使成五倍；作成一式五份；五倍的；五重的quintuplication 五倍quintupling 五倍quioning 外角构件；挤紧；楔紧quire 一刀；对折的一叠纸quirk 突然弯曲；遁辞；弯曲quisqueite 高硫钒沥青；硫沥青quit flowing pressure 停喷压力quit 离开；退出；放弃；解除；偿清；停止quiver 颤声；一闪；颤动；摇动quiverful 大量的quiz 知识测验；难题quizzes quiz的复数Qujionlepis 曲靖鱼属qun 群qunatum 量；量子；和quoin 外角；角落；隅石；楔形支持物；夹紧quorum 法律顾问quot 引用的；开价的quot 引用语；行市；估价单quota agreement 生产限额协议quota allocation of production 生产配额quota cost 定额成本quota of budget 预算定额quota of budgetary estimate 概率定额quota of capital construction 基本建设定额quota system 限额进出口制quota 份额quotation of prices 报价quotation 引证quote 引号；引文；引用；把…放在引号内；报quoteworthy 有引用价值的quotient convergence factor 比值收敛因子quotient group 商群quotient of difference 增量比quotient 商数；份额quotient-difference algorithm 商差算法quotient-multiplier register 乘数商数寄存器quotiety 率quotoent system 限额进出口制qv 见qwasi-time domain method 伪时域法QWERTY keyboard QWERTY盘R a T 抽油杆和油管R and M 修理与维护r c 橡胶包裹的r c 遥控R wave R波R 半径R 比r 残余的R 第三纪R 电阻率R 范围r 竿r 河流R 基R 接收器R 兰金度数R 雷诺数R 列氏温度r 伦琴R 逆动r 稀有的R 右R 原始的R 阻力R&D 研究与发展R' 圆半径弧分数R'' 雷氏秒数R'' 圆半径弧秒数R-C coupling 阻容耦合R-C 阻容的r-equivalent 伦琴当量R-M spread 研究法-马达法辛烷值差R-mode factor analysis R-型因子分析R-mode space R-型空间R-mode statistical method R-型统计法r-number r值R-signal 电阻性信号r-strategist 特化种R-unit 伦琴单位R. 半径R. 比R. 后R. 江R. 铁道R. 已注册的R. 右r.a.l 左右R.A.S 英国皇家航空协会R.C 旋转变流机R.C 研究中心R.C 阻容R.C.E.E.A. 无线电通信及电子学工程协会R.F.U. 随时可使用的R.H. 相对湿度R.H. 右r.h.s. 右方R.I. 保留指数R.I. 放射性同位素R.I. 放射性同位素指示剂R.I. 复现指数R.M.T. 读取磁带R.N. 雷诺数R.P.C. 遥控台R.T. 放射性同位素指示剂R.T. 射线探伤访验R.T.C. 自记式温度控制器RA 放射性RA 辐射RA 记录准确度Ra 镭RA 洛氏硬度A级RA 实数加RA 随机存取RA 作用半径raabsite 钠闪云煌岩RAB tool 钻头处电阻率测井仪rabbet 插孔rabbit 清管器rabble 搅拌棒rabbler 刮九Rabinowinwitsch model 拉宾诺维奇模race knife 划线刀race rotation 空转race 赛跑RACE 随机存取计算机设备raceme 外消旋体racemization 外消旋作用raceway 电缆管道racheting device 棘轮装置racing 空转；急转rack and gear drive 齿条-齿轮传动rack and gear jack 齿条-齿轮式千斤rack and pinion jack 齿条-小齿轮千斤顶rack and pinion 齿条-小齿轮rack back 在井架中排立钻杆rack bar sluice valve 齿条式闸门阀rack circle 圆齿条rack earth 机壳地线rack jack 齿条式千斤顶rack mechanism 齿条机构rack of barrels 桶堆rack pipe 排管rack pricing 离炼厂定价rack rail 齿轨rack rent 高额地租rack tooth 齿条齿rack up 排放完rack wheel 棘轮rack 架racker 排管器racking arm 系管臂racking back 在井架中排立钻杆racking board 二层台racking capacity 排立根量racking cone 钻杆排置锥座racking of drill pipe 钻杆排放racking of drum 堆桶racking pipe 排管racking platform 二层台racking 架；震动racon 雷达信标Rad 放射的RAD 快速存取磁盘rad 拉德rad. 半径rad. 根数rad. 弧度rad. 无线电rad. 无线电报rad. 无线电员radac 快速数字自动计算radan 多普勒雷达自动导航radar altimeter 雷达测高仪radar antenna 雷达天线radar band 雷达波段radar base map 雷达导航图radar beacon 雷达信标radar beam 雷达波束radar buoy 雷达浮标radar coverage 雷达覆盖范围radar depression angle 雷达俯角radar doppler 多普勒雷达radar imaginary 雷达成象radar indicated face 雷达显示表面radar interaction 雷达干扰radar jamming 雷达干扰radar map 雷达地图radar mapping 雷达地形显示图radar mast 雷达天线杆radar microwave technique 雷达微波技术radar mosaic 雷达综合图radar navigation 雷达导航radar performance figure 雷达性能指标radar photography 雷达摄影术radar pilotage 雷达领航radar presentation 雷达显示radar range finder 雷达测距仪radar reflection interval 雷达反射时间间隔radar reflection 雷达反射radar reflectivity 雷达反射率radar remote sensing 雷达遥感radar resolution 雷达分辨率radar responder 雷达应答器radar return 雷达回波radar scanning 雷达扫描radar shadow 雷达盲区radar surveying 雷达测量radar target 雷达目标radar 雷达radar-probing system 雷达探测系统radar-rock units 雷达岩石单位radar-transparency 雷达透视radargrammetry 雷达测量radarman 雷达员radarphototheodolite 雷达摄影经纬仪radarscope photography 雷达摄影学radarscope 雷达示波器RADD 列地址radechon 雷得康管radiac 放射性检测仪radiacmeter 核辐射剂量计radiagraph 活动焰切机radial adaptive multiple suppression 径向自适应压制多次波radial advance 径向推进radial air-cooled engine 星型气冷式发动机radial angle 径向角radial arm bearing 横力臂支承radial arm 旋臂radial array 径向排列radial bearing disk 止推轴承盘radial bearing lower drive sub 下部径向轴承传动接头radial bearing upper drive sub 上部径向轴承传动接头radial bearing 径向轴承radial bore length 水平井眼长度radial characteristic 径向特性radial circular flow 径向环流radial clearance 径向间隙radial component 径向部分radial conductive heat transfer 径向热导传热radial coning 径向锥进radial coordinates 径向坐标radial crack 放射状裂隙radial crushing strength 中心破碎强度radial davit 转动式吊艇杆radial differential temperature log 径向微差井温测井radial displacement 径向驱替radial drilling machine 旋臂钻床radial engine 星型发动机radial feed 径向给进radial flow tray 径流塔板radial flow 径向流radial fluid flow 平面径向流radial force 径向力radial gradient 径向梯度radial groove 径向沟槽radial height 径向高度radial histogram 径向直方图radial impeller pump 径向叶轮泵radial inward flow 径向向内流radial load 径向载荷radial migration 辐射迁移radial multiple-suppression method 径向多次压制法radial node 径向结点radial outward flow 径向向外流radial packing 径向盘根radial piston motor 径向活塞马达radial play 径向间隙radial plunger pump 径向柱塞泵radial reactor 径向反应器radial refraction 径向折射radial resolution 径向分辨率radial response 径向响应radial rift 放射断陷radial shaft seal ring 径向轴密封环radial shooting 径向激反radial shrinkage 径向收缩radial slot 沿径槽radial steady-state flow equation 径向稳定流动方程radial steam-front advance 径向蒸汽前缘推进radial strain 径向应变radial stress 径向应力radial support bearing 径向支承轴承radial survey 径向观测radial symmetry 径向对称radial thrust bearing 径向止推轴承radial tolerance 径向容许偏差radial trace 径向记录道radial turbine 径流式涡轮radial velocity 径向速度radial vibration 径向振动radial waterflooding 环状注水radial wire cord tire 钢丝子午线轮胎radial wobble 径向震摆radial 辐向的radial-inlet impeller 径向进口式叶轮radialization 辐射；放射radian frequency 角频率radian measure 弧度radian 弧度radiance contour map 辐射外形图；发光度外形图radiance 光亮度；辐射率；辐射性能radiancy =radianceradiant coil 辐射段炉管radiant energy 辐射能radiant flux density 辐射能量密度radiant heat sensor 辐射热传感器radiant heat zone 辐射热带radiant heat 辐射热radiant heater 辐射式加热炉radiant intensity 辐射强度radiant matter 辐射物radiant power 辐射功率radiant quantity 辐射量radiant rays 辐射线radiant section 辐射段radiant surface absorptivity 辐射表面吸收率radiant temperature sensitivity 辐射热感温灵敏度radiant tube 辐射管radiant type fiber 辐射型纤维radiant wall tubes 辐射壁管radiant 辐射源radiant-type furnace 辐射炉radiaoctive family 放射系Radiastarte 射华蛤属radiate 放射radiated noise 辐射噪声radiated solar energy 辐射太阳能radiated structure 射状构造radiated wave 辐射波radiating body 辐射体radiating heat 辐射热radiating matter 放射物质radiation absorber 辐射吸收剂radiation balance 辐射平衡radiation belt 辐射带radiation characteristic 辐射特性radiation chemistry 放射化学radiation counter 辐射计数器radiation crosslinking 辐射交联radiation damage 辐射线损伤radiation degradation 辐射降解radiation detector 辐射探测器radiation dosimetry 辐射剂量测定法radiation ecology 辐射生态学radiation effect 辐射效应radiation efficiency 辐射效率radiation energy 辐射能radiation estimator 辐射剂量计radiation grafting 辐射接枝radiation heat transfer 辐射热传递radiation heat 辐射热radiation heater 辐射加热器radiation induced crosslinking 辐射诱导交联radiation induced grafting 辐射诱导接枝radiation initiation 辐射引发radiation intensity 辐射强度radiation ionization 辐射电离radiation level 辐射强度radiation logging 放射性测井radiation loss 辐射损失radiation method 辐射法radiation pattern 辐射模式；辐射特性图radiation peak 辐射最大值；辐射峰值radiation polymerization 放射聚合radiation pyrometer 辐射高温计radiation resistance 抗辐射性radiation resistant finish 防辐射整理radiation section 辐射段radiation sensitizer 辐射敏化剂radiation shield 辐射屏蔽radiation source 辐射源radiation temperature 辐射温度radiation wall thinkness measure device 辐射测壁厚仪radiation 辐射radiation-free zone 无辐照区域radiation-generating machine 辐射发生器radiation-initiated crosslinking 辐射诱导交联radiation-initiated polymerization 辐射引发聚合radiationless transition 无辐射跃迁radiationmeter 放射线计Radiatisporites 辐毛大孢属radiator shutter 散热器风门片radiator 辐射体radiator-type cooling unit 散热器式冷却装置radical catalyst 游离基催化剂radical copolymerization 游离基共聚合radical expression 根式radical four-spot patern 基本四点井网radical polymerization 游离基聚合radical scavenger 游离基清除剂radical sedimentation basin 辐流式沉淀池radical sign 根号radical 基radical-anion initiator 游离基-阴离子引发剂radicand 被开方数radication 开方radices radix的复数radicle 基；根radii radius 的复数radio detection 无线电检测radio direction finder 无线电测向仪radio direction finding 无线电测向radio distance-measuring 无线电测距radio echo sounding 无线电回波探测radio electronics 无线电电子学radio emission 无线电发射radio engineering 无线电工程radio examination X射线透视法radio facsimile 无线电传真radio finder 无线电测向仪radio frequency 射频radio indicator 放射性同位素指示剂radio interference 无线电干扰radio interferometry 无线电干涉测量radio modulation 无线电调制radio modulator 无线电调制器radio navigation aids 无线电导航设备radio navigation transmitter 无线电导航发射机radio navigation 无线电导航radio pager unit 无线电呼唤装置radio position fixing 无线电定位radio positioning 无线电定位radio prospecting 放射性勘探radio reception 无线电接收radio relay station 无线电中继站radio research ship 无线电通信试验船radio responder 无线电应答器radio scanner 无线电扫描仪radio scattering 射电散射radio sonobuoy 无线电声呐浮标radio spectrum 射频频谱radio station 无线电台radio survey 无线电测量radio telemetering 无线电遥测；无线电遥测的radio telemetry buoy 无线电遥测浮标radio telemetry seismic data acquisition system 无线电遥测地震数字采集系统radio teletype 电传打字机radio thin-layer chromatography 放射薄层色谱法radio tick 无线电报时信号radio tower 无线电天线塔radio transceiver system 无线电收发系统radio transmission 无线电发射radio transmitter 无线电发射机radio wave propagation 无线电波传播radio 无线电radio- 放射radio-altimeter 无线电测高计radio-apparatus 无线电台radio-controlled pump station 无线电控制泵站radio-direction-finder method 无线电测定方位法radio-fixing 无线电定位radio-frequency amplifier 高频放大器radio-frequency choke 射频扼流圈radio-frequency coil 高频线圈radio-frequency drying 高频干燥radio-frequency field 射频场radio-frequency formation heating 地层射频加热radio-frequency interference 射频干扰radio-frequency location system 射频定位系统radio-frequency oscillator 射频振荡器radio-frequency reading 用高频扫描快速读出radio-frequency signal 高频率信号radio-halo 放射晕radio-label 放射性同位素示踪radio-link 无线电通信联络radio-micrometer 高灵敏度辐射计radio-microwave telemetering system 无线电-微波遥测系统radio-positioning navigation 无线电定位导航radio-positioning network 无线电定位网格radio-positioning station 无线电定位台radioacoustics 无线电声学radioactinium 放射性锕radioactivation analysis 活化分析；放射活化分析radioactive age determination 放射性年龄测定radioactive anomaly 放射性异常radioactive ash 放射性尘埃radioactive bullet 放射性子弹radioactive bulletlocator 放射性子弹定位器radioactive carbon dating 放射性碳年代测定法radioactive cement 放射性水泥radioactive chain 放射性衰变链radioactive concentration 放射性浓度radioactive constant 放射常数radioactive contamination 放射性污染radioactive decay 放射性衰变radioactive density meter 放射性密度计radioactive detector 放射性检测器radioactive disintegration 放射性衰变radioactive drug 放射性制剂radioactive element 放射性元素radioactive foil 放射性金属薄片radioactive heat 放射性热radioactive indicator 放射性指示剂radioactive isotope equipped go-devil 放射性同位素刮管器radioactive isotope 放射性同位素radioactive leak 放射性泄漏radioactive logging 放射性测井radioactive mineral 放射性矿物radioactive nucleus 放射性核radioactive nuclide 放射性核素radioactive occurrence 放射性矿床radioactive pollutant 放射性污染物radioactive prospecting 放射性勘探radioactive source 放射性源radioactive standardization 放射性标准化radioactive static eliminator 放射性静电消除器radioactive tracer log 放射性示踪剂测井radioactive tracer survey 放射性示踪物测量法radioactive tracer 放射性指示剂；放射性示踪剂radioactive transformation 放射性转化；放射性蜕变radioactive waste 放射性废物radioactive well logging 放射性测井radioactive 放射性的radioactive-tracer method 放射性示踪法radioactive-tracer-fibre 放射性示踪纤维radioactivity anomaly 放射性异常radioactivity background 放射性本底radioactivity decay 放射性衰变radioactivity equilibrium 放射性平衡radioactivity indicator 放射性强度指示器radioactivity level 放射性能级radioactivity log 放射性测井radioactivity prospecting 放射性勘探radioactivity standard 放射性标准radioactivity survey 放射性勘探radioactivity well logging 放射性测井radioactivity 放射性；放射radioalarm equipment 无线电报警器radioamplifier 高频放大器radioanalysis 放射性分析radioanalytical chemistry 放射分析化学radioassay 放射性检验radioastronomy 射电天文学radioautocontrol 无线电自动控制器radioautogram 无线电传真radioautograph 放射自显影radioautography 放射自显影术radiobeacon buoy 无线电浮航标radiobeacon 无线电信标radiobeam 无线电电波radiobearing 无线电方位radiobiochemistry 放射生物地球化学radiobiology 放射生物学radiobroadcast 无线电广播；用无线电广播radiocall sign 无线电呼号radiocarbon age 放射性碳年龄radiocarbon C14 放射性碳radiocarbon chronology 放射性碳测定年代法radiocarbon dating 放射性碳测定年龄radiocarbon stratigraphy 放射性碳地层学radiocarbon tracer 放射性碳示踪物radioceramic 高频瓷radiocesium 放射性铯radiochannel 波道radiochemicak analysis 放射化学分析radiochemistry 放射化学radiochromatogram 放射性色谱图radiochromatograph 辐射色层分离谱。

Waves1_Field Theory(波动理论)

标量场：
等值面：
u u x, y , z u x, y, z const
(1.1)(1ຫໍສະໝຸດ 2)同理有等值线，等高线。性质：等值面充满了标量场所在空间而且互不相交。
1.1.2 矢量场及其矢量线
如果定义场的物理量是矢量，就称这个场为矢量场。
例如：力场，速度场，电场，磁场等等。
由最后一个方程得： x y z 16
2 2

2
R2
这就是要求的矢量管方程。
数量又分：
纯标量 — 与坐标方向的变化无关的数量。例如：温度，质量。
赝标量 — 与坐标方向的变化相关的数量。
例如：体积，角度，面积……等都是赝标量。以体积为例，
a c
V a b c bx
b

Heinrich Rudolf Hertz (Feb. 22, 1857 – Jan. 1, 1894) was a German physicist who clarified and expanded the electromagnetic theory of light that had been put forth by Maxwell. He was the first to satisfactorily demonstrate the existence of electromagnetic waves by building an apparatus to produce and detect VHF or UHF radio waves.
Course Outline Calendar
《波动理论》教学大纲《波动理论》教学日历
Course Goal
通过本课程教学使学生掌握连续介质中声波，电磁波的基本性质及其运动规律以及量子力学的基本知识。具有分析，处理和解决声波，电磁波以及量子力学基本问题的能力。为今后的学习和工作打下基础。

Spin Torque and its Relation to Spin Filtering

a r X i v :c o n d -m a t /0310392v 1 [c o n d -m a t .m e s -h a l l ] 16 O c t 2003Spin Torque and its Relation to Spin FilteringWonkee Kim and F.MarsiglioDepartment of Physics,University of Alberta,Edmonton,Alberta,Canada,T6G 2J1(Dated:February 2,2008)The spin torque exerted on a magnetic moment is a reaction to spin ﬁltering when spin-polarized electrons interact with a thin ferromagnetic ﬁlm.We show that,for certain conditions,a spin transmission resonance (STR)gives rise to a failure of spin ﬁltering.As a consequence,no spin is transfered to the ferromagnet.The condition for STR depends on the incoming energy of electrons and the thickness of the ﬁlm.For a simple model we ﬁnd that when the STR condition is satisﬁed,the ferromagnetic ﬁlm is transparent to the incoming electrons.PACS numbers:75.70.Ak,72.25.-b,85.75.-dSince the spin torque problem was conceptualized[1,2]and observed experimentally[3,4,5,6],enormous at-tention has been paid to the spin torque of a mag-netic moment,driven by a spin-polarized current,both theoretically[7,8,9,10,11,12]and experimentally[13,14,15,16,17].These discoveries also open a door to new magnetic devices and applications to,for example,mag-netic random access memory[4],spin-wave ampliﬁcation by stimulated emission of radiation[13],and nanoscale microwave sources[17].However,it is still necessary to understand and explore the physics underlying this phe-nomenon.In particular,the signiﬁcance of the thickness of the ferromagnetic ﬁlm has not been fully studied at present.The key interaction associated with the spin torque is an interaction between the incoming spins (s )and the magnetic moment (M ):−2J H s ·M ,where J H is the coupling strength.Thus,the Hamiltonian for this prob-lem has two ingredients;one is the kinetic energy of the incoming electrons and the other the interaction energy with the moment in the ﬁlm.The magnetic moment is assumed to originate from the local spins in the ferro-magnet and its magnitude M 0is a constant.As we illustrate in what follows,the spin torque arises as a reaction to spin ﬁltering.Suppose a spin polar-ized electron beam enters normally to the ferromagnetic ﬁlm.After spin ﬁltering,incoming electrons lose their spin components perpendicular to the magnetic moment.Because of conservation laws,this spin is transferred as a torque exerting on the moment.Interestingly,such a mechanism for ‘spin transfer’implies that no spin torque will take place if the incoming spin is not ﬁltered.In this paper we scrutinize a simple model to understand what conditions are necessary for zero spin transfer and concomitant absence of spin ﬁltering.No spin will be transfered from the incoming spins to the magnetic moment when the condition for a spin transmission resonance (STR)is satisﬁed.STR is a purely quantum mechanical phenomenon and is similar to the well known particle transmission resonance (PTR)[18]for a potential barrier.In our case the spin state of incoming electrons remains unaltered even after interact-ing with the magnetic moment in the ferromagnet and,thus,no spin ﬁltering occurs.Since the spin torque is a reaction to spin ﬁltering,the magnetic moment does not experience a spin torque.For a given energy of incoming electrons,this phenomenon is periodic with a thickness depending only on the interaction energy and fundamen-tal constants like the electron mass.STR is one of the unique characteristics of spin transfer from a current to a moment,and can distinguish this mechanism unambigu-ously from that obtained through an applied magnetic ﬁeld (in this case the ﬁeld would be induced by the ap-plied current).When a spin torque is exerted on the magnetic mo-ment,it will align parallel to the direction of incoming spins after a relaxation time τ0.Thus,a signature of zero spin transfer is that τ0→∞.Using the adiabatic approximation,we derive the equations of motion for the magnetic moment and obtain an analytic form of τ0.The adiabatic approximation is valid if τ0is much longer than a time scale incoming electrons spend on interacting with the magnetic moment.Obviously,this approximation is always applicable near STR.Plots of τ0as a function of the thickness of the ferromagnetic ﬁlm and the energy of incoming electrons illustrate the physics associated with STR.In the derivation of the equations of motion for the magnetic moment,it is necessary to obtain the electron wave function inside the ﬁlm to evaluate the expectation value of the spin operator.For simplicity,we consider a single-domain ferromagnet as in Refs.[1,2,8,9,10,11].Depicted in Fig.1is the quantum mechanical problem we consider to obtain the electron wave function.Region II represents the ferromagnetic ﬁlm with the thickness L while regions I and III are non-ferromagnetic.Since the ﬁlm is parallel to the YZ plane,the Schr¨o dinger equation relevant to our problem is one-dimensional.We suppose incoming electrons with momentum k along the X axis.The direction of the polarized spins is chosen to be Z axis.Then the incoming wave function |ψin is |+ e ikx ,where |+ is the spin-up state in the lab frame.The in-coming energy ǫin =(¯h k )2/2m ,where m is the electron mass.We will utilize a normalization constant C to ob-tain dimensionless equations of motion for the magnetic2ZXIIIIIIFIG.1:Quantum mechanical problem associated with the spin transfer.Region II represents the ferromagnetic ﬁlm with the thickness L .Regions I and III are non-ferromagnetic.moment[12].The direction of the magnetic moment is deﬁned by θand φinside the ferromagnetic ﬁlm.Fora given direction of the magnetic moment,we solve the Schr¨o dinger equation to obtain the electron wave func-tion.In region I,the wave function consists of the incoming |ψin and reﬂected |ψre wave function while in region III,there is only the transmitted |ψtr wave function.The reﬂected and transmitted wave functions are expressed in terms of eigenstates |χσ of the interaction 2J H M ·s such that 2J H M ·s |χσ =±J H M 0|χσ ,where σ=↑or ↓,and +(−)is for σ=↑(↓).We assume that the fer-romagnetic ﬁlm is suﬃciently clean that the mean free path of electrons within the ﬁlm is much longer than the ﬁlm thickness.Therefore the convergence factor intro-duced in Refs.[2,12]is not necessary,and we can inves-tigate the signiﬁcance of the thickness explicitly.Be-cause of the interaction,the momentum is spin split;k σ=√2mJ H M 0−k and the correspondingwave function decays exponentially.In this case,how-ever,STR will not occur,as one might expect based on the usual PTR conditions.Now the wave functions in regions I,II,and III can be written as follows:|ψI =|+ e ikx+ R ↑|χ↑ χ↑|+ +R ↓|χ↓ χ↓|+e −ikx|ψII = A ↑e ik ↑x +B ↑e −ik ↑x |χ↑ χ↑|+ + A ↓e ik ↓x +B ↓e −ik ↓x|χ↓ χ↓|+|ψIII = T ↑|χ↑ χ↑|+ +T ↓|χ↓ χ↓|+e ikx .(1)The coeﬃcients R σ,A σ,B σ,and T σare determined by the boundary conditions of wave functions at x =0and x =L ;namely, ±|ψI (0) = ±|ψII (0) , ±|ψII (L ) = ±|ψIII (L ) ,and similar relations for their derivatives.Some straightforward algebra yieldsR σ=(k 2−k 2σ) 1−e 2ik σL(k +k σ)2−(k −k σ)2e 2ik σLB σ=2k (k σ−k )e 2ik σL (k +k σ)2−(k −k σ)2e 2ik σL.(2)It is worthwhile noting the similarity between our case and the one-dimensional potential barrier problem.At a glance,one can see the above coeﬃcients are exactly the same as those for the potential barrier except for their two-fold nature due to the spin index.In fact,the two-fold nature can be mapped onto a potential well for σ=↑and a potential barrier for σ=↓.Note that PTR takes place in a potential barrier as well as in a potential well.Therefore,conditions for STR are eﬀectively those for PTR for the corresponding barrier and well at the same time.For PTR,zero reﬂectance guarantees a transmission resonance;this is not the case for STR.If k σL =n σπ(n σ=1,2,3,···),then R σ=0.However,STR does not occur yet because T σ=e i (k σ−k )L ;in other words,it is not guaranteed that −|ψIII =0,which means the spin state in region III can not be represented only by |+ .Since the incoming wave function has only |+ ,non-zero −|ψIII indicates that spin is transfered to the magnetic moment.The condition for STR is k σL =(2n σ−1)πor 2n σπwith n ↓<n ↑due to k ↓<k ↑.If the above con-dition is satisﬁed,we obtain +|ψIII =e ik (x −L )and −|ψIII =0.This means that the transmitted wave function remains unaltered even after interacting with the magnetic moment in the ferromagnetic thin ﬁlm ex-cept for an additional phase e −ikL depending only on the thickness.Consequently,spin ﬁltering fails completely3under this condition.Let us examine the condition for STR in more de-tail.Suppose 2n σπand the incoming energy is larger than the interaction energy J H M 0by a factor of η;ǫin =ηJ H M 0,and k ↑=√η−1k 0L ,where k 0=√2[1−(n ↓/n ↑)2]L 0,where L 0=π/k 0.For k σL =(2n σ−1)π,a similar constraint can be obtained by re-placing n σwith n σ−1/2.This analysis tells us that the STR condition can be satisﬁed by controlling ηand L ;for example,if η=5/4and L =2L 0,then STR takes place.Another example is for η=5/3and L =√6L 0,2√6L 0,···.This is inherently a quantum mechanical property and completely diﬀerent from the eﬀects of a current-induced magnetic ﬁeld on the magnetic moment.Using the wave function in region II,|ψII ,we evalu-ate the expectation value of the spin operators to derive equations of motion for the magnetic moment for an ar-bitrary case.If the STR condition is met,we will be able to see its signature in the equations.Since the spin ex-pectation is evaluated by s i =(1/2) ψII |σi |ψII ,where σi (i =x,y,z )are Pauli matrices,we obtains x =αm x −βm y −γm z m x s y =αm y +βm x −γm z m ys z =αm z +γ1−m 2z (3)whereα=12Ldx Im C ∗↓C ↑γ=1dτ=−βm z m x +γm ydm ydτ=β 1−m 2z .(5)Note that the equation for m z does not depend on other components of m .This equation can be solved analyti-cally and we obtainm z (τ)=tanh βτ+11−m 0 (6)where m 0is the initial value of m z at τ=0and |m 0|<1.We found for η≤1,βis positive deﬁnite.However,for η>1,β≥0depending on ηand the thickness L .When STR occurs,it can be shown analytically that β=0.Then one may assume that the magnetic moment will precess with a frequency γbased on Eq.(5);however,one can show that γalso vanishes under the condition for STR.Consequently,the magnetic moment remains a constant in this case.If β>0,we obtain an asymptotic expression for m z (τ):m z (τ)≃1−1−m 06L 0.For comparison,η=1(solid)and η=3/2(dashed curve)are also plotted.The singularities illustrated in Fig.2are strong;for example,τ0≈(L −2L 0)−2for η=5/4.There-fore,it should be measurable as long as the ferromagnetic ﬁlm is reasonably smooth.We also plot τ0as a function ηfor given values of L in Fig.3.For L =2L 0and√4adiabatic approximation,the beam intensity may not betoo large because if so,τ0could be comparable with a typical time incoming electrons spend on interacting withthe magnetic moment.However,the adiabatic approxi-mation is always applicable near STR regardless of thebeam intensity sinceτ0→∞under the STR conditions. For an experimental test one could use the experimental setup in Refs.[20,21]or the ferromagnet-normal-metal-ferromagnet(F1NF2)junction.If the STR condition issatisﬁed in F1,then F1is transparent to the incoming spins.Therefore,the spin torque will appear only in F2. In summary,we investigated the conditions for spin transmission resonance(STR),and their consequences. We found that STR will occur for a variety of widths which are multiples of a fundamental thickness(for given electron energy).This is a quantum mechanical property and indicates the signiﬁcance of the thickness of the fer-romagneticﬁlm.When the STR condition is satisﬁed, the magnetic moment in the ferromagneticﬁlm remains unaltered since no spin transfer occurs.[1]J.C.Slonczewski,J.Magn.Magn.159,L1(1996);195,L261(1999)[2]L.Berger,Phys.Rev.B54,9353(1996).[3]M.Tsoi et al.,Phys.Rev.Lett.80,4281(1998).[4]E.B.Myers,D.C.Ralph,J.A.Katine,R.N.Louie,andR.A.Buhrman,Science285,867(1999).[5]J.A.Katine,F.J.Albert,R.A.Buhrman,E.B.Myers,and D.C.Ralph,Phys.Rev.Lett.84,3149(2000).[6]J.-E.Wegrowe et al.,Europhys.Lett.56,748(2001)[7]Y.Bazaliy,B.A.Jones,and S.-C.Zhang,Phys.Rev.B57,R3213(1998).[8]J.Z.Sun,Phys.Rev.B62,570(2000).[9]X.Waintal,E.B.Myers,P.W.Brouwer,and D.C.Ralph,Phys.Rev.B62,12317(2000).[10]M.D.Stile and A.Zangwill,Phys.Rev.B66,014407(2002).[11]S.Zhang,P.M.Levy,and A.Fert,Phys.Rev.Lett.88,236601(2002).[12]W.Kim and F.Marsiglio,cond-mat/0307633[13]M.Tsoi et al.,Nature406,46(2000).[14]F.J.Albert et al.,Phys.Rev.Lett.89,226802(2002).[15]Y.Ji,et al,Phys.Rev.Lett.90,106601(2003).[16]J.Grollier et al.,Phys.Rev.B67,174402(2003).[17]S.I.Kiselev et al.,Nature425,380(2003).[18]See,for example,L.SchiﬀQuantum Mechanics,page101(McGraw-Hill,New York,1968)[19]A.H.Mitchell,Phys.Rev.105,1439(1957).[20]ssailly et al.,Phys.Rev.B50,13054(1994).[21]D.Oberli et al.,Phys.Rev.Lett.81,4228(1998).5values ofη.When the condition for STR is satisﬁed,τ0→∞becauseβ→0.The singular behavior is periodic.The perioddepends onη.Forη=5/4,it is2L0while forη=5/3it is√6L0,τ0→∞whenη=5/4and5/3,respec-tively.For any other value of L,τ0isﬁnite as shown by thesolid curve(L=L0)and the dashed curve(L=2.2L0).。

EXACT_PERIODIC-WAVE_SOLUTIONS_FOR_(2+1)-DIMENSIONAL_BOUSSINESQ_EQUATION_AND_(3+1)-DIMENSIONAL_KP_EQU

tain de rivatives (this is true for the e quation s c on side red h ere). In th is p roce ss we take the integration con stants to b e ze ro. T he n ext cruc ial step is to exp ress th e solu tions of th e resu ltin g O DE b y the Jac obi e lliptic- fun ction meth od in Ref. [12], u (ξ ) c an be ex pre sse d as a ﬁn ite p ower se rie s of J acob i ellip tic sine fu nc tion , sn ξ , i.e., the an satz u( ξ ) =
d cn ξ = −sn ξ d n ξ , dξ d dξ dn ξ = −m 2 sn ξ cn ξ . (8)
In this artic le, for Jacob i e llip tic fu nc tions, we u se the n otation sn ξ, cn ξ, d n ξ w ith argu me nt ξ an d mo du lu s parame ter m (0 < m < 1). T he param eter n in Eq. (4) will b e ﬁ xe d b y balan cing th e h ighe st ord er of de rivative term an d the n online ar term in th e non lin ear OD E Eq. (3) by u sin g Eq. (5). Su bstituting Eq . (4) (w ith ﬁx ed valu e of n ) in to the re du ce d non linear O DE (3) an d equ ating the c oeﬃ cients of variou s p owers of sn ξ to ze ro we get a se t of algeb raic e quation s for aj , k , l , s , an d ω . S olving th em c onsistently we obtain re lation s am ong the p arWave Solut ions for (2+1)-Dimen sional Bou ssines q Equ at ion an d ( 3+ 1)-D im ens ional K P Equ at ion∗

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a r X i v :q u a n t -p h /9905015v 1 5 M a y 1999Wave Function Interpretation and Quantum Mechanics EquationsAndrey V.Novikov-Borodin ∗Institute for Nuclear Research,Russian Academy of Sciences117312Moscow,60-th October Anniversary prospect,7a.Russia(February 1,2008)The quantum mechanics description of a physical object stretched in space and stable in timefrom the relativistic space-time properties point of view,introduced in special theory of relativity,isconsidered and analysed.The mathematical model of physical objects is proposed.This model givesa possibility to unite a description of corpuscular and wave properties of real physical objects,i.e.ﬁelds and particles.There are substantiated an approach and a mathematical pattern which give apossibility to describe physical object not only in causal,but also in absolute remote ﬁelds of theMinkowski space.Applying the proposed approach to the microcosm description,one can get theequations that in passage to the limit transfer to such quantum mechanics equations as Schr˝o dinger,Klein-Gordon-Fock and in particular case -the wave equation.The event nature of the receivedequations is discussed.It is shown that all mentioned equations reﬂect the space-time relativisticproperties during the description of the invariant and non-invariant physics object characteristics.03.65.Sq,03.65.-w,11.15.Kc∗E-mail address:Novikov@al20.inr.troitsk.ru INTRODUCTION The predictions brilliantly proved in experiments won for the quantum theory the reputation of one of the most successful physical theories.However,up to present,the disputes about its meaning and limits of its implementation are not quiet yet.This is an unique phenomenon in the history of science [1,2].The Nobel Prize laureate in physics M.Gell-Mann characterised the quantum physics as a discipline “full of mysteries and paradoxes,that we do not completely understand but are able to use.As we know,it perfectly operates in the physics reality description,but as sociologists would say,it is anti-intuitive discipline.The quantum physics is not a theory,but limits,in which,as we suppose,any correct theory needs to be included”[3].The logistic analysis of a quantum mechanics as a science leads to the conclusion about its incompleteness and non-completability,in consequence of an inconsistency of the quantum objects,that is ﬁxed in a corpuscular-wave dualism [4].The theory incompleteness is an original “payment”for a tendency to create a non-contradictory description of contradictory objects.One of consequences of the quantum mechanics logistic analysis is a proof of an absence of a positive decision for a hidden parameter method,from point of view that “there are no any possibilities for more complete description in standard quantum mechanics theory limits.Its realization needs a quantum mechanics cre-ation on a principal diﬀerent basis”.The facts of the particles and anti-particles annihilation with the photon and neutrino creation,the birth of particles from diﬀerent classes during the high energy photons interactions are the circumstantial evidence of the uniﬁed originof ﬁelds and particles.Do not discussing about “a forced formalism”,i.e.a science penetration into the ﬁelds with diﬀerent from “everyday”,principal new forms and meanings,it would be desirable to decrease the formal apparatus as possible,by changing it to the system of views.From this point of view,the development of physical object models,which give a possibility to unite the description of corpuscular and wave properties of real objects,i.e.ﬁelds and particles,has a conceptual meaning.Models need to correlate with the existing quantum mechanics approach,so as it has a brilliant experimental conﬁrmation.Moreover,although some quantum mechanics postulates and concepts should be a corollary from the properties of the proposed model and properties of the space,where the object exists.If the relativistic properties are included in the space description,the corresponding expressions describing the object behaviour should have a relativistic nature and in passage to the limit should be transfer to well-known quantum mechanics equations.At any probability,if Minkowski space is examined,the absolute remote ﬁelds have to be included in the physical object description.An eﬀort has been undertaken to solve mentioned problems and “to pave a way”for the complement the existing quantum mechanics theory for the full,correct,non-contradictory theory,dreamed by Louis de Broglie,mentioned by Marry Gell-Mann,looked for by Ilya Prigogine.I.PHYSICAL OBJECTIn special theory of relativity the object evolution is examined in a four-dimension space-time continuity with a pseudo-Euclidean metric.The supposition about the space-time continuity strikes against the conceptual problem, that we will call the scale problem.Let’s consider the four-dimensional space-time as some mathematical set.The Cantor’s power of a neighbourhood of any space point is equal to the power of whole space.The question is:what deﬁnes the observed size of a physics object,for example,elementary particles?The size of the observer could not be a reason.Moving this way we will come to the dilemma about the initial appearance of a hen or an egg.The speed of light as a fundamental constant connects space and time measurements but,apparently,is not good for a role of the scale coeﬃcient.In all probability the problem can be solved by introducing in a description the discreteness. Considering a time as some parameter characterising the changing of processes in space and putting these processes in order during the analyses in a chronological sequence,realising the causality principle,the hypothesis about the space discreteness can be introduced.This way it is not diﬃcult to demand the time continuity as some abstract parameter.However,of course,it is not necessary to refuse completely from the possibility of the time discreteness. Whether or not the discreteness is necessary.Let’s consider the possible variants of putting the events in order in inertial frames of reference.We will leave the question of the space discreteness open.A conventional approach is the following[5].Some frame is introduced in the four-dimensional continuity,which is represent a set of four continuous marks(x,y,z,τ)=( r,τ)over the space and time coordinates.It is established, that the inﬁnite set of the equivalent frames exists,and these frames are connected to each other with the help of four continued diﬀerentiable functions with the non-zero functional ually,this demand is connected to the principle of the equivalence of inertial frames of references.It is considered that some property,unchangeable with these transformations,can correspond to each point.The property,expressed by the number,that“by order”don’t change during the transformations of the frames of references,is called invariant or scalar.It is said about an invariant or scalarﬁeld if this correspondence takes place not only for one concrete point but some number is compared with every point from some deﬁned region,and all these numbers reﬂect the same invariant property.Thus,the scalarﬁeld is deﬁned by the function against coordinatesφ( r,τ),that can be interpreted as some continuous physical object. For the stable in time physical object,due to the invariance of values in its every point,the operation integral can be composed for every point and by the principle of the minimum eﬀect the trajectory of the object motion may be deﬁned.This trajectory will represent the chain of the events putting in order in time.We will consider this approach as the classical one.It often needs to have deal with non-invariant characteristics of physical objects.Let’s pose a set of one or more numbers(g( r,τ),h( r,τ),...)in some inertial frame of references,each of that is not a scalar.If there is a functional on one or more elements of this set,that is a scalar or a scalarﬁeld,the process of putting events in order may be done,although on an indirect way or with some limitations.We will call such sets of numbers functional,also as the correspondingﬁelds.Let’s introduce a point functional,that is important for us.Further we will call it the normalised functional.Let’s combine the function f( r,τ)=g( r,τ)+ih( r,τ),where i is an imaginary unit.The corresponding scalarﬁeld we will deﬁne as follows:φ( r,τ)=|f( r,τ)|2=g( r,τ)2+h( r,τ)2.(1) Note,that the function f( r,τ)deﬁnes the normalised functionalﬁeld.The invariant coordinate transformations in diﬀerent frames of references in special theory of relativity are given by Lorentz transformations:x′=x,y′=y,z′=γ(z−βτ),τ′=γ(τ−βz),(2) whereβ=V/c,γ=1/g′( r′,τ′)is the limited variation function on eachﬁnite interval ofτ′,it can be represented as a sum of the average value<g′>T=g′0( r′),some number of periodical components and non-periodical component g′a[6]:g′( r′,τ′)=g′0( r′)+∞k=1g′k( r′)cos(ω′kτ′+α′k)+g′a( r′,τ′).(3)Considering g′( r′,τ′)as a part of the functionalﬁeld(1),we will deﬁne thisﬁeld as:ψ′( r′,τ′)=∞k=0q′k( r′)exp(iω′kτ′)+q′a( r′,τ′).(4)whereω′0=0,the limit of<ψ′exp(iωτ′)>T with T→∞is equal to q′k( r′)=g′k( r′)exp(iα′k( r′))withω=ω′k, (k=0,1,2,...),and is equal to zero for all other values ofω.The analogous limit for the non-periodical component always is equal to zero for any r′from V′.Functions g′k( r′)andα′k( r′)are real.In frame K the considered function will be deﬁned asψ( r,τ)=ψ′( r′( r,τ),τ′( r,τ)),that,with taking into account (2)and,designatingξ=γ(z−βτ),η=γ(τ−βz)−τ,may be represented as follows:ψ( r,τ)=∞k=0q k(x,y,ξ)exp[iω′k(η+τ)]+q a( r,τ).(5)For everyﬁxed harmonics(5)the scalarﬁeld(1)corresponding to the introduced normalised one will be equal to squared amplitude of the corresponding harmonics.As far as the scalar sum is also a scalar,the result scalarﬁeld corresponding to(5)is deﬁned as:φ( r,τ)=∞k=0|q k(x,y,ξ)|2=∞ k=0g2k( r,τ).(6)The important distinguish of the normalisedﬁeld(5)from the scalar one(6)is an oscillation,resonant nature of theﬁrst one.It is necessary to note that the established correspondence between(5)and(6)has not reciprocally a single meaning,because,for example,the information about the mutual phases of harmonics is loosing.However, in considering only one harmonic of the stable physical object function,this limitation is not important.But the information about frequency will be still loosing.II.QUANTUM MECHANICS BASIC EQUATIONSOmitting the corresponding indexes ofψ,q,ωfor the notation simplicity,we will represent the k-th harmonics of the spectrum expansion(5)as follows:ψ( r,τ)=ψb( r,τ)exp(iωτ),ψb( r,τ)=q(x,y,ξ)exp(iωη).(7) Partial derivatives by r andτfor functionψb will be expressed in the following way:∂ψb∂z =γqξe iωη−iγωβqe iωη,∂ψb∂τ2=γ2β2qξξe iωη−2iγ(γ−1)ωβqξe iωη−ω2(γ−1)2qe iωη,∂2ψbψb∂ψb2ωψb∇2ψb=1q+ωHere∇2≡∂2/∂x2+∂2/∂y2+∂2/∂z2is a Laplace operator.The second term in the right part of the equation speeds to zero fast enough(∼β4)with non-relativistic velocities.If it is possible to separate the variables in some frame of references or at least to separate the time variable in the function q,so∇2q/q=u(x,y,z)and,supposingω=mc/¯h, where m and¯h are some constants(usually m is understood as a rest mass,¯h is a Planck constant),we will get:−i¯h cγ∂ψb2m∇2ψb= ¯h22 ψb.(11)Designating¯h2u(x,y,z)/2m=U(x,y,z),we will get in non-relativistic case in passage to the limit(γ→1)the Schr˝o dinger equation(conjugated to usually used)[7].It is known that U(x,y,z)has a meaning of the potential energy of the particle in the forceﬁeld,andψb( r,τ)is agree with the de Broglie’s description of the particle wave properties.The equation may be interpreted in the following way.The lengthy in space physical object is changing by an external ﬁeld,moving or changing of the object internal structure will depend on thisﬁeld.In distinguish of the Schr˝o dinger equation,the equation(10)and,with some stipulations,(11)have to be true also in the relativistic case.It is necessary to pay attention to the particularity of the described passage to the limit to the potential function of the external forcedﬁeld,because an interaction can be as complete as partial and also with new physical objects creation. Combining the expressions analogous to(9)for functionψ( r,τ),it is possible to cancel imaginary terms in right part of the expressions.The following equation can be got:1∂τ2−∇2ψ =− ∇2q−β2q zz[1]I.Prigogine,I.Stengers.Time,Chaos,Quantum.-Progress,Moscow1994.[2]L.de Broglie.Les Incertitudes d’Heisenberg et l’Interpretation Probabiliste de la Mecanique Ondulatore.-Gauthier-Villars,Bordas,Paris1982.[3]M.Gell-Mann.Questions for the Future./in:The Nature of Matter,Wolfson College Lectures1980.-Wolfson College,Oxford1981.[4]V.S.Meskov.Syntactical Analysis of the theory completeness problem:the quantum mechanics and arithmetic./in:Inves-tigations on non-classical logic,VI Soviet-Finnish Colloquium.-Nauka,Moscow1989.[5]E.Schr˝o dinger.Space-time structure.-Cambridge at the University Press,1950//Expanding Universes.-Cambridge at theUniversity Press,1956.[6]G.Korn,A.Korn.Mathematical Handbook.-McGraw-Hill Book Company,Inc.,NY-Toronto-London,1961.[7]ndau,E.M.Lifschits.Theoretical Physics,v.3:The Quantum Mechanics.-Nauka,Moscow1989.[8]V.S.Vladimirov.Mathematical Physics Equations.-Nauka,Moscow1981.。

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