Mathematical description

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  • This book is intended for graduate students, researchers, and reservoir engineers who want to understand the mathematical description of the chromatographic mechanisms that are the basis for gas injection processes for enhanced oil recovery. Readers familiar with the calculus of partial derivatives and properties of matrices (including eigenvalues and eigenvectors) should have no trouble following the mathematical development of the material presented.

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  • This report is based on a process of the same name is given at Stanford University in fall quarter, 1987. Below is a description of stores: CS 209. Write the text matter of mathematical techniques and effective presentation of mathematics and computer science. A term paper on a topic of your choice, this paper may be used for credit in another course.

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  • Although much of its discovery process is descriptive and qualitative, chemistry is fundamentally a quantitative science. It serves a wide range of human needs, activities, and concerns. The mathematical sciences provide the language for quantitative science, and this language is growing in many directions as computational science in general continues its rapid expansion. A timely opportunity now exists to strengthen and increase the beneficial impacts of chemistry by enhancing the interaction between chemistry and the mathematical sciences.

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  • Algebra is a wonderful tool for testing and predicting our understanding of the world. The Xs, Ys and Zs in the algebra mean something real. Algebra lets us take a word description of the world and change it into a mathematical description which is really useful. Clothing designers use algebra to work out how best to cut cloth, engineers use algebra to design cars, boats and aeroplanes and the next generation of medicines customised to our genetic individuality will use algebra. Plumbers and carpet fitters use algebra to work out how to cut pipes or carpets to fit a space...

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  • .HWEI P. HSU is Professor of Electrical Engineering at Fairleigh Dickinson University. He received his B.S. from National Taiwan University and M.S. and Ph.D. from Case InsThe concept and theory of signals and systems are needed in almost all electrical engineering fields and in many other engineering and scientific disciplines as well. In this chapter we introduce the mathematical description and representation of signals and systems and their classifications. We also define several important basic signals essential to our studies.titute of Technology.

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  • The concept and theory of signals and systems are needed in almost all electrical engineering fields and in many other engineering and scientific disciplines as well. In this chapter we introduce the mathematical description and representation of signals and systems and their classifications. We also define several important basic signals essential to our studies.

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  • Before entering into the different techniques of optical metrology some basic terms and definitions have to be established. Optical metrology is about light and therefore we must develop a mathematical description of waves and wave propagation, introducing important terms like wavelength, phase, phase fronts, rays, etc. The treatment is kept as simple as possible, without going into complicated electromagnetic theory.

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  • We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast incompressible flow. Our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small in an arbitrarily short time, provided that the flow amplitude is large enough. The necessary and sufficient condition on such flows is expressed naturally in terms of the spectral properties of the dynamical system associated with the flow. In particular, we find that weakly mixing flows always enhance dissipation in this sense. ...

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  • Moir´ Methods. Triangulation e Figure 3.2 is an illustration of two interfering plane waves. Let us look at the figure for what it really is, namely two gratings that lie in contact, with a small angle between the grating lines. As a result, we see a fringe pattern of much lower frequency than the individual gratings. This is an example of the moir´ effect and the resulting fringes are e called moir´ fringes or a moir´ pattern. Figures 3.4, 3.8 and 3.9 are examples of the same e e effect. The mathematical description of moir´ patterns resulting from the superposition e...

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  • Introduction: Most electrochemical reactions take place at the interface of two or more phases. Hence the area of reaction plays a vital role in determining the efficiency of an electrochemical process, just like in any surface reaction. There are several ways to increase the available area for reaction in an electrochemical cell: multiple electrodes are stacked alternatively, bipolar electrodes are used, and, sometimes, the reaction surface is modified by etching or coating with large surface area particles. ...

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  • There are few physical phenomena so generally studied which are as misunderstood as the phenomenon of flight. Over the years many books have been written about flight and aeronautics (the science of flight). Some books are written for training new aeronautical engineers, some for pilots, and some for aviation enthusiasts. Books written to train engineers often quickly delve into complicated mathematics, which is very useful for those who wish to make detailed calculations.

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  • In this paper we introduce a method for partial description of the Poisson boundary for a certain class of groups acting on a segment. As an application we find among the groups of subexponential growth those that admit nonconstant bounded harmonic functions with respect to some symmetric (infinitely supported) measure µ of finite entropy H(µ). This implies that the entropy h(µ) of the corresponding random walk is (finite and) positive. As another application we exhibit certain discontinuity for the recurrence property of random walks. ...

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  • The goal of this paper is to describe all closed, aspherical Riemannian manifolds M whose universal covers M have a nontrivial amount of symmetry. By this we mean that Isom(M ) is not discrete. By the well-known theorem of Myers-Steenrod [MS], this condition is equivalent to [Isom(M ) : π1 (M )] = ∞. Also note that if any cover of M has a nondiscrete isometry group, then so does its universal cover M . Our description of such M is given in Theorem 1.2 below. The proof of this theorem uses methods from Lie theory, harmonic maps,...

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  • Having discussed individual components of industrial servo drives from an operation point of view and a mathematical descriptive point of view, the next step is to combine these components into a block diagram for the complete servo drive. The block diagram is a powerful method of system analysis. In the block diagram each component in a servo system can be described by the ratio of its output to input. Thus the output of one component is the input to the next component.

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  • Such jobs would then be gone, to be replaced by jobs requiring much more sophisticated mathematical training. The mathematics needed for these machines, as was case with engines, has been the main impediment to actual wide-scale implementation of such robotic mechanisms. Recently, it has become clear that the key mathematics is available, (the mathematics of algebraic and geometric topology, developed over the last 80 - 90 years), and we have begun to make dramatic progress in creating the programs needed to make such machines work.

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  • Physical theories allow us to make predictions: given a complete description of a physical system, we can predict the outcome of some measurements. This problem of predicting the result of measurements is called the modelization problem, the simulation problem, or the forward problem. The inverse problem consists of using the actual result of some measurements to infer the values of the parameters that characterize the system. While the forward problemhas (in deterministic physics) a unique solution, the inverse problem does not.

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  • Mathematical modelling is the process of formulating an abstract model in terms of mathematical language to describe the complex behaviour of a real system. Mathematical models are quantitative models and often expressed in terms of ordinary differential equations and partial differential equations. Mathematical models can also be statistical models, fuzzy logic models and empirical relationships. In fact, any model description using mathematical language can be called a mathematical model.

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  • Characteristic cohomology classes, defined in modulo 2 coefficients by Stiefel [26] and Whitney [28] and with integral coefficients by Pontrjagin [24], make up the primary source of first-order invariants of smooth manifolds. When their utility was first recognized, it became an obvious goal to study the ways in which they admitted extensions to other categories, such as the categories of topological or PL manifolds; perhaps a clean description of characteristic classes for simplicial complexes could even give useful computational techniques.

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  • The goal of this work is to give a precise numerical description of the K¨hler cone of a compact K¨hler manifold. Our main result states that the a a K¨hler cone depends only on the intersection form of the cohomology ring, the a Hodge structure and the homology classes of analytic cycles: if X is a compact K¨hler manifold, the K¨hler cone K of X is one of the connected components of a a the set P of real (1, 1)-cohomology classes {α} which are numerically positive on analytic cycles, i.e. Y αp 0 for every irreducible analytic...

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  • The space of embedded minimal surfaces of fixed genus in a 3-manifold II; Multi-valued graphs in disks By Tobias H. Colding and William P. Minicozzi II* 0. Introduction This paper is the second in a series where we give a description of the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R3 . We show here that if the curvature of such a disk...

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