1.Fundamentals; 2.Path Integrals—Elementary Properties and Simple Solutions; 3.External Sources, Correlations, and Perturbation Theory; 4.Semiclassical Time Evolution Amplitude; 5.Variational Perturbation Theory; 6.Path Integrals with Topological Constraints; 7.Many Particle Orbits 8.Statistics and Second Quantization; 9.Path Integrals in Polar and Spherical Coordinates; 10.Wave Functions; 11.Spaces with Curvature and Torsion; Schrodinger Equation in General Metric Affine Spaces; 12.New Path Integral Formula for Singular Potentials; 13.Path Integral of Coulomb System; 14.Solution of Further Path Integrals by Duru Kleinert Method; 15.Path Integrals in Polymer Physics; 16.Polymers and Particle Orbits in Multiply Connected Spaces; 17.Tunneling; 18.Nonequilibrium Quantum Statistics; 19.Relativistic Particle Orbits; 20.Path Integrals and Financial Markets.
Nuclear reactions: General approach An outline of the general theory and modeling of nuclear reactions can be given in many ways. A common classification is in terms of time scales: short reaction times are associated with direct reactions and long reaction times with compound nucleus processes. At intermediate time scales, pre-equilibrium processes occur. An alternative, more or less equivalent, classification can be given with the number of intranuclear collisions, which is one or two for direct reactions, a few for pre-equilibrium reactions and many for compound reactions, respectively. As a consequence, the coupling between the incident and outgoing channels decreases with the number of collisions and the statistical nature of the nuclear reaction theories increases with the number of collisions. Figs. 3.1 and 3.2 explain the role of the different reaction mechanisms during an arbitrary nucleon-induced reaction in a schematic manner. They will all be discussed in this manual. This distinction between nuclear reaction mechanisms can be obtained in a more formal way by means of a proper division of the nuclear wave functions into open and closed configurations , as detailed for example by Feshbach’s many contributions to the field. This is the subject of several textbooks and will not be repeated here. When appropriate, we will return to the most important theoretical aspects of the nuclear models in TALYS in Chapter 4.
As specific features of the TALYS package we mention • In general, an exact implementation of many of the latest nuclear models for direct, compound,pre-equilibrium and fission reactions. • A continuous, smooth description of reaction mechanisms over a wide energy range (0.001- 200MeV) and mass number range (12 A 339). • Completely integrated optical model and coupled-channels calculations by the ECIS-06 code . • Incorporation of recent optical model parameterisations for many nuclei, both phenomenological (optionally including dispersion relations) and microscopical. • Total and partial cross sections, energy spectra, angular distributions, double-differential spectra and recoils. • Discrete and continuum photon production cross sections. • Excitation functions for residual nuclide production , including isomeric cross sections . • An exact modeling of exclusive channel cross sections, e.g. (n, 2np), spectra, and recoils. • Automatic reference to nuclear structure parameters as masses, discrete levels, resonances, level density parameters, deformation parameters, fission barrier and gamma-ray parameters , generally from the IAEA Reference Input Parameter Library . • Various width fluctuation models for binary compound reactions and, at higher energies, multiple Hauser-Feshbach emission until all reaction channels are closed. • Various phenomenological and microscopic level density models. • Various fission models to predict cross sections and fission fragment and product yields, and neutron multiplicities. • Models for pre-equilibrium reactions, and multiple pre-equilibrium reactions up to any order. • Generation of parameters for the unresolved resonance range. • Astrophysical reaction rates using Maxwellian averaging. • Medical isotope production yields as a function of accelerator energy and beam current. • Option to start with an excitation energy distribution instead of a projectile-target combination,helpful for coupling TALYS with intranuclear cascade codes or fission fragment studies. • Use of systematics if an adequate theory for a particular reaction mechanism is not yet available or implemented, or simply as a predictive alternative for more physical nuclear models. • Automatic generation of nuclear data in ENDF-6 format (not included in the free release). • Automatic optimization to experimental data and generation of covariance data (not included in the free release). • A transparent source program. • Input/output communication that is easy to use and understand. • An extensive user manual. • A large collection of sample cases.
七、演绎法常用的句型 1.There are several reasons for …， but in general, they come down to three major ones. 有几个原因……，但一般，他们可以归结为三个主要的。 2.There are many factors that may account for …， but the following are the most typical ones. 有许多因素可能占…，但以下是最典型的。 3.Many ways can contribute to solving this problem, but the following ones may be most effective. 有很多方法可以解决这个问题，但下面的可能是最有效的。 4.Generally, the advantages can be listed as follows. 一般来说，这些优势可以列举如下。 5.The reasons are as follows.
Chapter 8 This covers the important topic of volatility and correlation modelling and forecasting . This chapter starts by discussing in general terms the issue of non-linearity in financial time series . The class of ARCH (AutoRegressive Conditionally Heteroscedastic) models and the motivation for this formulation are then discussed. Other models are also presented, including extensions of the basic model such as GARCH, GARCH-M, EGARCH and GJR formulations . Examples of the huge number of applications are discussed, with particular reference to stock returns. Multivariate GARCH models are described, and applications to the estimation of conditional betas and time-varying hedge ratios, and to financial risk measurement, are given. Chapter 9 This discusses testing for and modelling regime shifts or switches of behaviour in financial series that can arise from changes in government policy, market trading conditions or microstructure , among other causes. This chapter introduces the Markov switching approach to dealing with regime shifts. Threshold autoregression is also discussed, along with issues relating to the estimation of such models. Examples include the modelling of exchange rates within a managed floating environment, modelling and forecasting the gilt--equity yield ratio, and models of movements of the difference between spot and futures prices. Chapter 10 This new chapter focuses on how to deal appropriately with longitudinal data -- that is, data having both time series and cross-sectional dimensions. Fixed effect and random effect models are explained and illustrated by way of examples on banking competition in the UK and on credit stability in Central and Eastern Europe. Entity fixed and time-fixed effects models are elucidated and distinguished. Chapter 11 The second new chapter describes various models that are appropriate for situations where the dependent variable is not continuous. Readers will learn how to construct, estimate and interpret such models, and to distinguish and select between alternative specifications. Examples used include a test of the pecking order hypothesis in corporate finance and the modelling of unsolicited credit ratings. Chapter 12 This presents an introduction to the use of simulations in econometrics and finance . Motivations are given for the use of repeated sampling, and a distinction is drawn between Monte Carlo simulation and bootstrapping .The reader is shown how to set up a simulation, and examples are given in options pricing and financial risk management to demonstrate the usefulness of these techniques. Chapter 13 This offers suggestions related to conducting a project or dissertation in empirical finance. It introduces the sources of financial and economic data available on the Internet and elsewhere, and recommends relevant online information and literature on research in financial markets and financial time series. The chapter also suggests ideas for what might constitute a good structure for a dissertation on this subject, how to generate ideas for a suitable topic, what format the report could take, and some common pitfalls. Chapter 14 This summarises the book and concludes. Several recent developments in the field, which are not covered elsewhere in the book, are also mentioned. Some tentative suggestions for possible growth areas in the modelling of financial time series are also given.
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Mathematics for Computer Graphics Greg Turk, August 1997 "What math should I learn in order to study computer graphics?" This is perhaps the most common general question that students ask me about computer graphics. The answer depends on how deeply you wish to go into the field. If you wish to begin to use off-the-shelf graphics programs then the answer is that you probably do not need to know very much math at all. If you wish to take an introductory course in computer graphics, then you should read the first two sections below for my recommendations (algebra, trigonometry and linear algebra). If you want some day to be a researcher in graphics then I believe that you should consider your mathematics education to be an ongoing process throughout your career. If you do not particularly care for mathematics, is there still a chance of working in the field? Yes, a few areas within computer graphics are not much concerned with mathematical ideas. You should not give up on graphics just because you are not a math wizard. It is likely, however, that you will have more freedom in choosing research topics if you have a willingness to learn about new mathematical ideas. There is no absolute answer to what mathematics is important in computer graphics. Different areas within the field require different mathematical techniques, and your own interests will likely lead you towards some topics and may never touch others. Below are descriptions of a number of areas in mathematics that I believe are useful in computer graphics. Do not feel that you need to be an expert in each of these areas to become a graphics researcher! I deliberately included many areas below to give a fairly broad view of the mathematical ideas used in graphics. Many researchers, however, will never find the need to look at some of the topics that I mention below. Finally, although it should be clear from reading this, the opinions given within this document are entirely my own. It is likely that you would get a different list of topics or at least different emphases from other people who work in computer graphics. Now on to the list of topics. Algebra and TrigonometryHigh-school level algebra and trigonometry are probably the most important areas to know in order to begin to learn about computer graphics. Just about every day I need to determine one or more unknowns from a simple set of equations. Almost as often I need to perform simple trigonometry such as finding the length of the edge of some geometric figure based on other lengths and angles. Algebra and trigonometry are the subjects that will solve such day-to-day tasks in computer graphics. What about the geometry that we learn in high school? It may come as a surprise, but our high school geometry is not very often needed for most tasks in computer graphics. The reason for this is that geometry as it is taught in many schools actually is a course in how to construct mathematical proofs. While proof construction is definitely a valuable intellectual tool, the actual theorems and proofs from your geometry class are not often used in computer graphics. If you go to graduate school in a mathematics related field (including computer graphics) then you may well find yourself proving theorems, but this is not necessary in order to start out in graphics. If you have a good understanding of algebra and trigonometry then you are quite prepared to begin reading an introductory book in computer graphics. Most such books contain at least an abbreviated introduction to the next important area of mathematics for computer graphics, namely linear algebra. Book recommendation: Computer Graphics: Principles and Practice James Foley, Andries van Dam, Steven Feiner, John Hughes Addison-Wesley Linear AlgebraThe ideas of linear algebra are used throughout computer graphics. In fact, any area that concerns itself with numerical representations of geometry often will collect together numbers such as x,y,z positions into mathematical objects called vectors. Vectors and a related mathematical object called a matrix are used all the time in graphics. The language of vectors and matrices is an elegant way to describe (among other things) the way in which an object may be rotated, shifted (translated), or made larger or smaller (scaled). Linear algebra is usually offered either in an advanced high school class or in college. Anyone who wishes to work in computer graphics should eventually get a solid grounding in this subject. As I mentioned before, however, many textbooks in graphics give a reasonable introduction to this topic-- often enough to get you through a first course in graphics. Book recommendation: Linear Algebra and Its Applications Gilbert Strang Academic Press CalculusKnowledge of calculus is an important part of advanced computer graphics. If you plan to do research in graphics, I strongly recommend getting a basic grounding in calculus. This is true not just because it is a collection of tools that are often used in the field, but also because many researchers describe their problems and solutions in the language of calculus. In addition, a number of important mathematical areas require calculus as a prerequisite. This is the one area in mathematics in addition to basic algebra that can open the most doors for you in computer graphics in terms of your future mathematical understanding. Calculus is the last of the topics that I will mention that is often introduced in high school. The topics to follow are almost always found in college courses. Differential GeometryThis area of mathematics studies equations that govern the geometry of smooth curves and surfaces. If you are trying to figure out what direction is perpendicular to (points directly away from) a smooth surface (the "normal vector") then you are using differential geometry. Making a vehicle travel at a particular speed along a curved path is also differential geometry. There is a common technique in graphics for making a smooth surface appear rough known as "bump mapping", and this method draws on differential geometry. If you plan to do work with curves and surfaces for shape creation (called "modeling" in the graphics field) then you should learn at least the basics of differential geometry. Multivariable calculus is the prerequisite for this area. Book recommendation: Elementary Differential Geometry Barrett O'Neill Academic Press Numerical MethodsAlmost every time we represent and manipulate numbers in the computer we use approximate instead of exact values, and because of this there is always the possibility for errors to creep in. Moreover, there are often many different approaches to solving a given numerical problem, and some methods will be faster, more accurate or require less memory than others. The study of these issues goes by a number of names including "numerical methods" and "scientific computing". This is a very broad area, and several of the other areas of mathematics that I will mention can be considered sub-areas underneath this umbrella. These sub-areas include sampling theory, matrix equations, numerical solution of differential equations, and optimization. Book recommendation: Numerical Recipes in C: The Art of Scientific Computing William Press, Saul Teukolsky, William Vetterling and Brian Flannery Cambridge University Press Sampling Theory and Signal ProcessingOver and over in computer graphics we represent some object such as an image or a surface as a collection of numbers that are stored in a regular two-dimensional array. Whenever we do this we are creating a "sampled" representation of the object. A good understanding of sampling theory is important if we are to use and to control the quality of such representations. A common issue in sampling as it applies to graphics is the jagged edges that can appear on the silhouette of an object when it is drawn on a computer screen. The appearance of such jagged edges (one form of a phenomenon known as "aliasing") is very distracting, and this can be minimized by using well-understood techniques from sampling theory. At the heart of sampling theory are concepts such as convolution, the Fourier transform, and spatial and frequency representations of functions. These ideas are also important in the fields of image and audio processing. Book recommendation: The Fourier Transform and Its Applications Ronald N. Bracewell McGraw Hill Matrix EquationsThere are a wide variety of problems that come up in computer graphics that require the numerical solution of matrix equations. Some problems that need matrix techniques include: finding the best position and orientation to match one object to another (one example of a "least squares" problem), creating a surface that drapes over a given collection of points with minimal creases (thin-plate splines), and simulation of materials such as water or cloth. Matrix formulations of problems come up often enough in graphics that I rank this area very high on my list of topics to know. Book recommendation: Matrix Computations Gene Golub and Charles Van Loan Johns Hopkins University Press PhysicsPhysics is obviously a field of study in its own right and not a sub-category of mathematics. Nevertheless, physics and mathematics are closely tied to one another in several areas within computer graphics. Examples of graphics problems that involve physics include how light interacts with the surfaces of objects, how light bounces around in a complex environment, the way people and animals move, and the motion of water and wind. Knowledge of physics is important for simulating all of these phenomena. This is closely tied to solving differential equations, which I shall discuss next. Numerical Solutions of Differential EquationsIt is my belief that techniques for solving differential equations are extremely important to computer graphics. As we just discussed, much of computer graphics is devoted to simulating physical systems from the real world. How waves form in water and how an animal walks across the ground are two examples of physical simulation. Simulation of physical systems very often leads to numerical solutions of differential equations. Note that this is actually very different than symbolic solutions to differential equations. Symbolic solutions are exact answers, and usually can be found only for extremely simple sets of equations. Sometimes a college course called "Differential Equations" will only examine symbolic solutions, and this will not help much for most computer graphics problems. In physical simulation, one breaks the world down into little pieces that are represented as large vectors. Then the relations between the parts of the world are captured in the entries in matrices. Solving the matrix equations that arise is not usually done exactly, but is instead performed by carrying out a long series of calculations that yields an approximate solution as a list of numbers. This is what numerical solutions of differential equations are about. Note that the solution of matrix equations is an intimate part of numerical solutions to differential equations. OptimizationQuite often in computer graphics we are looking for a description of an object or a collection of objects that satisfies some desired goal. Examples include looking for the positions of lights that give a certain "feeling" to how a room is lit, figuring out how an animated character can move its limbs to carry out a particular action, and positioning shapes and text on a page so that the result does not look cluttered. Each of these examples can be stated as an optimization problem. Ten years ago there was little in the graphics literature that made use of optimization techniques, but the field is using optimization more and more in recent work. I think that optimization will continue to play an increasingly important role in computer graphics. Probability and StatisticsThere are a number of areas within computer graphics that make use of probability and/or statistics. Certainly when researchers carry out studies using human subject, they require statistical methods in order to perform the analysis of the data. Graphics related areas that often make use of human subjects include Virtual Reality and Human-Computer Interaction (HCI). In addition, many computer descriptions of the real world involve using various probabilities that a given action will occur. The probability that a tree limb will branch during growth or that a synthetic animal will decide to walk in a particular direction are two examples of this. Finally, some techniques for solving difficult equations make use of random numbers to estimate their solutions. An important example of this is a class of techniques known as Monte Carlo methods that are often used to determine how light propagates in an environment. These are just a few of the ways that probability and statistics are used in computer graphics. Computational GeometryComputational geometry is the study of efficient ways to represent and manipulate geometry within the computer. Typical problems include testing whether two objects collide, deciding how to break up a polygon into triangles, and finding the nearest point in a group to a given location. This area is a blend of algorithms, data structures and mathematics. Researchers in graphics who work on creating shapes (modeling) draw heavily upon this area. Book recommendations: Computational Geometry in C Joseph O'Rourke Cambridge University Press Computational Geometry: An Introduction Franco Preparata and Michael Shamos Springer-Verlag Concluding Words: Applied and Pure MathematicsOne common thread to many of the mathematical topics that are associate with graphics is that they are from the applied side instead of the theoretical side of mathematics. This should not come as a surprise. Many of the problems in computer graphics are closely tied to problems that physicists and engineers have studied, and the mathematical tools of the physicist and of the engineer are overwhelmingly the tools that graphics researchers use. Most of the topics that make up theoretical ("pure") mathematics are seldom put to use in computer graphics. This should not be taken as an absolute truth, however. We should pay attention to examples from other fields: molecular biology is now drawing upon knot theory for the study of DNA dynamics, and subatomic physics makes use of abstract group theory. Who can tell when a "pure" mathematics topic will be put to use in computer graphics? There are a few areas of mathematics that seem as though they ought to be important and yet never really play a large part in computer graphics. Perhaps the most interesting of these areas is topology. The usual one-sentence description of topology is the study of why a doughnut and a coffee cup are the same. The answer is that they are both surfaces with one hole. Here we are talking about ideas from topology. Aren't surfaces a big part of computer graphics? Yes, but it turns out that most of the ideas in topology that are useful to graphics can be learned in a first course in differential geometry. Differential geometry studies the *shapes* of surfaces, whereas topology studies things such as which parts of a surface are next to which other parts. I have seen very little topology that is put to use in graphics, and I believe that this is because much of topology is concerned with rather abstract sets, and that much of topology is far removed from the concepts in three dimensional Euclidean space that is so central to most of graphics. There are times when the formalism of topology (the symbolic notation) is a convenient way to express ideas in graphics, but the actual tools from abstract topology so seldom play a role in graphics. Study this beautiful subject for its own sake, but don't expect an immediate payoff for graphics! I have been asked a few times whether either abstract algebra (group theory, rings, etc.) or number theory play a role in computer graphics. Not much that I have seen. These subjects, like topology, are areas that are full of beautiful ideas. Unfortunately these ideas seldom find their way into computer graphics.
General form, INDEX function: INDEX( source,excerpt ) where source specifies the character variable or expression to search excerpt specifies a character string that is enclosed in quotation marks (' '). 可以用来挑选包含字符串的数据集子集 data hrd.datapool; set hrd.temp; if index(job,'word processing') 0; run;
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