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Classification of MatterMatter : anything that has __________ and takes up space∙ exists in three states (or phases)particles are packed tightlylow kinetic energy fixed shapenot compressibleparticles packed less tightly more kinetic energyshape depends on container not compressibleparticles are very spread out higher kinetic energyshape depends on container compressible∙ matter is made of particles1. ____________: the smallest building block of matter (eg. one atom of silver or Ag)2. ________________: a cluster of more than 1 atom (eg. CCl 4, H 2O, C 6H 12O 6)3. _______: an atom or molecule with a positive or negative charge (eg. silver ion Ag +, NO 3-, Mg 2+)∙ ____________: atom or molecule with a positive charge ∙ ____________: atom or molecule with a negative charge∙ the appearance of matter can be described as1. ____________________: the substance looks the same everywhere (uniform composition)2. ____________________: the substance does not look the same everywhere (variablecomposition)Matter can be classified depending on the composition.1. Match each classification with the correct description and example.2. Arrange the classifications into a flow chart on the next page.Classification of MatterSeparationsF i l t r a t i o nE v a p o r a t i o nD i s t i l l a t i o nfiltrateresiduemixture funnel filter paperC h r o m a t o g r a p h yChanges in Matter______________: absorbs heatKinetic Energy (KE)∙energy that molecules possess as a result of ___________________________ ∙average kinetic energy = __________________∙there are three types of KE’s1.Rotational Energy (E rot)o molecule rotates or spins around an axiso bond length and bond angles don’t change2.Vibrational Energy (E vib)o molecule “stretches”o bond length and bond angles change3.Translational Energy (E trans)o molecule travelso bond length and bond angles don’t changePhase ChangesHeating Curve of Chemical XTimeA/C/E:∙ kinetic energy (temperature) _______________∙ distance between particles begins to _______________B/D:∙ substance is absorbing heat to break ___________________ bonds∙ all heat is used to break these intermolecular bonds, so temperature stays _______________ ∙ when intermolecular bonds are broken, we get a phase change_____________________ undergo phase changes in fixed temperatures:Melting point (m.p): temperature at which (solid →liquid) Freezing point : temperature at which (liquid →solid) Boiling point (b.p): temperature at which (liquid →gas)Condensation temperature : temperature at which a (gas →liquid)Temp. (°C)Some Applications of Kinetic EnergyEnergy can be in the form of waves1.Microwave oven:o makes water molecules in food vibrate (KE _____________)o the high temperature water molecules “heat” food2.Infrared (IR) Spectroscopy: used to identify substanceso different bonds in a molecule ___________ difference amounts of energyo absorbance of energy can be plotted against wave number _______________o every molecule has a unique “fingerprint”。
1.what is the wave – particle duality theory? Does any matter have both wave and particle characteristics?(33号)1）Particle-like Character: light propagating through free space consisting of a stream of …photons‟ suggested by photoelectric effect. Its kin etic energy is given: Wave-like Character: its correctness is indicated by electron microscope as well as by diffraction and interference. The De Broglie wavelength of a particle moving with momentum mv is given by:2）any matter have both wave and particle characteristics2.What is the uncertainty principle?( For an example)Uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision. That is, the more precisely one property is known, the less precisely the other can be known.For an example （ Electrons' Diffraction ）the standard deviation of the X-distribution ：a x =∆the standard deviation of P ：Because ：ph a ==λλϕ,sin ，h p x x =∆∆ Because the in sub diffraction is bigger :h p x ≥∆∆3.Wavefunction and its meaning. (33号)λA wave function or wavefunction is a mathematical tool used in quantum mechanics to describe the momentary states of subatomic particles .)(0),(r P Et i e t r ⋅--ψ=ψStatistical explanation of wavefunctionThe values of the wave function are probability amplitudes （振幅） — complex numbers — the squares of the absolute values of which give the probability distribution that the system will be in any of the possible states.4.The solution of Schrodinger equation of the particles bound in one-dimensional potential wells. (1/2号)νεh k =mvh =λϕsin pa p x x =∆∆∴x p ∆Single particle in one dimensions ：Free particle ti x m ∂∂∂∂ψ=ψ- 2222 Time dependent5,What is the best obvious characteristics of crystal lattice ? (3/4号)The best obvious characteristics of crystal lattice is that atoms are arranged periodically in crystal lattic e.A crystal or crystalline solid is a solid material, whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions.6.what is the forbidden band, empty band, valence band ,conduction band? (5/6号)● allowed band: the energy band which allow to be occupied by electron● forbidden band: the region between allow band, in which electron is not allowedto occupy● empty band: the energy band in which electron cannot be found in each level ● valence band: the energy band corresponding to valence electron● conduction band: above Valence band the allow band which have the lowestenergye the theory of energy band to explain what is the insulator, semiconductor and conductor.Solution ：As is shown in the above picture , in metal the highest energy band filled by electrons is not full ，furthermore ，the density of electron in the energy band is v ery high , it has the same magnitude as the density of the atom, so the conductivity of metal is very high.In the case of insulator, there is an energy gap , a finite excitation energy is required to carry the electrons up over the gap into the next band . This can‟t be supplied by small constant electric field, then the conductivity is very low ，almost zero.As for semiconductor, the energy gap is small . At the temperature T there will be a small , but not zero, density of electrons excited by thermal fluctuations into the upper band. These electrons can easily carry a current, which would increase rapidly at higher temperature.8,What is the mobility of semiconductor? What are the factors which have effect on the mobility? (第4个ppt, 33-36页)（9/10号）Answer: It is the average drift velocity of carrier in unit electric field.assume the semiconductor is n-type semiconductor, electron concentration is n 0, the average drift velocity of electrons is v d .we know the current density ( J ) is :d d n qv n sqsv n s I J 00=== According to the ohm‟s law,E J n n σ= We can getn d n q n E v q n μσ00== , Ev d n =μ , it is the electron mobility Similarily p p q p μσ0= , p μis the hole mobilitySo in the actual semiconductor,p n q p q n μμσ00+=But in n-type semiconductor, n 0 >> p 0n q n μσ0=In p-type semiconductor, p 0 >> n 0p q p μσ0=In intrinsic semiconductor, n 0=p 0)(0p n q n μμσ+=载流子迁移率的影响因素很多，关于这方面比较系统的信息没有找到，但老师强调了一点，随着半导体中掺杂浓度的升高，其载流子的迁移率降低。
788PARTICULATE MATTER IN INJECTIONS注射剂中的微粒Change to read:This general chapter is harmonized with the corresponding texts of the European Pharmacopoeia and/or the Japanese Pharmacopoeia. These pharmacopeias have undertaken not to make any unilateral change to this harmonized chapter. Portions of the present general chapter text that are national USP text, and therefore not part of the harmonized text, are marked with symbols () to specify this fact.本通则已与欧洲药典和/或日本药典的对应章节进行了统一。
各国药典已承诺对于这个已统一的通则不会作出单方面的修改。
本通则为USP文本，因此其中会有一些没有统一的段落，文中以符号()进行了标示。
Particulate matter in injections and parenteral infusions consists of extraneous mobile undissolved particles, other than gas bubbles, unintentionally present in the solutions.注射剂和注射用输液中的微粒是指非故意存在于溶液中的除气泡以外的可移动的不溶性粒子。
For the determination of particulate matter, two procedures, Method 1 (Light Obscuration Particle Count Test) and Method 2 (Microscopic Particle Count Test), are specified hereinafter. When examining injections and parenteral infusions for subvisible particles, Method 1 is preferably applied. However, it may be necessary to test some preparations by the Light Obscuration Particle Count Test followed by the Microscopic Particle Count Test to reach a conclusion on conformance to the requirements.下文中介绍了微粒检测的两种方法，方法1（光阻法）和方法2（显微计数法）。
Quantum MechanicsQuantum Mechanics is a branch of physics that deals with the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles. It is a complex and fascinating field of study that has revolutionized our understanding of the world around us. However, it is also a subject that can be difficult to grasp, with concepts that challenge our intuition and require us to think in new ways. In this essay, I will explore the basics of Quantum Mechanics, its implications for our understanding of reality, and some of the controversies surrounding it.One of the key principles of Quantum Mechanics is the idea of wave-particle duality. This means that particles, such as electrons, can exhibit both wave-like and particle-like behavior, depending on the context. For example, when an electron is observed, it appears as a particle, but when it is not observed, it behaves like a wave. This concept challenges our everyday understanding of the world, where objects are either particles or waves, but not both.Another important principle of Quantum Mechanics is uncertainty. Thisprinciple states that it is impossible to know both the position and momentum of a particle with absolute certainty. The more precisely we know one of these values, the less precisely we can know the other. This principle has profound implications for our understanding of causality and determinism, as it suggests that the behavior of particles is inherently unpredictable.Quantum Mechanics also introduces the concept of superposition, which is the idea that a particle can exist in multiple states at the same time. For example, an electron can exist in two different energy states simultaneously. This concept is difficult to grasp, as it challenges our everyday experience of the world, where objects are either in one state or another, but not both.One of the most famous experiments in Quantum Mechanics is the double-slit experiment. In this experiment, a beam of particles, such as electrons, is fired at a screen with two slits. When the particles pass through the slits, they create an interference pattern on a detector behind the screen, as if they had behaved like waves. This experiment demonstrates the wave-particle duality of particles and the concept of superposition.The implications of Quantum Mechanics for our understanding of reality are profound. It suggests that the world is fundamentally uncertain and that particles can exist in multiple states at the same time. This challenges our everyday experience of the world, where things are either one way or another, but not both. It also raises questions about the nature of causality and determinism, asparticles seem to behave in unpredictable ways.There are also controversies surrounding Quantum Mechanics. One of the most famous is the Einstein-Podolsky-Rosen (EPR) paradox. This paradox suggests that if two particles are entangled, meaning they have a correlated quantum state, then measuring one particle will instantaneously affect the state of the other particle, even if they are separated by large distances. This concept challenges our understanding of causality and suggests that information can travel faster thanthe speed of light, which is not allowed by relativity.Another controversy is the interpretation of Quantum Mechanics. There are several interpretations of Quantum Mechanics, each with its own strengths and weaknesses. The most popular interpretation is the Copenhagen interpretation,which suggests that the act of observation collapses the wave function of a particle, causing it to behave like a particle rather than a wave. However, this interpretation has been criticized for being too anthropocentric and for not providing a clear explanation of how the act of observation causes the collapse.In conclusion, Quantum Mechanics is a complex and fascinating field of study that challenges our understanding of the world around us. Its principles of wave-particle duality, uncertainty, and superposition have profound implications forour understanding of reality. However, there are also controversies surrounding Quantum Mechanics, such as the EPR paradox and the interpretation of the theory. Despite these challenges, Quantum Mechanics has revolutionized our understandingof the world and continues to be an active area of research and discovery.。
a rXiv:g r-qc/4175v 116Jan24Matter Collineations of Some Static Spherically Symmetric Spacetimes M.Sharif ∗Department of Mathematics,University of the Punjab,Quaid-e-Azam Campus Lahore-54590,PAKISTAN.Abstract We derive matter collineations for some static spherically symmet-ric spacetimes and compare the results with Killing,Ricci and Cur-vature symmetries.We conclude that matter and Ricci collineations are not,in general,the same.Keywords:Isometries,Collineations 1Introduction There has been a recent literature [1-11,and references therein]which shows a significant interest in the study of various symmetries.These symmetries arise in the exact solutions of Einstein field equations given byG ab ≡R ab −1∗e-mail:hasharif@1are the important quantities which play a significant role in understanding the geometric structure of spacetime.A basic study of curvature collineations (CCs)and Ricci collineations(RCs)has been carried out by Katzin,et al[15] and a complete classification of CCs and RCs has been obtained by Qadir, et al[4-7,9].In this paper we shall analyze the properties of a vectorfield along which the Lie derivative of the energy-momentum tensor vanishes.Such a vector is called matter collineation.Since the energy-momentum tensor represents the matter part of the Einsteinfield equations and gives the matterfield sym-metries.Thus the study of matter collineations(MCs)seems more relevant from the physical point of view.The motivation for studying MCs can be discussed as follows.When we find exact solutions to the Einstein’sfield equations,one of the simplifica-tions we use is the assumption of certain symmetries of the spacetime metric. These symmetry assumptions are expressed in terms of isometries expressed by the spacetimes,also called Killing vectors which give rise to conservation laws[16,17].Symmetries of the energy-momentum tensor provide conserva-tion laws on matterfields.These symmetries are called matter collineations. These enable us to know how the physicalfields,occupying in certain re-gion of spacetimes,reflect the symmetries of the metric[18].In other words, given the metric tensor of a spacetime,one canfind symmetry for the phys-icalfields describing the material content of that spacetime.There is also a purely mathematical interest of studying the symmetry properties of a given geometrical object,namely the Einstien tensor,which arises quite naturally in the theory of General Relativity.Since it is related,via Einsteinfield equations,to the material content of the spacetime,it has an important role in this theory.There is a growing interest in the study of MCs[10,19,20and references therein].Carot,et al[19]has discussed MCs from the point of view of the Lie algebra of vectorfields generating them and,in particular,he discussed spacetimes with a degenerate T ab.Hall,et al[20],in the discussion of RC and MC,have argued that the symmetries of the energy-momentum tensor may also provide some extra understanding of the the subject which has not been provided by Killing vectors,Ricci and Curvature collineations.Keeping this point in mind we address the problem of calculating MCs for some static spherically symmetric spacetimes using some special techniques in this paper. It is hoped that some particular methods can be developed to solve partial differential equations involving in matter collineation equations for general2spacetimes.This would enable one to obtain a complete classification of general spacetimes according to their MCs.The distribution of the paper follows.In the next section,we give some basic definitions and write down the matter collineation equations.In sec-tion three we calculate MCs by solving matter collineation equations for some particular spacetimes.Final section carries a discussion of the results obtained.2Some Basic Facts and Matter Collineation EquationsLet(M,g)be a spacetime,M being a Hausdorff,simply connected,four dimensional manifold,and g a Lorentz metric with signature(+,-,-,-).A vectorξis called a MC if the Lie derivative of the energy-momentum tensor along that vector is zero.That is,LξT=o,(2) where T is the energy-momentum tensor and Lξdenotes the Lie derivative alongξof the energy-momentum tensor T.This equation,in a torsion-free space in a coordinate basis,reduces to a simple partial differential equation,T ab,cξc+T acξc,b+T bcξc,a=0,a,b,c=0,1,2,3.(3)where,denotes partial derivative with respect to the respective coordinate. These are ten coupled partial differential equations for four unknown func-tions(ξa)which are functions of all spacetime coordinates.Collineations can be proper or improper.A collineation of a given type is said to be proper if it does not belong to any of the subtypes.When we solve matter collineation equations,solutions representing proper collineations can be found.However,in order to be related to a particular conservation law,and its corresponding constants of the motion,the properness of the collineation type must be known.We know that every KV is an MC,but the converse is not always true. As given by Carot et al.[19],if T ab is non-degenerate,det(T ab)=0,the Lie algebra of the MCs isfinite dimensional.If T ab is degenerate,i.e.,det(T ab)= 0,we cannot guarantee thefinite dimensionality of the MCs.33Solution of the Matter Collineation Equa-tionsWe shall solve the MC equations for Minkowski,Einstein/anti-Einstein,de Sitter/anti-de Sitter,Schwarzschild,Riessner-Nordstrom and some Bertotti-Robinson like metrics.However,for Minkowski and Schwarzschild space-times,the Ricci tensor is zero,which implies the vanishing of the energy-momentum tensor.Hence the MC Eqs.(3)are satisfied for any arbitrary values ofξa.Thus in Minkowski and Schwarzschild spacetimes everyξa is a MC.In de Sitter/anti-de Sitter spacetimes,the energy-momentum tensor is related to the metric tensor byT ab=31−r2/D2dr2−r2dΩ2(5) the non-zero components of the energy-momentum tensor are given byT00=3κD2g ij,(i,j=1,2,3).(6)Substituting these values in Eqs.(3),we haveξ0=A(r,θ,φ),(7)43(1−r2/D2)ξ01−ξ1,0=0,(8)3ξ02−r2ξ2,0=0,(9)3ξ03−r2sin2θξ3,0=0,(10)rξ1+D2(1−r2/D2)ξ1,1=0,(11)ξ1+rξ2,2=0,(12)ξ1+r cotθξ2+rξ3,3=0,(13)ξ1,2+r2(1−r2/D2)ξ2,1=0,(14)ξ1,3+r2(1−r2/D2)sin2θξ3,1=0,(15)ξ2,3+sin2θξ3,2=0.(16) Solving Eqs.(11)-(16),we haveξ1=(1−r2/D2)1/2[B3(t)cosθ+B2(t,φ)sinθ],(17)ξ2=(1−r2/D2)1/2r sinθB2φ(t)+cotθC1φ(t,φ)+E(t,φ),(19) where B3is a function of time only while B2,C1and E are functions of t and φ.Using these equations together with Eqs.(7)-(10),wefinally arrive at the following resultsξ0=α0,(20)ξ1=(1−r2/D2)1/2[α1cosθ+(α2cosφ+α3sinφ)sinθ],(21)ξ2=(1−r2/D2)1/2r sinθ(−α2sinφ+α3cosφ)+cotθ(−α4sinφ+α5cosφ)+α6.(23)5Thus the MCs are given asξ=α0∂∂r−(1−r2/D2)1/2∂θ](24)+α2[(1−r2/D2)1/2sinθcosφ∂rcosθcosφ∂r sinθsinφ∂∂r+(1−r2/D2)1/2∂φ+(1−r2/D2)1/2∂φ]+α4[cosφ∂∂φ]+α5[sinφ∂∂φ]+α6∂∂t,(25)ξ(2)=(1−r2/D2)1/2cosθ∂rsinθ∂∂r +(1−r2/D2)1/2∂θ(27)−(1−r2/D2)1/2∂φ],ξ(4)=(1−r2/D2)1/2sinθsinφ∂rcosθsinφ∂r sinθcosφ∂∂θ−cotθsinφ∂∂θ+cosφ∂ξ(7)=∂κa2,T11=−1B+r(α0e t−α1e−t)+α2,(34)ξ1=α0e t+α1e−t,(35)ξ2=ξ2(x a),(36)ξ3=ξ3(x a).(37) Thus we haveξ=α0(−1∂t+∂B+r∂∂r)e−t+α2∂∂θ+ξ3(x a)∂αr)dt2−dr2−a2dΩ2,(39) ds2III=cosh2(c+√Table1:Comparison of KVs,RCs,CCs,and MCs for some specific Spherically Symmetric SpacetimesMetric KVs RCs CCs MCsarbitrary temporal and radial(functions of t and r only)CCs and three plus arbitrary second and third(functions of all spacetimes)MCs.In the other two Bertotti-Robinson like metrics,we do not get any information as the KVs,RCs,CCs and MCs are all the same.It would be interesting to extend this idea of classifying spacetimes with some minimal symmetry group in terms of their MCs and compare the general classification with KVs,RCs and CCs.To this end,one has to consider the simplest spacetimes which is the class of all spherically symmetric spacetimes. Then one can extend this by removing the condition of staticity,moving forward to cylindrical and plane symmetry and then reducing the minimal symmetry group further.Finally,it would be worthwhile to make comparison of the results with other classification schemes,e.g.,Petrov classification.It is hoped that some interesting feature will come out.9AcknowledgmentsThe author would like to thank Prof.Chul H.Lee for his hospitality atthe Department of Physics and Korea Scientific and Engineering Foundation (KOSEF)for postdoc fellowship at Hanyang University Seoul,KOREA.References[1]Tsamparlis,Michael and Apostolopouls,Pantelis S.:J.Math.Phys.41(2000)7573.[2]Contreras,G.Nunez,L.A.and Percoco,U.:Gen.Rel.and Grav.32(2000)285.[3]Camci,U.,Yavuz,˙I.,Baysal,H.,Tarhan,˙I.and Yilmaz,˙I.:Int.J.ofMod.Phys.D(to appear2001).[4]Bokhari,A.H.,Kashif,A.R.and Qadir,Asghar:J.Math.Phys.41(2000)2167.[5]Qadir,Asghar,Ziad,M.:Nuovo Cimento B113(1998)773.[6]Bokhari,A.H.,Qadir,Asghar,Ahmad,M.S.and Asghar,M.:J.Math.Phys.38(1997)3639.[7]Bokhari,A.H.,Amir,M.J.and Qadir,Asghar J.Math.Phys.35(1994)3005.[8]Melfo,A.,Nunez,L.Percoco,U.and Villapba:J.Math.Phys.33(1992)2258.[9]Bokhari,A.H.and Qadir,Asghar:J.Math.Phys.34(1993)3543.[10]Carot,J.and da Costa,J.:Procs.of the6th Canadian Conf.onGeneral Relativity and Relativistic Astrophysics,Fields mun.15,Amer.Math.Soc.WC Providence,RI(1997)179.[11]Carot,J.,Numez,L.A.and Percoco,U.:Gen.Rel.and Grav.29(1997)1223.[12]Noether,E.:Nachr,Akad.Wiss.Gottingen,II,Math.Phys.K12(1918)235.[13]Davis,W.R.and Katzin,G.H.:Am.J.Phys.30(1962)750.10[14]Bokhari,A.H.and Qadir,Asghar:J.Math.Phys.31(1990)1463.[15]Katzin,G.H.,Levine,J.and Davis,H.R.:J.Math.Phys.10(1969)617.[16]Misner,M.T.,Thorne,K.S.and Wheeler,J.A.:Gravitation(Freemann,San Francisco,1973).[17]Petrov,A.Z.:Einstein Spaces(Pergamon,Oxford,1969).[18]Coley,A.A.and Tupper,O.J.:J.Math.Phys.30(1989)2616.[19]Carot,J.,da Costa,J.and Vaz,E.G.L.R.:J.Math.Phys.35(1994)4832.[20]Hall,G.S.,Roy,I.and Vaz,L.R.:Gen.Rel and Grav.28(1996)299.[21]Qadir,Asghar and Ziad,M.:Procs.of the6th Marcel GrossmannMeeting eds.T.Nakamura and H.Sato(World Scientific1993);Ziad,M.:Ph.D.Thesis(Quaid-i-Azam University1991).[22]Bokhari,A.H.and Kashif,A.R.:J.Math.Phys.37(1996)3498.11。
