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On Some Chaotic Complex Nonlinear Systems

für 53.10€ kaufen ···· Rheinberg-Buch.de - Bücher, eBooks, DVD & Blu-ray
The study of chaotic complex nonlinear systems has become a subject of great interest during the last 30 years. The aim of this thesis is to introduce and study some chaotic complex nonlinear dynamical systems, for example, complex Chen and Lü systems . There are interesting cases of dynamical systems, where the main variables participating in the dynamics are complex, for example, when amplitudes of electromagnetic fields of laser systems are involved. Another example is when chaos synchronization is used for communications, where doubling the number of variables may be used to increase the content and security of the transmitted information. This monograph is mainly addressed to graduate students and senior researchers interested in the study of complex nonlinear systems. ····· 10361101857

BAND-LIMITED EXTRAPOLATION BY REGULARIZATION

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In this paper a regularized spectral estimation formula and a regularized iterative algorithm for band-limited extrapolation are presented. The ill-posedness of the problem is taken into account. First a Fredholm equation is regularized. Then it is transformed to a differential equation in the case where the time interval is {bf R}. A fast algorithm to solve the differential equation by the finite differences is given and a regularized spectral estimation formula is obtained. Then a regularized iterative extrapolation algorithm is introduced and compared with the Papoulis and Gerchberg algorithm. A time-frequency regularized extrapolation algorithm is presented in the two-dimensional case. The Gibbs phenomenon is analyzed. Then the time-frequency regularized extrapolation algorithm is applied to image restoration and compared with other algorithms. ····· 10361101835

Heteroclinic cycles in thermal convection models

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This book presents a global bifurcation study of a four-dimensional system of differential equations modeling the Rayleigh-Bernard convection. The Rayleigh and Prandtl numbers are two natural parameters on which the system depends. The investigation of the model proceeds through a combination of theoretical analysis and numerical computations. There are local bifurcations, corresponding to changes in stability of steady patterns, but the main changes are governed by curves of global bifurcations involving homoclinic and heteroclinic dynamics. A numerical investigation identifies codimension-two global bifurcations that organize the bifurcation diagram. Bifurcation analysis makes clear the unfolding of these bifurcations. The book is extracted from the doctoral thesis to the Unviversity of Amsterdam, under supervision of Dr. Ale Jan Homburg. ····· 10361101771

Introduction to Discontinuous Dynamical Systems

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The topics of this book are dynamical behaviour of a class of discontinuous maps including piecewise linear maps on the 2-torus and planar piecewise isometries, some preliminary symbolic dynamics approach to these maps, and some aspects of symbolic dynamics itself. At first, a class of piecewise linear parabolic maps on the torus are discussed. Then some area-preserving piecewise linear discontinuous maps of the plane are examined. Symbolic descriptions of the dynamics and admissibility conditions for itineraries of a class of linear maps on the 2-torus and some planar piecewise isometries are discussed. For the symbolic dynamical system itself, scrambled sets of shift maps are discussed, and some problems related to maximal scrambled sets are also discussed. For the subshifts generated by the orbit closures of certain non-periodic recurrent points, their chaotic properties are investigated. Moreover, a general and systematic discussion of various symbolic representations of iterated maps through subshifts are presented, and examples of partitions and representations of some discontinuous maps are given. ····· 10361101599

Teaching Learning Concepts in Calculus

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Calculus is a get way to higher order mathematics. In most countries calculus is introduced as a process involving infinitely many steps which is a paradigm shift to students as their pre-calculus concept involves finite logical steps to solve a problem. This book consist the study examining students difficulties and misconceptions in learning concepts of calculus at preparatory secondary schools. Accordingly, students conception of concepts in calculus, students misconceptions, and factors influencing the teaching-learning of concepts were surveyed. Documentaries, classroom observation, and achievement test were the instruments used for gathering the necessary data.The book has a potential benefit to mathematics teachers in that it provides them information about their students possible misconceptions. Over generalizing a limit just as a function value, the perception that a function must be defined at a point to have a limit at that point, and that a discontinuous function must have an asymptote were identified as misconceptions students have formed. ····· 10361101559

Generalized Fuzzy Topographic Topological Mapping

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Fuzzy Topographic Topological Mapping (FTTM) is a model for solving neuromagnetic inverse problem. FTTM consists of four topological spaces which are connected by three homeomorphisms. FTTM 1 and FTTM 2 were designed to present 3-D view of an unbounded single current and bounded multicurrent sources, respectively. It has been showed that FTTM 1 and FTTM 2 are homeomorphic and this homeomorphism will generate another 14 FTTM. There is a conjecture stated that if there exist n numbers of FTTM, then they will generate another new FTTM. In this book, the conjecture is proven by using geometrical features of FTTM. In the process, several definitions are developed. Some geometrical and algebraic properties of sequences of FTTM are identified and proven. A new conjecture is also proposed in this book. Surprisingly, the nonzero sequence of cube with combination of two, three and four FTTM appeared in Pascal s Triangle. ····· 10361101491

Flows in Graphs and Related Problems

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Flows in graphs present a basis for solving many problems in modern mathematics, having applications in practice and significant theoretical impact in various areas on discrete mathematics, such as graph coloring, labeling, covering of graphs, matroid theory, combinatorial optimization, and statistical physics. In the book are considered several theoretical aspects of flows in graphs. The results are divided into three parts. In the first part, nowhere-zero group- and integer-valued flows are studied, together with related areas regarding snarks and graph colorings. The second part contains results about cycle double coverings of graphs, hamiltonian cycles and dominating cycles. The last part is devoted to flows in combinatorial optimization and some related areas from transversal theory and latin squares. The work was presented as DSc. Thesis in the Academy of Sciences of Czech Republic. It can be useful for advanced students and researchers interested in combinatorics and graph theory. ····· 10361101357

FUZZY SIMILARITY MEASURES

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Similarity is a basic concept in in many research areas such as biology, chemistry, image retrieval, information retrieval, machine learning, psychology, cluster analysis, data mining, statistics etc. To make a general purpose definition of similarity measure as a mathematical concept is still a challenging task. Reflexivity and Symmetry are accepted as fundamental properties of similarity measures whreas there is a lack of consensus on the axioms of Monotonicity or Transitivity. In this monograph we focus on the study of relationship between concept of monotonicity of the fuzzy similarity relations with the concept of strong and weak fuzzy transitivity. ····· 10361101345

Qualitative Study of Nonlinear Difference Equations

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We establish a global convergence result for the higher order difference equation where k is a positive integer and are positive initial conditions and then apply this result to show that, under appropriate hypotheses, every positive solution of the difference equation, converges to a period p solution, where the period p is easily determined in terms of the coefficients. Also we present some known results and derive several new ones on the boundedness and the global stability of the solutions of the difference equation We study the global stability, the boundedness nature, and the periodic character of the positive solutions of the difference equation which is interesting in its own right, but which may also be viewed as describing a population model. We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument of the form. ····· 10361101274

Prospective teachers learning mathematics trough mathematical modeling

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When prospective teachers are engaged in mathematical modeling, a third silent partner - the computer - always plays a role in the didactical contract. It is hard to argue against a solution which was delivered from a computer software. Many students accept and interpret quite useless results from a model which has been used wrongly or been selected by wrong assumptions. This book will give examples from three different but consecutive studies on how prospective teachers learn mathematics through mathematical modeling. ····· 10361101179

Multiscale Finite Element Methods For Second Order Elliptic BVPs

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In this book the convergence of the multiscale finite element method (MsFEM) for second order elliptic equations with oscillating coefficient in two space dimension is studied. Such equations often arise in composite materials and flows in porous media. The main purpose is to understand the theoretical background of this method and its convergence analysis. The oscillating coefficient is assumed to be of two scales and is periodic in the large scale. The MsFEM is capable of correctly capturing the large scale components of the solution on a coarse grid without accurately resolving all the small scale features in the solution. This is accomplished by incorporating the local microstructure of the differential operator into the finite element base functions. As a consequence, the base functions are adapted to the local properties of the differential operator. ····· 10361101135

Introduction to New Geometric Approaches in Finance

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This book unlocks the door to many major questions regarding modeling and forecasting in finance. We propose new static and dynamic geometric approaches to financial indicators, credit risk and bankruptcy measurements. The book will be a useful reference for researchers and practitioners in business and finance facing risk management, market ranking modeling and analysis of credit risk and bankruptcy. The book is also useful text of new modeling approach for static and dynamic measurements in science, technology and engineering. ····· 10361101059

Rabin style speed-up of proofs

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One of the main problems of quantitative study of proofs is speed-up phenomenon, that is a situation, where two systems are compared such that some theorems have much shorter proof in one of them. For the first time such problem on the proof steps was considered for arithmetical systems by Gödel. Now many results in this field are well-known. In all of them by comparison of two systems for every recursive function can be pointed one formula or infinite set of formula, which has speed-up. We introduce the common notion of proof complexity (by analogy to Blum computational complexity), the notion of ordinary theory and formulate some conditions for any pair of theory, which are enough for possibility of the most generalized (Rabin style) speed-up, i.e. for arbitrary general recursive function there exists n0 such that for every nn0 there is provable in both theories formula n such that its proof complexity in stronger theory is no more than n and in the weaker theory is greater than (n). Many pair systems with above conditions are considered as well as the constructive description of hard provable formulas for some pair systems is given. ····· 10361100988

GALERKIN BOUNDARY INTEGRAL ANALYSIS OF THE GRAD-SHAFRANOV EQUATION

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Galerkin Boundary Element Method(GBEM) is a powerful technique to solve partial differential equations. In this work the method is presented by solving the axisymmetric Laplace`s equation. Later the Grad-Shafranov Equation(GSE) is solved by means of this powerful technique. The GSE is a simplification of ideal MHD in two dimensions. The resulting equation is a nonlinear, elliptic partial differential equation. The GBEM is well suited for solving this type of equations in `irregular domains` such as unbounded and irregular shape domains. ····· 10361100934

Large Deviations Analysis to the Performance of Distributed Detection

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This book studies the performance of distributed detection systems by means of large deviation techniques under two distinct models. In the first model, the error performance is investigated as the number of sensors tends to infinity by assuming that the i.i.d. sensor data are quantized locally into m-ary messages and transmitted to the fusion center for binary hypothesis testing. It is found that when the second moment of the post-quantization log-likelihood ratio is unbounded, the Neyman-Pearson error exponent becomes a function of the test level whereas the Bayes error exponent remains unaffected. Also shown is that in Bayes testing, the equivalence of absolutely optimal and best identical-quantizer systems is not limited to error exponents but extends to the actual Bayes errors up to a multiplicative constant. In the second model, the null and alternative distributions become spatially correlated Gaussian, differing in the mean. The issue considered includes whether contiguous marginal likelihood ratio quantizers are optimal. It is shown that this is not true in general, and a sufficient condition is obtained under the case of a single observation per sensor. ····· 10361100746

Besov spaces on fractals

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A physical state in a domain is often described by a model containing a linear partial differential equation. As an example of this, consider the steady state temperature distribution in a homogenous isotropic body. The problem, called Dirichlet`s problem, is to find a function u, given that u=f in the interior of the body and u=g on the surface (where u denotes the laplacian of u). The solution depends on f and g, but also on the geometry of the surface S. If the given functions f and g, as well as the subset S of 3-space, are smooth enough, then there exists a unique solution. However, since there are numerous non-smooth structures in nature, it is clear that the study of Dirichlet`s problem in the case when f, g and S are less smooth becomes an important task. Function spaces defined on subsets of n-space originates from the study of Dirichlet`s problem in the non-smooth case of f, g and S. An important class of functions in this respect are Besov spaces, defined in n-space in the 60`s. In the 80`s Besov spaces were extended to d-sets, typically fractal sets with non-integer local dimension d. In this book we extend Besov space theory to sets with varying local dimension. ····· 10361100712

Mathematical Modeling of Traffic Flow

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Mathematical modeling of traffic flow deals with the development of a new higher order anisotropic continuum model for highway traffic flow. The model comprises a system of two nonlinear partial differential equations. The work has been compiled in the form of seven chapters with each chapter focusing on the development of traffic flow model towards real world. Some qualitative properties together with linear stability analysis have been studied. Motivated by the importance of traffic modeling, in this book a series of flow situations to uncover some of the fundamental aspects of traffic flow are examined. Finite difference method is used as a tool to solve the governing system of highly nonlinear partial differential equations. Numerical solutions so obtained are analysed and interpreted physically. The results are displayed in form of graphs. The mathematical software Matlab (version 7.0) together with programming software C++ is heavily used for algebraic and numerical computations throughout the book. ····· 10361100638

Some Fixed Point Theorems and Their Applications

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The notion of Banach operator pair is used as a new class of noncommuting maps. The common fixed point theorems for Banach operator pair have been proved. The concept of g-nonexpansive, g-asymptotically nonexpansive, asymptotically regular, p-starshaped sets have been used. An attempt has been made to obtain the best approximation to the common fixed point of Banach operator pair.The concept of orbital continuity has been used to obtain the existence of common fixed points of Banach operator pair. Generalized contractive type condition for three mappings is defined and obtained some common fixed point results for these mappings. Some applications of fixed point theory to functional difference equation are given. The existence of solutions to boundary value problems of functional difference equation between its lower and upper solutions is obtained. The Schauder s fixed point theorem has been used in proving the existence of solution. Using maximum principles the existence of extremal solutions of fourth order BVP of functional difference equations between its lower and upper solutions are obtained. ····· 10361100331

Engineering Mathematics

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Engineering Mathematics is crucial to all aspects of engineering and technology, the understanding of which is necessary for every engineering student. The present book highlights the developments concerned with the engineering mathematics and the material is so structured that the ordinary students build up their knowledge and understanding gradually. The interactive examples have been carefully designed to encourage students to engage fully in the problem-solving process. ····· 10361100302

Affine Elastic Curves in R^2 and R^3

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This book is devoted to the study of the variational properties of affine curves invariant under centroaffine transformations or equiaffine transformations in two and three-dimensional affine space. It can be considered as a counterpart of the study of the classical Euclidean elastic curves. The basic idea here is to replace the Euclidean space with an affine space. We try to develop some properties about the affine curve which is invariant under some specific subgroups of the affine groups A(2) and A(3). We consider the critial curves of the curvature energy functionals related to the affine curvature or centroaffine curvature of the nondegenerate curve or starlike curve repectively. We completely solve the motion equation by using the Jacobi elliptic functions and finally solve the structure equation by using Killing fields and the classification of the special linear group for the starlike curves. ····· 10361100262

A History of the Theory of Types

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This work traces the development of the theory of types from its origins in the early 20th century through its various forms until the mid 1950s. Attention is paid to the reception of this theory after the publication of the second edition of Whitehead and Russell s `Principia Mathematica`. I examine the decline of the theory over four decades, focusing on its modification by logicians such as Ramsey, Carnap, Church, Quine, Gödel, and Tarski. Finally, the view of the theory of types as a many-sorted first-order theory is discussed. It is shown that a revival of the ramified theory of types in the 1950s coincided with the consideration of cumulative type hierarchies which substantially altered the form of the theory. The theory was altered even more drastically in its change from a many-sorted theory to a one-sorted theory. This final standardization made it not much different from first-order Zermelo-Fraenkel set-theory. The theory of types, whose developments are traced in this work, therefore lost its prominence as the foundation for mathematics and logic. This historical analysis will be of interest primarily to those working in the History and Philosophy of Mathematics. ····· 10361100250

A Study on Intuitionistic Fuzzy Matrices

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This monogram is so written that it is self contained for independent study as well and hope it very much useful for cognition of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy set, generalized intuitionistic fuzzy sets, generalized interval-valued intuitionistic fuzzy sets, generalized intuitionistic fuzzy matrices, generalized interval-valued intuitionistic fuzzy matrices and neutrosophic intuitionistic fuzzy sets. The arrangement and presentation is simple. The chapters are arranged in logical order. The theorems and propositions have been stated carefully and whenever necessary complete proofs of the theorems and propositions have been given. Also numerical examples are given for concretization of the theorems and propositions. It is hope that the readers will benefit immensely from this monogram. ····· 10361100189

Development of Some Lacunary Interpolation by S. F. and Application

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The aim of this thesis was the development of the study of lacunary interpolation by spline functions and their applications by changed the boundary condition for quantic and sixtic spline functions, and the algorithm was used to find the new absolute error between the original function and the spline function, and also the error bounded between the derivatives of original function and the derivatives of spline functions. Firstly, the object of this work is to show that the change of the boundary conditions and the class of spline functions have effect on minimizing error bounds theoretically and practically, and for application, the )NEB( algorithm was used. Secondly, in this study, (0, 4) lacunary interpolation was generalized by quantic spline function to obtain, the existence, uniqueness, and error bounds for the generalized (0, 4) lacunary interpolation by quantic spline. Finally, the lacunary interpolation problem consisted of finding the sixth degree spline of deficiency four, interpolating the data given on the function value with first and fourth order in the interval [0,1]. Also, an extra initial condition was prescribed on the second derivative of the functions. ····· 10361100004

Mathematical Modelling of Dispersion of Atmospheric Aerosols

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The growth of population, indiscriminate establishment of industries, auto-mobiles etc., are some of the major causes for the atmospheric pollution, besides power shortage. There is a growing concern that pollution together with accelerated growth and development of nations may alter the climate due to the release of large amount of soot, carbon emission and other pollutants into the atmosphere in the form of ultra-fine dust particles which are suspended in the atmosphere called aerosols. They play an important role in the atmospheric processes favouring cloud formation due to large size aerosols and having adverse effects on health, depending on their size due to coagulation process. This book focuses on mathematical modelling of dispersion of aerosols in the presence/absence of electric field and first order chemical reaction using different dispersion models. The problems addressed here are representative of aerosol removal mechanisms. In order to keep the environmental problems mathematically tractable few simplifying assumptions have been made to the extent that they do not obscure the actual phenomena which was purportedly modelled in a restrictive yet representative sense. ····· 1036199981

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