An Automated Approach for Constructing Road Network Graph from Multispectral Images

"Series expansion" redirects here. For other notions of the term, see series.As the degree of the Taylor polynomial rises, it approaches the correct function. This image shows sin x and Taylor approximations, polynomials of degree 1, 3, 5, 7, 9, 11 and 13.The exponential function (in blue), and the sum of the first n+1 terms of its Taylor series at 0 (in red).In mathematics, the Taylor series is a representation of a function as an infinite sum of terms calculated from the values of its derivativesat a single point. It may be regarded as the limit of the Taylor polynomials. Taylor series are named after English mathematician Brook Taylor. If the series is centered at zero, the series is also called a Maclaurin series, named after Scottish mathematician Colin Maclaurin.DefinitionThe Taylor series of a real or complex function f(x) that is infinitely differentiable in a neighborhood of a real or complex number a, is the power serieswhich in a more compact form can be written aswhere n! is the factorial of n and f (n)(a) denotes the n th derivative of f evaluated at the point a; the zeroth derivative of f is defined to be f itself and (x−a)0 and 0! are both defined to be 1.Often f(x) is equal to its Taylor series evaluated at x for all x sufficiently close to a. This is the main reason why Taylor series are important.In the particular case where a= 0, the series is also called a Maclaurin series.[edit] ExamplesThe Maclaurin series for any polynomial is the polynomial itself. The Maclaurin series for (1 −x)−1 is the geometric seriesso the Taylor series for x−1 at a = 1 isBy integrating the above Maclaurin series we find the Maclaurin series for −log(1 −x), where log denotes the natural logarithm:and the corresponding Taylor series for log(x) at a = 1 isThe Taylor series for the exponential function e x at a = 0 isThe above expansion holds because the derivative of e x is also e x and e0 equals 1. This leaves the terms (x− 0)n in the numerator and n! in the denominator for each term in the infinite sum.[edit] ConvergenceThe sine function (blue) is closely approximated by its Taylor polynomial of degree 7 (pink) for a full period centered at the origin.The Taylor polynomials for log(1+x) only provide accurate approximations in the range −1 < x≤ 1. Note that, for x > 1, the Taylor polynomials of higher degree are worse approximations.Taylor series need not in general be convergent, but often they are. The limit of a convergent Taylor series of a function f need not in generalbe equal to the function value f(x), but often it is. If f(x) is equal to its Taylor series in a neighborhood of a, it is said to be analytic in this neighborhood. If f(x) is equal to its Taylor series everywhere it is called entire. The exponential function e x and the trigonometric functions sine and cosine are examples of entire functions. Examples of functions that are not entire include the logarithm, the trigonometric function tangent, and its inverse arctan. For these functions the Taylor series do not converge if x is far from a.Taylor series can be used to calculate the value of an entire function in every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for entire functions include:1.The partial sums (the Taylor polynomials) of the series can be usedas approximations of the entire function. These approximations are good if sufficiently many terms are included.2.The series representation simplifies many mathematical proofs.Pictured on the right is an accurate approximation of sin(x) around the point a = 0. The pink curve is a polynomial of degree seven:The error in this approximation is no more than |x|9/9!. In particular, for |x| < 1, the error is less than 0.000003.In contrast, also shown is a picture of the natural logarithm function log(1 + x) and some of its Taylor polynomials around a = 0. These approximations converge to the function only in the region −1 < x≤ 1; outside of this region the higher-degree Taylor polynomials are worse approximations for the function. This is similar to Runge's phenomenon.Taylor's theorem gives a variety of general bounds on the size of the error in R n(x) incurred in approximating a function by its n th-degree Taylor polynomial.[edit] HistoryThe Greek philosopher Zeno considered the problem of summing an infinite series to achieve a finite result, but rejected it as an impossibility: the result was Zeno's paradox. Later, Aristotle proposed a philosophicalresolution of the paradox, but the mathematical content was apparently unresolved until taken up by Democritus and then Archimedes. It was through Archimedes's method of exhaustion that an infinite number of progressive subdivisions could be performed to achieve a finite result.[1] Liu Hui independently employed a similar method a few centuries later.[2]In the 14th century, the earliest examples of the use of Taylor series and closely-related methods were given by Madhava of Sangamagrama.[3] Though no record of his work survives, writings of later Indian mathematicians suggest that he found a number of special cases of the Taylor series, including those for the trigonometric functions of sine, cosine, tangent, and arctangent. The Kerala school of astronomy and mathematics further expanded his works with various series expansions and rational approximations until the 16th century.In the 17th century, James Gregory also worked in this area and published several Maclaurin series. It was not until 1715 however that a general method for constructing these series for all functions for which they exist was finally provided by Brook Taylor[4], after whom the series are now named.The Maclaurin series was named after Colin Maclaurin, a professor in Edinburgh, who published the special case of the Taylor result in the 18th century.[edit] PropertiesThe function e−1/x²is not analytic at x= 0: the Taylor series is identically 0, although the function is not.If this series converges for every x in the interval (a−r, a + r) and the sum is equal to f(x), then the function f(x) is said to be analytic in the interval(a−r, a+ r). If this is true for any r then the function is said to be an entire function. To check whether the series converges towards f(x), one normally uses estimates for the remainder term of Taylor's theorem. A function is analytic if and only if it can be represented as a power series; the coefficients in that power series are then necessarily the ones given in the above Taylor series formula.The importance of such a power series representation is at least fourfold. First, differentiation and integration of power series can be performed term by term and is hence particularly easy. Second, an analytic function can be uniquely extended to a holomorphic function defined on an open disk in the complex plane, which makes the whole machinery of complex analysis available. Third, the (truncated) series can be used to compute function values approximately (often by recasting the polynomial into the Chebyshev form and evaluating it with the Clenshaw algorithm).Fourth, algebraic operations can often be done much more readily on the power series representation; for instance the simplest proof of Euler's formula uses the Taylor series expansions for sine, cosine, and exponential functions. This result is of fundamental importance in such fields as harmonic analysis.Another reason why the Taylor series is the natural power series for studying a function f is given by the probabilistic interpretation of Taylor series. Given the value of f and its derivatives at a point a, the Taylor series is in some sense the most likely function that fits the given data.Note that there are examples of infinitely differentiable functions f(x) whose Taylor series converge, but are not equal to f(x). For instance, the function defined pointwise by f(x) = e−1/x² if x≠ 0 and f(0) = 0 is an example of a non-analytic smooth function. All its derivatives at x = 0 are zero, so the Taylor series of f(x) at 0 is zero everywhere, even though the function is nonzero for every x≠ 0. This particular pathology does not afflict Taylor series in complex analysis. There, the area of convergence of a Taylor series is always a disk in the complex plane (possibly with radius 0), and where the Taylor series converges, it converges to the function value. Notice that e−1/z²does not approach 0 as z approaches 0 along the imaginary axis, hence this function is not continuous as a function on the complex plane.Since every sequence of real or complex numbers can appear as coefficients in the Taylor series of an infinitely differentiable function defined onthe real line, the radius of convergence of a Taylor series can be zero.[5] There are even infinitely differentiable functions defined on the real line whose Taylor series have a radius of convergence 0 everywhere.[6]Some functions cannot be written as Taylor series because they have a singularity; in these cases, one can often still achieve a series expansion if one allows also negative powers of the variable x; see Laurent series. For example, f(x) = e−1/x² can be written as a Laurent series.[edit] List of Taylor series of some common functionsSee also List of mathematical seriesThe cosine function in the complex plane.An 8th degree approximation of the cosine function in the complex plane.The two above curves put together.Several important Maclaurin series expansions follow.[7] All these expansions are valid for complex arguments .Exponential function:Natural logarithm:Finite geometric series:Infinite geometric series:Variants of the infinite geometric series:Square root:Binomial series (includes the square root for α = 1/2 and the infinite geometric series for α = −1):with generalized binomial coefficientsTrigonometric functions:where the B s are Bernoulli numbers.Hyperbolic functions:Lambert's W function:The numbers B k appearing in the summation expansions of tan(x) and tanh(x) are the Bernoulli numbers. The E k in the expansion of sec(x) are Euler numbers.[edit] Calculation of Taylor seriesSeveral methods exist for the calculation of Taylor series of a large number of functions. One can attempt to use the Taylor series as-is and generalize the form of the coefficients, or one can use manipulations such as substitution, multiplication or division, addition or subtraction of standard Taylor series to construct the Taylor series of a function, by virtue of Taylor series being power series. In some cases, one can also derive the Taylor series by repeatedly applying integration by parts. Particularly convenient is the use of computer algebra systems to calculate Taylor series.[edit] First exampleCompute the 7th degree Maclaurin polynomial for the function.First, rewrite the function as.We have for the natural logarithm (by using the big O notation)and for the cosine functionThe latter series expansion has a zero constant term, which enables us to substitute the second series into the first one and to easily omit terms of higher order than the 7th degree by using the big O notation:Since the cosine is an even function, the coefficients for all the odd powers x, x3, x5, x7, . . . have to be zero.[edit] Second exampleSuppose we want the Taylor series at 0 of the function.We have for the exponential functionand, as in the first example,Assume the power series isThen multiplication with the denominator and substitution of the series of the cosine yieldsCollecting the terms up to fourth order yieldsComparing coefficients with the above series of the exponential function yields the desired Taylor series[edit] Taylor series as definitionsClassically, algebraic functions are defined by an algebraic equation, and transcendental functions (including those discussed above) are defined by some property that holds for them, such as a differential equation. For example the exponential function is the function which is everywhere equal to its own derivative, and assumes the value 1 at the origin. However, one may equally well define an analytic function by its Taylor series.Taylor series are used to define functions in diverse areas of mathematics. In particular, this is true in areas where the classical definitions of functions break down. For example, using Taylor series, one may defineanalytical functions of matrices and operators, such as the matrix exponential or matrix logarithm.In other areas, such as formal analysis, it is more convenient to work directly with the power series themselves. Thus one may define a solution of a differential equation as a power series which, one hopes to prove, is the Taylor series of the desired solution.[edit] Taylor series in several variablesThe Taylor series may also be generalized to functions of more than one variable withFor example, for a function that depends on two variables, x and y, the Taylor series to second order about the point (a, b) is:where the subscripts denote the respective partial derivatives.A second-order Taylor series expansion of a scalar-valued function of more than one variable can be compactly written aswhere is the gradient and is the Hessian matrix. Applyingthe multi-index notation the Taylor series for several variables becomesin full analogy to the single variable case.[edit] See also∙Taylor's theorem∙Linear approximation∙Power series∙Laurent series∙Holomorphic functions are analytic— a proof that a holomorphic function can be expressed as a Taylor power series ∙Newton's divided difference interpolation∙Difference engine∙Mean value theorem[edit] Notes1.^ Kline, M. (1990) Mathematical Thought from Ancient to Modern Times.Oxford University Press. pp. 35-37.2.^Boyer, C. and Merzbach, U. (1991) A History of Mathematics. John Wileyand Sons. pp. 202-203.3.^"Neither Newton nor Leibniz - The Pre-History of Calculus and CelestialMechanics in Medieval Kerala". MAT 314. Canisius College. Retrieved on 2006-07-09.4.^ Taylor, Brook, Methodus Incrementorum Directa et Inversa [Direct andReverse Methods of Incrementation] (London, 1715), pages 21-23(Proposition VII, Theorem 3, Corollary 2). Translated into English inD. J. Struik, A Source Book in Mathematics 1200-1800 (Cambridge,Massachusetts: Harvard University Press, 1969), pages 329-332.5.^ Exercise 12 on page 418 in Walter Rudin, Real and Complex Analysis.McGraw-Hill, New Dehli 1980, ISBN 0-07-099557-56.^ Exercise 13, same book7.^ Most of these can be found in (Abramowitz & Stegun 1970).。

移民火星计划作文作文英语In the not-so-distant future, humanity stands on the brink of a monumental leap; the colonization of Mars. This essay will delve into the intricacies of the Mars Immigration Project, exploring its scientific, technological, and social implications.The Scientific Frontier:Mars has long captivated the imaginations of scientists and the public alike. The red planet's similarities to Earth, such as its day length and the presence of water, make it an ideal candidate for colonization. The Mars Immigration Project aims to establish a sustainable human presence on the planet, which would require a deep understanding of Martian geology, climate, and potential resources.Technological Marvels:The project hinges on cutting-edge technologies that are yet to be fully realized. Spacecraft capable of transporting humans and the necessary equipment to Mars must be developed. These crafts must be efficient, reliable, and capable of sustaining life during the long journey. Upon arrival, advanced robotics and automated systems will be essential for constructing habitats and infrastructure.Sustainable Living:The establishment of a self-sufficient colony is paramount. Scientists are researching ways to utilize Martian soil andresources for agriculture and construction. Energy production will likely rely on solar and nuclear power, given Mars' distance from the Sun and the potential for nuclear reactors.The Human Element:The psychological and physiological effects of long-termspace travel and living in a Martian environment cannot be understated. Astronauts will need to be carefully selectedand trained to cope with the isolation, confinement, and the unique challenges of life on Mars. Medical facilities and research into Martian health will be crucial.International Collaboration:The Mars Immigration Project transcends national boundaries.It is a venture that requires the collaboration of nations, pooling resources, knowledge, and expertise. This endeavor could serve as a model for global cooperation in tackling humanity's most pressing challenges.Ethical Considerations:As we venture into this new frontier, ethical questions arise. How will we respect and preserve the Martian environment?What are the implications for the rights and responsibilities of those who choose to leave Earth behind? These arequestions that must be addressed as we move forward.The Future Awaits:The Mars Immigration Project is not just about survival; it's about growth and exploration. It represents the next chapterin human evolution, where we become a multi-planetary species. The journey to Mars is fraught with challenges, but it alsoholds the promise of incredible discoveries and a legacy that will inspire generations to come.In conclusion, the Mars Immigration Project is a beacon of human ambition, a testament to our innate desire to explore and to push the boundaries of what is possible. As we look to the stars, we also look to our future, and the potential for a new home beyond our own planet.。

Case Study: Unearthing Success Stories and Learning Valuable Lessons In the realm of business, education, and various other fields, case studies serve as powerful tools for understanding realworld scenarios and extracting meaningful insights. A case study delves into the details of aparticular situation, allowing us to analyze the context, identify challenges, and uncover the strategies that led to success or failure. Let's explore some key aspects of case studies and how they can benefit us.Embracing the Depth of Human ExperienceThe Art of ProblemSolvingLessons in AdaptabilityChange is the only constant, and case studies are a testament to this adage. They showcase how individuals and groups adapt to shifting circumstances, often demonstrating remarkable flexibility and resourcefulness. By examining these instances of adaptation, we can learn how to be more agile in our own lives and careers, ready to pivot when the winds of change blow.The Power of ReflectionCase studies also serve as a mirror, reflecting our own values, biases, and assumptions. They invite us to question our preconceived notions and consider alternative perspectives. This reflective practice is crucial for personal growth and for developing a more empathetic understanding of the world around us.Inspiring ActionFinally, case studies are a call to action. They inspire us to apply the lessons learned to our own contexts, to experiment with new approaches, and to strive for excellence. They remind us that every challenge presents an opportunity for growth, and that success is often the result of a willingness to learn from the experiences of others.Unlocking the Potential for Future InnovationAs we delve deeper into the world of case studies, we uncover a treasure trove of knowledge that can spark future innovation. These detailed accounts of past endeavors are not merely historical records; they are blueprints for constructing new ideas and strategies. Here's how case studies continue to shape our approach to innovation: Identifying Patterns for Predictive InsightsFostering a Culture of Continuous LearningThe study of case histories fosters a culture of continuous learning within organizations and educationalinstitutions. It encourages individuals to seek out new information, to question the status quo, and to remain curious about the world around them. This culture of learning is a fertile ground for innovation, as it keeps minds open to new possibilities and solutions.Facilitating CrossDisciplinary CollaborationEnhancing Critical Thinking SkillsGuiding Ethical DecisionMakingEthics play a pivotal role in innovation, and case studies often explore the ethical dimensions of decisions. They provide a framework for understanding the consequences of our actions on various stakeholders and society at large. By examining the ethical implications within case studies, we are better equipped to innovate responsibly and sustainably.In essence, case studies are not just a retrospective look at what has been; they are a forwardlooking tool that can guide us toward a future rich with innovation. They are a reminder that the past is a stepping stone to the future, and that learning from history, we can create a more dynamic and prosperous tomorrow.。

The Growth Challenge增长的挑战Executives and managers within almost every business today, both within the Private and Public sectors complain about the difficulties in achieving one or more of the following objectives:执行官和经理们整天忙于公务，在自己或公共的部门中抱怨达成以下或者更多目标的困难性1.How to develop a market focused growth strategy that has a high probability to benecessary and sufficient for achieving and sustaining the required growth rate financial targets set by their shareholders.1. 怎样发展一个关注市场的增长战略，这样的战略可以确保公司达到以及位置股东所设定的财务增长目标。

2. How to Achieve and maintain total synchronization between departmental goals, measurements and projects with the overall business strategy in a way that will align priorities and focus and prevent ¡°local optimization¡± and ¡°silo thinking¡±2. 怎样可以达到以及维持部门目标，绩效，项目与总体商业策略的同步性，从而可以调整优先级及关注程度，以及避免局部最优化。

请求外教帮助指导英语的作文范文全文共3篇示例，供读者参考篇1Dear English Tutor,I am writing to you today to request your assistance in improving my English writing skills. As an international student, mastering written English has been one of my greatest challenges. While I have made significant progress in my spoken English through daily practice and immersion, composingwell-structured and coherent essays remains a formidable task for me.My primary struggle lies in effectively organizing my thoughts and ideas into a logical and cohesive piece of writing. Often, I find myself grappling with the proper flow and structure of an essay, leading to disjointed and potentially confusing passages. Additionally, I sometimes struggle to convey my intended meaning accurately, which can undermine the overall clarity and impact of my writing.Another area where I seek your guidance is in refining my vocabulary and sentence construction. While I have a decentgrasp of English grammar, I frequently find myself relying on overly simplistic vocabulary or repetitive sentence structures, which can make my writing feel dull and monotonous. I aspire to achieve a more sophisticated and engaging writing style, one that captivates the reader and effectively communicates my ideas.Furthermore, I would greatly appreciate your input on developing a stronger argumentative voice in my essays. Often, I find myself presenting information in a neutral or passive manner, rather than asserting a clear stance or position. I recognize the importance of crafting persuasive arguments and supporting them with well-reasoned evidence, but I struggle to strike the right balance between objectivity and advocacy.Beyond these specific areas of concern, I am eager to learn from your expertise and experience in teaching English writing. Your guidance on techniques for brainstorming, outlining, drafting, and revising essays would be invaluable. I am particularly interested in strategies for conducting thorough research, integrating sources effectively, and ensuring that my writing adheres to academic conventions and standards.I understand that improving my English writing skills will require consistent effort and dedication on my part. However,with your support and guidance, I am confident that I can overcome these challenges and develop into a more proficient and confident writer. Your insights and feedback will be instrumental in helping me refine my writing abilities and better prepare me for academic and professional pursuits in an English-speaking environment.I am deeply grateful for your time and consideration. I look forward to the opportunity to work with you and benefit from your expertise. Please let me know if you require any additional information or if there is a specific time that would be convenient for us to discuss my writing goals and develop a plan for improvement.Thank you for your assistance.Sincerely,[Your Name]篇2Dear Mr. Jenkins,First of all, I want to express my sincere gratitude for your dedication to teaching us English. Your engaging lessons and patient guidance have been invaluable in helping me improvemy English skills. However, as I approach the upcoming English composition assignment, I find myself in need of your expert assistance.Writing a well-structured and coherent essay in English has always been a challenge for me. Despite my best efforts, I often struggle to articulate my thoughts clearly and effectively. The thought of composing a compelling piece that adheres to the conventions of English writing fills me with trepidation.One of my primary concerns is organizing my ideas in a logical and cohesive manner. While I may have a wealth of thoughts and insights to share, I sometimes find it difficult to present them in a structured and easy-to-follow format. I tend to jump from one point to another without proper transitions, which can make my writing appear disjointed and confusing.Additionally, I often encounter difficulties in using appropriate vocabulary and idiomatic expressions. Although I have a decent grasp of English grammar, I struggle to convey my intended meaning with the precise words and phrases that would make my writing more engaging and impactful. I find myself defaulting to simpler, more literal expressions, which can make my writing sound dull and lacking in nuance.Another area where I could use your guidance is in developing a strong thesis statement and supporting arguments. Crafting a clear and compelling thesis that encapsulates the central idea of my essay is a skill I have yet to master. Furthermore, I frequently struggle to provide convincing evidence and examples to back up my claims, weakening the overall persuasiveness of my writing.Beyond these specific concerns, I also worry about adhering to the conventions of English academic writing. Proper formatting, citation styles, and adherence to stylistic guidelines are aspects that often elude me, potentially compromising the professionalism and credibility of my work.I understand that improving one's writing skills is a gradual process that requires consistent practice and feedback. That is why I am reaching out to you, Mr. Jenkins, for your invaluable guidance and support. Your expertise and experience in teaching English composition would be an immense asset in helping me overcome these challenges.I would be incredibly grateful if you could spare some time to review my drafts and provide constructive feedback. Your insights into areas where I need improvement, as well as suggestions for how to strengthen my writing, would beinvaluable. Additionally, if you could provide me with resources or exercises specifically tailored to address my weaknesses, it would greatly aid my learning process.Furthermore, if you have the availability, I would deeply appreciate the opportunity to schedule one-on-one sessions with you. During these sessions, we could discuss my work in greater depth, allowing you to provide personalized guidance and address any specific questions or concerns I may have.I am fully committed to improving my English writing skills and am willing to put in the necessary effort and dedication. With your expert guidance and my unwavering determination, I am confident that I can overcome these challenges and produce a composition that not only meets the assignment requirements but also showcases my growth as a writer.Thank you, Mr. Jenkins, for considering my request. I eagerly await your response and look forward to the opportunity to work closely with you on this important endeavor.Sincerely,[Your Name]篇3Dear English Teacher,I am writing to you today to seek your valuable guidance and expertise in improving my English writing skills. As an international student, mastering the art of written expression in English is crucial for my academic and professional success. However, I find myself encountering several challenges that hinder my progress in this area.Firstly, I struggle with organizing my thoughts and ideas in a coherent and logical manner. Often, my writing feels disjointed, and my arguments lack flow and clarity. I find it challenging to structure my essays effectively, transitioning smoothly between paragraphs and maintaining a consistent train of thought throughout the piece. Guidance on proper essay structure and techniques for coherent writing would be invaluable.Secondly, I experience difficulties in expressing myself with precision and clarity. Despite having a decent grasp of vocabulary, I sometimes struggle to convey my intended meaning accurately. I tend to use imprecise language or convoluted sentences, which can obscure the central message I aim to convey. Improving my ability to articulate my thoughts concisely and precisely would greatly enhance the quality of my writing.Furthermore, I often find myself grappling with issues related to grammar, punctuation, and style. While I have studied the rules of English grammar extensively, applying them consistently in my writing remains a challenge. Unfamiliar with the nuances of academic writing conventions, I frequently make errors in punctuation and stylistic choices, which can detract from the overall quality of my work. Guidance in these areas would be immensely beneficial.Additionally, I struggle with developing and supporting my arguments effectively. While I may have interesting ideas or perspectives to share, I often find it challenging to provide solid evidence, examples, or logical reasoning to substantiate my claims. This weakness can undermine the persuasiveness and credibility of my writing. Instruction on techniques for constructing well-supported and convincing arguments would be invaluable.Moreover, I face difficulties in adopting an appropriate tone and voice for different writing contexts. Whether it's an academic essay, a formal report, or a creative piece, I sometimes struggle to strike the right balance and adapt my writing style to suit the specific purpose and audience. Guidance on how to modulate my tone and voice effectively would be greatly appreciated.Lastly, I often find the revision and editing process to be daunting. While I recognize the importance of proofreading and refining my work, I sometimes struggle to identify and address weaknesses in my writing。

英国小说英文作文模板Title: Crafting a Template for Writing English Essays on British Novels。

Introduction:In the realm of English literature, British novels stand as towering pillars of storytelling prowess, often exploring intricate themes, complex characters, and societal issues. Crafting an essay on such novels requires a structured approach that delves into the narrative, characters, themes, and the socio-historical context. This essay will provide a template for constructing insightful English essays on British novels.1. Introduction:Begin with a captivating opening sentence or quote related to the novel under discussion.Provide essential background information about the author and the novel.Introduce the central themes or issues explored in the novel.2. Plot Summary:Offer a concise summary of the plot, outlining the major events and developments.Avoid excessive detail but ensure key plot points are covered.Use present tense when narrating the plot events to create immediacy.3. Character Analysis:Analyze the main characters in depth, discussing their personalities, motivations, and development throughout the novel.Provide textual evidence to support character analysis.Explore the relationships between characters and their significance in the narrative.4. Themes and Symbols:Identify and discuss the prominent themes explored in the novel, such as love, power, identity, or social class.Examine how these themes are developed and conveyed through the storyline and character interactions.Analyze symbolic elements in the novel and their deeper meanings.5. Socio-Historical Context:Situate the novel within its socio-historicalcontext, discussing relevant events, ideologies, orcultural movements of the time.Explore how the author's background and historical circumstances influenced the creation of the novel.Consider the novel's relevance and resonance with contemporary issues or concerns.6. Literary Techniques:Analyze the author's use of literary techniques such as symbolism, imagery, foreshadowing, or narrative structure.Discuss how these techniques contribute to the overall effectiveness of the novel and enhance its themes and meanings.Provide specific examples from the text toillustrate the application of these techniques.7. Critical Evaluation:Offer a balanced critique of the novel, highlighting its strengths and weaknesses.Engage with different interpretations and critical perspectives on the novel.Formulate your own opinion on the novel's significance and enduring impact.8. Conclusion:Summarize the key points discussed in the essay, emphasizing the novel's significance within the broader context of English literature.Offer some final thoughts on the enduring relevance or cultural significance of the novel.End with a thought-provoking closing statement that leaves a lasting impression on the reader.Conclusion:Constructing an effective English essay on a British novel requires a systematic approach that encompasses plot analysis, character study, thematic exploration, socio-historical context, literary analysis, and critical evaluation. By following this template, students can develop insightful essays that demonstrate a deep understanding of the novel and its place within theliterary canon.。

An Implementation of FP-Growth Algorithm Based on High Level DataStructures of Weka-JUNG Framework1Shui Wang*Corresponding author,2Le Wang1Software School, Nanyang Institute of Technology, seawan@2School of Innovation Experiment, Dalian University of Technology, wangleboro@doi:10.4156/jcit.vol5. issue9.30AbstractFP-Growth is a classical data mining algorithm; most of its current implementations are based on programming language's primitive data types for their data structures; this leads to poor readability & reusability of the codes. Weka is an open source platform for data mining, but lacks of the ability in dealing with tree-structured data; JUNG is a network/graph computation framework. Starting from the analysis on Weka's foundation classes, builds a concise implementation for FP-Growth algorithm based on high level object-oriented data objects of the Weka-JUNG framework; comparison experiments against Weka's built-in Apriori implementation are carried out and its correctness is verified. This implementation has been published as an open source Google Code project.Keywords: FP-Growth Algorithm, Frequent Itemset Mining, Weka, JUNG1. IntroductionFP-growth (frequent pattern growth) [1] uses an extended prefix-tree (FP-tree) structure to store the database in a compressed form. It adopts a divide-and-conquer approach to decompose both the mining tasks and the databases. It uses a pattern fragment growth method to avoid the costly process of candidate generation and testing used by Apriori.Weka [2] is an open source data mining framework, integrates multiple algorithms for classification, clustering, association rule, etc, and supports abundant data I/O and visualization functionalities. But it lacks the ability to support tree-structured data type directly, and up to version 3.6 it has not implemented FP-Growth algorithm [5]. In its data mining monograph [3], information about Weka's internal data structure or data processing work flow is still insufficient; this makes it difficult to build customized algorithm based on this platform.JUNG [6][9] is a universal graph/network framework; its functionality includes construction, computation and visualization of graphs, trees and forests.FP-growth implementations based on primitive data types of programming languages lack reusable high-level data structures such as tree, itemset etc., and therefore are hard to read or migrate, or to modify for customized algorithms.This paper analyzes the basic data structure and fundamental classes of both the Weka and JUNG frameworks, gives a concise implementation for FP-Growth algorithm based on high level object-oriented data objects of the two frameworks, and compares its result against Weka's build-in Apriori implementation to verify its correctness, provides a "cloneable" template for data mining programmers to build their own algorithms on this integrated platform.2. Related workAlthough there're lots of papers discussing various derivatives or improvements of the FP-Growth algorithm, only a few of them talked about the implementation details beyond the skeleton description of the algorithm itself. Some student implementations can be found such as in [11], but usually they are poor documented and not general applicable, and/or without thorough testing. This situation makes it difficult for learners to study/research existing coding methods - they have to begin from scratch even if they just want to make a small modification to the original algorithm.Xinyu Wang et al [12] tested 3 different approaches for constructing the tree node: the vector approach, the linked list approach and the binary tree approach. They found that (upon their testingdatasets), contrary to common beliefs, the vector approach had the best performance. However, a vector is not a "natural" way to manifest a tree, and nor the "binary tree" approach.C. Borgelt [13] gave a C implementation of the FP-Growth algorithm, with his own specialized memory allocation management module. The initial FP-tree is built as a simple list of integer arrays. This list is sorted lexicographically and can be turned into an FP-tree with a recursive procedure. The proposed 2 projecting approaches do not need parent-too-child pointers, so the structure of tree node can be more compact. Despite this implementation's technical merits, its C coding style and complex data structures make it difficult to be used as educational purpose or fast application prototype building.Zi-guang Sun [14] discussed an implementation approach using STL (Standard Template Library) in C++ programming language. He argued that STL's "set" data type was implemented with a black-red tree with O(logN) searching time complexity, and could help boost the performance when constructing the header table & FP-trees despite its relatively higher memory cost. Although high-level data types were used in this implementation, these types were not intuitive.The purpose of this paper is to provide an intuitive, concise source code implementation for the FP-Growth algorithm, using high-level data types (with affordable performance loss of course), to make it easy to be adopted for education or application prototype building.3. High-level data types and functions in Weka & JUNG framework3.1. Weka's layered data structureTo deal with data transactions in a unified way, Weka provides several data types to serve this purpose; these data objects can be analogized to database terms such as transaction, table, record and field; they can be categorized into several layers as follows [4]:(1) DataSource: the source where we obtain the data; usually a data file;(2) Instances: the collection of data transactions, or database;(3) Instance: a single transaction, or record;(4) Item: a unique value for a field; this is an abstract class, its subclass such as NominalItem or NumericalItem should be used in practice for nominal items or numerical items respectively.Association rule mining uses NominalItem as its data structure; the built-in "equals()" function is used to determine where two items belong to the same field (i.e. getAttribute()returns the same value) and their values (or precisely, the index of their values) are also the same. Note that the frequency (or "support") of the two items are not compared. Item's innate "compareTo()" function compares their frequencies and attribute name with descending order, that is, the natural order of Items is the descending order on their frequencies.In Weka, an Item's "value" is represented by an "index" of the value domain; the real meaning of this index can only be obtained by referencing the underlying Attribute object. Class "Attribute" contains attribute information of a data field, including its name and value domain;e.g., suppose the attribute's value domain is {"Li", "Wang", "Zhang"}, a nominal item with a value index of 0 corresponds to "Li", and a value index of 1 corresponds to "Wang".Besides the above mentioned 4 layers of data objects, an "ItemSet" object represents the collection of one or more data items; its inner structure is an array of integers, each of which represents the value index of one item; the size of this array is the length of this itemset.Apriori-like algorithms use horizontal representation for transactions, in which the basic data element is "Instance" (aka transaction or record); FP-Growth algorithm uses vertical presentation of data, i.e., it uses data "Items" to construct the FP-trees; its implementation requires the ability of tree computation.3.2. Tree computation in JUNGJUNG has powerful support for network/graph computation & visualization functionalities [6]; Tree and Forest are special cases of Graph, and JUNG provides dedicated APIs for them. A straight-forward implementation of Tree interface is "DelegateTree", which is in fact a subclass derived from DirectedGraph. Core methods of this class include:addVertex(V vertex): add a vertex as the root node.●addChild(E edge, V parent, V child): add a child node under vertex "parent"; the "edge"object must be specified.●getPath(V vertex): get all the vertices from root to node "vertex".The idea of this paper is this: use Weka's NominalItem data object as JUNG Tree's node element, to code a concise implement for the FP-Growth algorithm.4. Constructing the header tableA "Header Table" in FP-Growth algorithm is a map from an item to its total support; the map is sorted in descending order of support. In the construction of a header table, operations such as searching, inserting, modifying and deleting of a certain item in the map is required; and to ensure the efficiency of these operations, a data structure that supports fast retrieval of data item (such as hashtable or tree) is required.Also, because the map should be sorted in descending order of support, mechanism that supports automatic sorting should be enforced on this map. We choose Apache's TreeBidiMap [7] to do this trick. TreeBidiMap establishes a bi-directional map between the key and the value elements. Bi-direction means that the key and the value are exchangeable: you can seek the value corresponding to a specified key, and you can also seek a key corresponding to a specified value: both operations should be performed efficiently.These features of the TreeBidiMap class requires that both key and value should be comparable (i.e., implement the Comparable interface and overload the compareTo() method) and there should be a 1-to-1 relationship between all keys and values. Because the support of different items might be the same, so we define a customized HeaderCount class with an attribute of random value to impose the 1-to-1 relationship between items and supports.Figure 1 is the class used in header table representing an item's support; the "link" attribute is the link table required by FP-Growth algorithm. So we can define the header table as: TreeBidiMap<HeaderCount, NominalItem>Note that here we use the HeaderCount object as the "key" of the map merely for the convenience of coding; for a bi-directional map, key and value are exchangeable.TreeBidiMap is one of the collection classes in “Apache Commons”project [8]; it is a bi-direction tree structure implemented using the red-black tree approach, and comparison operation is performed during its construction, so all the nodes should implement Comparable interface. Detailed structure of the NominalItem class is discussed in the next section.Data type 1: header table:class HeaderCount implements Comparable<HeaderCount> {int count = 1;//total supportdouble random = Math.random();Vector<NominalItem> link = new Vector<NominalItem>();public int compareTo(HeaderCount arg0) {if (arg0 == this) return 0;long r = count - arg0.count;if (r < 0) return 1;else if (r > 0) return -1;else {//impose "unequal" for different objectsreturn (random <= arg0.random) ? 1 : -1;}}}Figure 1. Class HeaderCount for the header table5. Constructing FP-treesThere are two types of data stored in an FP-tree: items and supports. Items that come from different transactions but belong to the same field and with the same value may share one node(if they have common prefix) or reside on different nodes; but JUNG framework do not allow different nodes to be "equal", so the "item" object in a FP-Growth implementation must satisfy the following two conditions:(1) It must be able to distinguish between items that has the same attribute and value but from different transactions.(2) It must also be able to identify the above mentioned items to be a special kind of "equal".Because the NominalItem class only overloads Item's equals() method in which its attribute is compared, it can not distinguish items from different transactions; so we define a new class for nominal items named "OrderedNominalItem", with a "serial" property indicating its transaction id; equals() method is also rewritten to ensure its effectiveness when constructing a JUNG Tree object with OrderedNominalItem nodes.In the construction process of the header tables (data type is TreeBidiMap) and FP-Trees (data type is DelegateTree of JUNG), comparative operations are performed when adding or deleting nodes. The original compareTo()method only compares item's frequency & attribute's name; this strategy gives an "equal" result for those items that belong to the same field (attribute) but with different values. So our comparison strategy is: compare item's frequency, name of attribute and item value consecutively, as shown in Figure 2.Condition (2) is met by method equalsWithoutOrder(), in which comparison is made without involving the serial property; this method is called when seeking a specified item in a collection when only the item's attribute & value are compared, see seekItemInCollection() method in class FpTree [8]; this seeking operation is needed when adding a new node to the existing FP-tree.Data type 2: comparator of OrderedNominalItem:public boolean equals(Object o) {if (serial != ((OrderedNominalItem) o).serial)return false;return super.equals(o);}public int compareTo(Item o) {OrderedNominalItem comp = (OrderedNominalItem) o;// 1. first, frequencyif (comp.getFrequency() < m_frequency) {return -1;}if (comp.getFrequency() > m_frequency) {return 1;}// 2. then, by nameint c = m_().compareTo(comp.getAttribute().name());if (c != 0)return -1 * c;// 3. last, by valueif (m_valueIndex < comp.getValueIndex())return 1;else if (m_valueIndex > comp.getValueIndex())return -1;elsereturn 0;}Figure 2. Comparator used in OrderedNominalItem6. Algorithm descriptionUsing the high-level data types in Weka and JUNG framework along with data objects from Apache Collections, the computation process of FP-Growth algorithm can have a simple description.Figure 3 is the work flow of the initial process on transaction database; it constructs the first FP-tree and header table with two scans. From this point on, the mining process becomes mining on FP-trees. Figure 3. Initial process for transaction databaseThe main mining method is defined as mineDbtree(dbTree, dbHeader); it is a recursive function with two basic steps:(1) Traverse the header table and construct subtrees;(2) Mine the subtree (with recursive function call to mineDbtree());Each subtree is a new transaction database, we can handle it with just the same way we handle the original database:(1) First scan, construct header table;(2) For each transaction, sort its items in header table's order;(3) Second scan, construct transaction tree;(4) Mine the resulted transaction tree (recursive call to mineDbtree ).This process is demonstrated in Figure 4.Figure 4. Mining process on subtreesMining the transaction tree comprises two main steps:(1) Obtaining the subtree corresponding to the header table items (getSubtree ).(2) Mining the resulted subtree (mineSubtree ).Although the actual code may seem a little different, but the idea inside getSubtree() is quite simple: traverse the link table and get all the branches corresponding to each item; each branch is obtained by simply invoke:List<OrderedNominalItem> branch = tree .getPath(link item );Algorithm 1: construction of the initial fp-tree://1.Initialization:Initialize instances object from a data source (e.g. a file);//2.First Scan, create initial header table:For each instance in instances :Split it into items (OrderedNominalItem objects)Construct header table (data type: TreeBidiMap<HeaderCount, OrderedNominalItem>)Delete unfrequent items from header table//3.Second scan, create initial FP-Tree and link table:Construct dbTree;(data type: DelegateTree<OrderedNominalItem, Long>)Construct link table(data type:Vector)//4.now do the mining on dbTtreemineDbtree(dbTree, dbHeader)Algorithm 2: mining sub-tree:mineSubtree(Vector<List<OrderedNominalItem>>subtree) {//1. Traverse subtree build header tableTreeBidiMap<HeaderCount, OrderedNominalItem>header;//2. Sort items in transaction//3. Rebuild transaction treeDelegateTree<OrderedNominalItem, Long> fptree;//4. Mine the resulted treemineDbtree(fptree, header);After removing its root & leaf node, branch is a list of nodes that consists one transaction of the subtree. All such branches form a new transaction database, which can be mined recursively using mineDbtree. Recursion termination condition: the resulting subtree is empty.Mining process of the subtree is illustrated in Figure 5.Algorithm 3: mining transaction-tree:mineDbtree(dbtree, dbheader) {Vector<List<OrderedNominalItem>> subtree;HeaderCount headerItem = stKey();// traverse from the tail of the header tablewhile (headerItem != null) {// 1. get subtree for this itemsubtree = getSubtree(dbtree, headerItem);// if subtree is null, go to nextif (subtree == null) {headerItem =dbheader.previousKey(headerItem);continue;}// 2. subtree miningmineSubtree(subtree);// next item in header tableheaderItem =dbheader.previousKey(headerItem);}}Figure 5. Mining the transaction tree7. Implementation and experimentsThe approach described in this paper has been implemented and published as an open source project on Google Code™; the project URL is:/p/weka-jung-fpgrowth/JUNG & Weka's supporting package that is needed for compiling can be download at [5][9]; the Apache Collections support is included in JUNG package.We created a simple GUI (see Figure 6) for testing different data sets. The favorite type for the data file is "arff" which is the standard in Weka [5], while other types such as "csv" are also supported.As shown in Figure 6, button "Read Datafile" loads data from a file into a DataSource object and parses it to an Instances object; button "Apriori->FP" uses the Weka's built in Apriori algorithm to find all the frequent patterns, and button "Show FP" lists these patterns in the window. "FP-Tree" is our implementation: it applies the FP-Growth algorithm upon the above mentioned Instances and shows the results.Experiments have been performed to check its correctness; data sets used in these experiments are downloaded from UCI Machine Learning Repository [10]. The computer that runs the experiments has a software environment of Windows XP and JDK 1.6.0_14 with a hardware configuration of Intel® Core2 Duo CPU (2.8GHz) & 3GB memory. Source code compilation is done with MyEclipse V7.5.Because we only want to check the correctness (instead of performance) of this implementation, a simple comparison with the result of the built-in Apriori algorithm should suffice. Table 1 is the testing result on the classical "Breast Cancer" dataset, and clearly it out performs the Apriori implementation (which is also a Weka based program), and Figure 6 is the runtime screen shot of this test for the minimum support value setting to 0.5. We have not tested our implementation against FP-Growth's C++ implementations because we consider there is no comparability between these two approaches and the overhead of our complex data objects is obvious.Figure 6. A graphic user interface of our implementationTable 1. Runtime Comparison with Weka-Apriori ImplementationMini Sup Apriori(ms) FP-Tree/JUNG-Weka(ms)0.5 156 630.2 375 780.1 906 2190.02 overflow 15948. Conclusion and discussionUtilizing the combined framework of Weka and JUNG, together with other high-level data types from Apache Collections, algorithms (such as FP-Growth) that need sophisticated data structures (such as trees, graphs etc) could be implemented concisely with less effort and yet higher reusability; the overhead on complex data objects and its downside impact on runtime efficiency can be overlooked when human labor cost is a more important factor.This implementation does not use Weka's built-in NominalItem data type directly as JUNG tree's node class, because from experiments we find that if the internal attribute such as m_frequency is changed via its public method then this object will no longer be considered as a composing node of the tree; this odd behavior forced the customized OrderedNominalItem class to have a redundant data attribute for the item's support, and the course of this remains further study.Utilizing the high-level data types of JUNG has other benefits: JUNG provides powerful visualization functionalities, which can be used to present graphical illustration of the mining results such as needed when dealing with visualization requirements [15]. In fact, setting the boolean variable "showtrees" to "true" will cause our program to visualize all FP-trees it create, one example of such trees is shown in Figure 7.Thoughts on further research work include implementing other algorithms that need tree computation and visualization, such as the "cluster first" strategy proposed in [16], and text mining for mind map [17].Figure 7. Visualization of an FP-tree9. References[1]Jiawei Han, Jian Pei, Yiwen Yin, and Runying Mao, “Mining frequent patterns without candidategeneration”, Data Mining and Knowledge Discovery, vol. 8, no. 1, pp.53-87, 2004.[2]Mark Hall, Eibe Frank, Geoffrey Holmes, Bernhard Pfahringer, Peter Reutemann, Ian H. Witten,“The WEKA Data Mining Software: An Update”, SIGKDD Explorations, vol.11, no. 1, 2009. [3]Eibe Frank, Ian H. Witten. Data Mining: Practical Machine Learning Tools and Techniques[M].Morgan Kaufmann, 2005.[4]Guang-li Yu, Ying Zhan and Shui Wang, “Analysis on Weka Foundation Classes and AlgorithmExtending Method”, Journal of Nanyang Institute of Technology, vol. 1, no. 6, pp. 9-11, 2009. [5]Weka (Machine Learning Group at University of Waikato). Data mining with open sourcemachine learning software in Java [/~ml/weka/]. Accessed in Sep.2010.[6]Shui Wang, Yu-jun Ma, “Introduction to JUNG: Network/Graph Computation Framework on Javaplatform”. (to be published).[7]Apache Software Foundation. Apache Commons [/collections/].Accessed in Sep 2010.[8]Shui Wang, Le Wang. Source code of this paper [/p/weka-jung-fpgrowth/downloads/]. 2010.[9]Joshua O'Madadhain, Danyel Fisher, Tom Nelson et al. Java Universal Network/GraphFramework [/]. Accessed in Sep 2010.[10]Frank, A. & Asuncion, A. UCI Machine Learning Repository [/ml]. Irvine,CA: University of California, School of Information and Computer Science. Accessed in Sep 2010.[11]CSDN, Java source for FP-Growth [/source/665781]. Accessed in Sep2010.[12]Xinyu Wang, Xiaoping Du, Kunqing Xie, “Research on Implementation of the FP-GrowthAlgorithm”, Computer Engineering and Applications, vol. 40, no. 9, pp. 174-176, 2004. (in Chinese).[13]C. Borgelt. An implementation of the FP-growth algorithm. In Proceeding of OSDM 2005, pp.1-5,2005.[14]Zi-guang Sun, “Analysis and implementation of the algorithm of FP-growth”, Journal of GuangxiInstitute of Technology, vol. 16,no. 3, pp. 64-67, 2004. (in Chinese).[15]Jinlong Wang, Can Wen, Shunyao Wu, Huy Quan Vu , “A Visual Mining System for ThemeDevelopment Evolution Analysis of Scientific Literature”, JDCTA: International Journal of Digital Content Technology and its Applications, vol. 4, no. 3, pp. 21-23, 2010.[16]Lilin FAN, “Research on Classification Mining Method of Frequent Itemset”, JCIT: Journal ofConvergence Information Technology, vol. 5, no. 8, pp. 71-77, 2010.[17]Shui Wang, Le Wang, “Mindmap-NG: A novel framework for modeling effective thinking”, InProceeding of the 3rd IEEE International Conference on Computer Science and Information Technology (ICCSIT), vol.2, pp.480-483, July 2010.。

元器件交易网ML6554PRODUCT SPECIFICATIONPin ConfigurationPin DescriptionPin Name Function1V DD Digital supply voltage2PV DD1 Voltage supply for internal power transistors 3V L1 Output voltage/ inductor connection 4P GND1 Ground for output power transistors 5P GND2 Ground for output power transistors 6V L2 Output voltage/inductor connection 7PV DD2 Voltage supply for internal power transistors 8D GND Digital ground 9V DD Digital supply voltage10V FB Input for external compensation feedback 11VREF IN Input for external reference voltage 12SHDN Shutdown active low. CMOS input level 13AGND Ground for internal reference voltage divider 14VREF OUT Reference voltage output15V CCQVoltage reference for internal voltage divider 16AV CCAnalog voltage supply元器件交易网PRODUCT SPECIFICATIONML6554Absolute Maximum RatingsAbsolute maximum ratings are those values beyond which the device could be permanently damaged. Absolute maximum ratings are stress ratings only and functional device operation is not implied.Operating ConditionsElectrical CharacteristicsUnless otherwise speci fied, AV CC = V DD = PV DD = 3.3V ±10%, T A = Operating T emperature Range (Note 1) Notes1.Limits are guaranteed by 100% testing, sampling, or correlation with worst-case test conditions.2.Infinite heat sink ParameterMin.Max.Units PV DD4.5V Voltage on Any Other PinGND – 0.3V IN + 0.3V Average Switch Current (I AVG ) 3.0A Junction Temperature150°C Storage Temperature Range-65150°C Lead Temperature (Soldering, 10 sec)150°C Thermal Resistance ( θJC )(Note 2)2°C/W Output Current, Source or Sink3.0AParameterMin.Max.Units Temperature Range, CU suffix 070°C Temperature Range, IU suffix -40+85°C PV DD Operating Range 2.0 4.0V V CCQ Operating Range1.44.0VSymbol Parameter ConditionsMin.Typ. Max.UnitsSwitching Regulator V TT Output Voltage, SSTL_2(See Figure 1)I OUT = 0, V REF = open V CCQ = 2.3V 1.12 1.15 1.18V V CCQ = 2.5V 1.22 1.25 1.28V V CCQ = 2.7V 1.32 1.35 1.38V I OUT = ±3A, V REF = openV CCQ = 2.3V 1.09 1.15 1.21V V CCQ = 2.5V 1.19 1.25 1.31V V CCQ = 2.7V 1.28 1.35 1.42V VREF OUTInternal Resistor DividerI OUT = 0V CCQ = 2.3V 1.139 1.15 1.162V V CCQ = 2.5V 1.238 1.25 1.263V V CCQ = 2.7V 1.337 1.35 1.364V Z INV REF Reference Pin InputImpedanceVCCQ = 0100k Ω Switching Frequency650kHz ∆ V OFFSET Offset Voltage V TT – VREF OUTAV CC = 2.5V No Load VCCQ = 2.5–2020mV Supply I Q Quiescent CurrentI OUT = 0, no loadV CCQ = 2.5VI VCCQ 610µA I AVCC0.5 1.0mA I AVCC SD 0.20.5mA I VDD0.25 1.0mA I VDD SD 0.2 1.0mA I PVDD100250µA Buffer IREFOutput Load Current3mA元器件交易网元器件交易网ML6554PRODUCT SPECIFICATIONPRODUCT SPECIFICATION ML6554ML6554PRODUCT SPECIFICATIONFigure 3. Alternate Application CircuitAn alternate application circuit for the ML6554 is shown in Figure 3. The number of external components is reduced compared to the circuit in Figure 2. This is achieved by replacing four, 0.1µF bypass capacitors with one, low ESR, 10µF ceramic capacitor placed right next to U1. Two 100Ωresistors are also eliminated. High value, surface-mount MLC capacitors were not available when the original appli-cation circuit (Figure 2) was developed. Both application circuits offer the same electrical performance but that shown in Figure 2 has a reduced bill-of-materials. Table 2 shows the recommended parts list for the circuit of Figure 3.PRODUCT SPECIFICATION ML6554ML6554PRODUCT SPECIFICATIONFigure 6. Top SilkFigure 7. Top LayerFigure 8. Bottom LayerPRODUCT SPECIFICATION ML6554ML6554PRODUCT SPECIFICATIONTable 1. Recommend Parts List for SSTL-2 Termination Circuit in Figure 2.Table 2. Recommend Parts List for Figure 3.Item Qty DescriptionManufacturer / Part Number Designator Resistors12100Ω1210 SMD Panasonic/ERJ-8ENF1000V R1, R2211k Ω 1210 SMD Panasonic/ERJ-8ENF1001V R532100k Ω1210 SMD Panasonic/ERJ-8ENF1003V R3, R4Capacitors430.1µF 1210 Film SMD Panasonic/ECV3VB1E104K Panasonic/ECU-V1H104KBW C2, C8, C951820µF 2V Solid Elect. SMD Sanyo/2SV820M Os Con C162330µF Tant 6.3V 100m ΩAVX/TPSE337M006R0100C5, C6711nF 1210 Film SMD Panasonic/ECU-V1H102KBM C7820.1µF 0805 Film Panasonic/ECJ-2VF1C104Z C3, C4ICS91ML6554 Bus Terminator Power SOP Package ML6554CU or ML6554IUU1Magnetics1013.3µH 5A inductor SMDCoilcraft/D03316P-332HC Pulse Eng./ P0751.332T Gowanda/SMP3316-331M XFMRS inc./XF0046-S4L1Other111Scope probe socket Tektronics/131-4353-00TP112112 Pin breakaway strip Sullins/PTC36SAAN (36 PINS)I/O, standoffsItem Qty DescriptionManufacturer / Part Number Designator Resistors12100k Ω 0805 SMD Panasonic/ERJ-8ENF1000V R1, R3211k Ω 0805 SMD Panasonic/ERJ-8ENF1000V R2Capacitors310.1µF, 1210 Film SMD Panasonic/ECV3VB1E104K Panasonic/ECU-V1H104KBW C241820µF 2V Solid Elect. SMD Sanyo/2SV820M Os Con C152330µF Tant 6.3V 100m ΩAVX/TPSE337M006R0100C5, C6611nF 1210 Film SMD Panasonic/ECU-V1H102KBM C47110µF 6.3V Ceramic TDK/C2012X5R0J106M C3ICS81ML6554 Bus Terminator Power SOP Package ML6554CU or ML6554IUU1Magnetics913.3µH 5A inductor SMDCoilcraft/D03316P-332HC Pulse Eng./ P0751.332T Gowanda/SMP3316-331M XFMRS inc./XF0046-S4L1Other101Scope probe socket Tektronics/131-4353-00TP111112 Pin breakaway strip Sullins/PTC36SAAN (36 PINS)I/O, standoffsFigure 12. Test Board Layout for ΘJA vs. Airflow Table 3. Termination Solutions Summary By Buss TypeBus Description DrivingMethod VDDQ VTT V REFFairchildSolutionsIndustrySystemComponentsGTL+GunningTransceiverBus Plus Open Drain5v or 3.3VNote 101.5V±10%Note121.0V±2%Note 11ML6554CU;Mode: V REFInput = 1.5V,V CC = 5V300 to 500MHzProcessor;PC Chipsets;GTLP 16xxxBuffers;Fairchild,Texas Instr.SSTL_2Series StubTerminatedLogic for 2V SymmetricDrive,SeriesResistance2.5V±10%0.5x(V DDQ)±3%2.5V ML6554CUor ML6553CS;Mode: V REFInput = Floatingor Forced,V CC = 3.3VSSTL SDRAM;Hitachi,Fujitsu,NEC, Micro,MitsubishiRAMBUS RAMBUSSignalingLogic Open Drain NoneSpecified2.5V 2.0V ML6553CS;Mode: V REFInput = Open,V CC = V DDQnDRAM,RAMBUS,Intel, ToshibaLV-TTL Low VoltageTTL Logic orPECL or3.3V VME SymmetricDrive3.3±10%V DDQ/2 3.3V ML6553CS;Mode: V REFInput = Open,VCC = VDDQProcessors orbackplanes;LV-TTLSDRAM,EDO RAMDISCLAIMERFAIRCHILD SEMICONDUCTOR RESERVES THE RIGHT TO MAKE CHANGES WITHOUT FURTHER NOTICE TO ANY PRODUCTS HEREIN TO IMPROVE RELIABILITY, FUNCTION OR DESIGN. FAIRCHILD DOES NOT ASSUME ANY LIABILITY ARISING OUT OF THE APPLICATION OR USE OF ANY PRODUCT OR CIRCUIT DESCRIBED HEREIN; NEITHER DOES IT CONVEY ANY LICENSE UNDER ITS PATENT RIGHTS, NOR THE RIGHTS OF OTHERS.LIFE SUPPORT POLICYFAIRCHILD’S PRODUCTS ARE NOT AUTHORIZED FOR USE AS CRITICAL COMPONENTS IN LIFE SUPPORT DEVICES OR SYSTEMS WITHOUT THE EXPRESS WRITTEN APPROVAL OF THE PRESIDENT OF FAIRCHILD SEMICONDUCTOR CORPORATION. As used herein:1.Life support devices or systems are devices or systemswhich, (a) are intended for surgical implant into the body, or (b) support or sustain life, or (c) whose failure to perform when properly used in accordance with instructions for use provided in the labeling, can be reasonably expected to result in significant injury of the user.2. A critical component is any component of a life supportdevice or system whose failure to perform can bereasonably expected to cause the failure of the life support device or system, or to affect its safety or effectiveness.。

循迹小车制作英语作文Building a Line Follower RobotLine follower robots are autonomous vehicles that are designed to follow a predefined path marked by a line or track. These robots use sensors to detect the line and adjust their movement accordingly to stay on the designated path. The process of designing and constructing a line follower robot can be an engaging and educational experience, allowing individuals to explore the principles of robotics, electronics, and programming.The first step in building a line follower robot is to understand the basic components and their functions. At the core of the robot is a microcontroller, which serves as the "brain" of the system. The microcontroller is responsible for processing sensor inputs, making decisions, and controlling the robot's movement. Commonly used microcontrollers for line follower robots include Arduino, Raspberry Pi, and various microcontrollers from manufacturers like Atmel, Texas Instruments, and Microchip.The sensors used in a line follower robot are typically infrared (IR) sensors or reflective sensors. These sensors are positioned on the underside of the robot and are used to detect the line or track. When the sensor detects the line, it sends a signal to the microcontroller, which then adjusts the robot's movement accordingly. The numberof sensors used can vary, with some designs incorporating a single sensor and others using multiple sensors to improve the robot's tracking accuracy.The robot's movement is typically controlled by a set of motors, such as DC motors or stepper motors, which are connected to the microcontroller. The microcontroller sends signals to the motors to control the speed and direction of the robot's movement. In a basic line follower robot, the motors are often connected to the robot's wheels, allowing it to move forward, backward, and turn as neededto follow the line.In addition to the core components, a line follower robot may also include additional features or components to enhance its capabilities. For example, some robots may incorporate a display or LED indicators to provide visual feedback on the robot's status or performance. Others may include wireless communication modules, such as Bluetooth or Wi-Fi, to enable remote control or data transmission.The software or programming aspect of a line follower robot is crucial, as it determines the robot's behavior and decision-making process. The microcontroller's programming is typically done using a programming language such as C, C++, or Arduino's own programming language. The code must be designed to read the sensor inputs, interpret the line's position, and send appropriate commands to the motors to keep the robot on the designated path.One of the key challenges in building a line follower robot is ensuring that the robot can accurately follow the line, even in the presence of variations or obstacles. This may require fine-tuning the sensor placement, adjusting the motor control algorithms, and implementing advanced techniques like proportional-integral-derivative (PID) control or adaptive algorithms.Beyond the technical aspects, building a line follower robot can also be a valuable learning experience. It allows individuals to develop skills in problem-solving, critical thinking, and hands-on engineering. The process of designing, constructing, and programming the robot can foster a deeper understanding of robotics, electronics, and computer science principles.Moreover, line follower robots can be used in a variety of applications, such as automated guided vehicles (AGVs) in industrial settings, educational demonstrations, or even as part of roboticscompetitions and challenges. These applications can further inspire and motivate individuals to continue exploring the field of robotics and seek new opportunities for innovation.In conclusion, building a line follower robot is a rewarding and educational endeavor that allows individuals to apply their knowledge of electronics, programming, and engineering to create a functional autonomous vehicle. By understanding the core components, designing the mechanical and electrical systems, and developing the software, individuals can gain valuable hands-on experience and contribute to the growing field of robotics.。

人教版八年级上册英语基础训练第一单元达标测试Embarking on the journey of learning a new language opens up a world of opportunities. As students of the eighth grade begin their exploration of English, they encounter a variety of themes that not only enhance their linguistic skills but also broaden their cultural horizons. The first unit of the People's Education Press textbook for eighth grade serves as an introduction to this adventure, laying the foundation for a solid understanding of English.The unit starts with the basics of grammar, an essential building block for constructing clear and correct sentences. Understanding subjects, predicates, and objects allows students to form simple sentences, which is the first step in communication. As they progress, they learn about the different types of sentences: declarative, interrogative, imperative, and exclamatory, each serving a unique purpose in expression.Vocabulary is another cornerstone of language learning. This unit introduces students to a carefully selected set of words that are both practical and relevant to their daily lives. Through various exercises, students practice using these new words in context, enhancing their ability to remember and apply them.Pronunciation and intonation are also covered, with audio resources providing models for students to imitate. Accurate pronunciation is crucial, as it affects the clarityof communication. Intonation, the rise and fall of the voice in speaking, conveys emotions and attitudes, adding depth to the spoken word.Cultural insights are woven throughout the unit, offering glimpses into the English-speaking world. These cultural tidbits not only make the learning process more interesting but also help students develop a global perspective.The unit includes a range of activities designed to cater to different learning styles. Visual learners benefit from the colorful illustrations and charts, auditory learners fromthe listening exercises, and kinesthetic learners from the role-play and group work. This multimodal approach ensures that every student has the chance to engage with the material in a way that suits them best.Assessment is an integral part of the learning process, and the unit concludes with a test that measures students' understanding of the material covered. This test is not just a means of evaluation but also a tool for reflection, allowing students to identify their strengths and areas for improvement.In conclusion, the first unit of the eighth-grade English textbook is more than just a collection of lessons; it is a carefully crafted experience designed to ignite a passion for the English language. Through a blend of grammar, vocabulary, pronunciation, cultural knowledge, and diverse activities, students are equipped with the tools they need to communicate effectively and to continue their journey of language learning with confidence and enthusiasm.This document, adhering to the guidelines provided, aims to encapsulate the essence of the first unit, ensuring that the content is accurate, lively, concise, and logically connected, thus reflecting a high standard of document quality without deviating from the topic at hand. 。