Mathematical Modeling Of Random And Deterministic Phenomena

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Mathematical Modeling of Random and Deterministic Phenomena

Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone
Mathematical Modeling of Random and Deterministic Phenomena Book PDF

Author : Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone
Publisher : John Wiley & Sons
Page : 308 pages
File Size : 46,6 Mb
Release : 2020-04-28
Category : Mathematics
ISBN : 9781786304544

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Mathematical Modeling of Random and Deterministic Phenomena by Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone Pdf

This book highlights mathematical research interests that appear in real life, such as the study and modeling of random and deterministic phenomena. As such, it provides current research in mathematics, with applications in biological and environmental sciences, ecology, epidemiology and social perspectives. The chapters can be read independently of each other, with dedicated references specific to each chapter. The book is organized in two main parts. The first is devoted to some advanced mathematical problems regarding epidemic models; predictions of biomass; space-time modeling of extreme rainfall; modeling with the piecewise deterministic Markov process; optimal control problems; evolution equations in a periodic environment; and the analysis of the heat equation. The second is devoted to a modelization with interdisciplinarity in ecological, socio-economic, epistemological, demographic and social problems. Mathematical Modeling of Random and Deterministic Phenomena is aimed at expert readers, young researchers, plus graduate and advanced undergraduate students who are interested in probability, statistics, modeling and mathematical analysis.

Theory and Simulation of Random Phenomena

Ettore Vitali,Mario Motta,Davide Emilio Galli
Theory and Simulation of Random Phenomena Book PDF

Author : Ettore Vitali,Mario Motta,Davide Emilio Galli
Publisher : Springer
Page : 235 pages
File Size : 52,5 Mb
Release : 2018-06-13
Category : Science
ISBN : 9783319905150

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Theory and Simulation of Random Phenomena by Ettore Vitali,Mario Motta,Davide Emilio Galli Pdf

The purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.

Probability and Partial Differential Equations in Modern Applied Mathematics

Edward C. Waymire
Probability and Partial Differential Equations in Modern Applied Mathematics Book PDF

Author : Edward C. Waymire
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 49,9 Mb
Release : 2010-06-14
Category : Mathematics
ISBN : 9780387293714

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Probability and Partial Differential Equations in Modern Applied Mathematics by Edward C. Waymire Pdf

"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations. This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.

Engineering Fluid Dynamics

C. Kleinstreuer
Engineering Fluid Dynamics Book PDF

Author : C. Kleinstreuer
Publisher : Cambridge University Press
Page : 562 pages
File Size : 41,7 Mb
Release : 1997-02-28
Category : Science
ISBN : 0521496705

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Engineering Fluid Dynamics by C. Kleinstreuer Pdf

A practical approach to the study of fluid mechanics at the graduate level.

An Introduction to Stochastic Modeling

Howard M. Taylor,Samuel Karlin
An Introduction to Stochastic Modeling Book PDF

Author : Howard M. Taylor,Samuel Karlin
Publisher : Academic Press
Page : 410 pages
File Size : 44,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269276

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An Introduction to Stochastic Modeling by Howard M. Taylor,Samuel Karlin Pdf

An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Mathematics of Random Phenomena

P. Krée,C. Soize
Mathematics of Random Phenomena Book PDF

Author : P. Krée,C. Soize
Publisher : Springer
Page : 438 pages
File Size : 43,9 Mb
Release : 2012-03-08
Category : Science
ISBN : 9400947712

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Mathematics of Random Phenomena by P. Krée,C. Soize Pdf

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.

Mathematical Models in Cell Biology and Cancer Chemotherapy

M. Eisen
Mathematical Models in Cell Biology and Cancer Chemotherapy Book PDF

Author : M. Eisen
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 41,8 Mb
Release : 2013-03-13
Category : Mathematics
ISBN : 9783642931260

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Mathematical Models in Cell Biology and Cancer Chemotherapy by M. Eisen Pdf

The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and drug models can be used to study the effects of different methods of administering drugs. The least harmful method of drug administration, according to a given criterion, can be found by applying optimal control theory. The prerequisites for reading this book are an elementary knowledge of ordinary differential equations, probability, statistics, and linear algebra. In order to make this book self-contained, a chapter on cell biology and a chapter on control theory have been included. Those readers who have had some exposure to biology may prefer to omit Chapter I (Cell Biology) and only use it as a reference when required. However, few biologists have been exposed to control theory. Chapter 7 provides a short, coherent and comprehensible presentation of this subject. The concepts of control theory are necessary for a full understanding of Chapters 8 and 9.

Mathematics and Philosophy 2

Daniel Parrochia
Mathematics and Philosophy 2 Book PDF

Author : Daniel Parrochia
Publisher : John Wiley & Sons
Page : 276 pages
File Size : 53,9 Mb
Release : 2023-04-14
Category : Mathematics
ISBN : 9781394209378

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Mathematics and Philosophy 2 by Daniel Parrochia Pdf

From Pythagoreans to Hegel, and beyond, this book gives a brief overview of the history of the notion of graphs and introduces the main concepts of graph theory in order to apply them to philosophy. In addition, this book presents how philosophers can use various mathematical notions of order. Throughout the book, philosophical operations and concepts are defined through examining questions relating the two kinds of known infinities – discrete and continuous – and how Woodin's approach can influence elements of philosophy. We also examine how mathematics can help a philosopher to discover the elements of stability which will help to build an image of the world, even if various approaches (for example, negative theology) generally cannot be valid. Finally, we briefly consider the possibilities of weakening formal thought represented by fuzziness and neutrosophic graphs. In a nutshell, this book expresses the importance of graphs when representing ideas and communicating them clearly with others.

Traditional Functional-Discrete Methods for the Problems of Mathematical Physics

Volodymyr Makarov,Nataliya Mayko
Traditional Functional Discrete Methods for the Problems of Mathematical Physics Book PDF

Author : Volodymyr Makarov,Nataliya Mayko
Publisher : John Wiley & Sons
Page : 282 pages
File Size : 42,7 Mb
Release : 2024-02-23
Category : Science
ISBN : 9781394276653

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Traditional Functional-Discrete Methods for the Problems of Mathematical Physics by Volodymyr Makarov,Nataliya Mayko Pdf

This book is devoted to the construction and study of approximate methods for solving mathematical physics problems in canonical domains. It focuses on obtaining weighted a priori estimates of the accuracy of these methods while also considering the influence of boundary and initial conditions. This influence is quantified by means of suitable weight functions that characterize the distance of an inner point to the boundary of the domain. New results are presented on boundary and initial effects for the finite difference method for elliptic and parabolic equations, mesh schemes for equations with fractional derivatives, and the Cayley transform method for abstract differential equations in Hilbert and Banach spaces. Due to their universality and convenient implementation, the algorithms discussed throughout can be used to solve a wide range of actual problems in science and technology. The book is intended for scientists, university teachers, and graduate and postgraduate students who specialize in the field of numerical analysis.

Disorder and Critical Phenomena Through Basic Probability Models

Giambattista Giacomin
Disorder and Critical Phenomena Through Basic Probability Models Book PDF

Author : Giambattista Giacomin
Publisher : Springer Science & Business Media
Page : 140 pages
File Size : 51,5 Mb
Release : 2011-07-16
Category : Language Arts & Disciplines
ISBN : 9783642211553

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Disorder and Critical Phenomena Through Basic Probability Models by Giambattista Giacomin Pdf

Understanding the effect of disorder on critical phenomena is a central issue in statistical mechanics. In probabilistic terms: what happens if we perturb a system exhibiting a phase transition by introducing a random environment? The physics community has approached this very broad question by aiming at general criteria that tell whether or not the addition of disorder changes the critical properties of a model: some of the predictions are truly striking and mathematically challenging. We approach this domain of ideas by focusing on a specific class of models, the "pinning models," for which a series of recent mathematical works has essentially put all the main predictions of the physics community on firm footing; in some cases, mathematicians have even gone beyond, settling a number of controversial issues. But the purpose of these notes, beyond treating the pinning models in full detail, is also to convey the gist, or at least the flavor, of the "overall picture," which is, in many respects, unfamiliar territory for mathematicians.

Modeling with Stochastic Programming

Alan J. King,Stein W. Wallace
Modeling with Stochastic Programming Book PDF

Author : Alan J. King,Stein W. Wallace
Publisher : Springer
Page : 0 pages
File Size : 40,7 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 3031545494

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Modeling with Stochastic Programming by Alan J. King,Stein W. Wallace Pdf

This is an updated version of what is still the only text to address basic questions about how to model uncertainty in mathematical programming, including how to reformulate a deterministic model so that it can be analyzed in a stochastic setting. This second edition has important extensions regarding how to represent random phenomena in the models (also called scenario generation) as well as a new chapter on multi-stage models. This text would be suitable as a stand-alone or supplement for a second course in OR/MS or in optimization-oriented engineering disciplines where the instructor wants to explain where models come from and what the fundamental modeling issues are. The book is easy-to-read, highly illustrated with lots of examples and discussions. It will be suitable for graduate students and researchers working in operations research, mathematics, engineering and related departments where there is interest in learning how to model uncertainty. Alan King is a Research Staff Member at IBM's Thomas J. Watson Research Center in New York. Stein W. Wallace is a Professor of Operational Research and head of Center for Shipping and Logistics at NHH Norwegian School of Economics, Bergen, Norway.

Focus on Probability Theory

Louis R. Velle
Focus on Probability Theory Book PDF

Author : Louis R. Velle
Publisher : Nova Publishers
Page : 212 pages
File Size : 48,8 Mb
Release : 2006
Category : Mathematics
ISBN : 1594544743

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Focus on Probability Theory by Louis R. Velle Pdf

Probability theory is the mathematical theory of random (non-deterministic) phenomena. This book presents the latest research in the field.

Introductory Statistics and Random Phenomena

Manfred Denker,Wojbor Woyczynski
Introductory Statistics and Random Phenomena Book PDF

Author : Manfred Denker,Wojbor Woyczynski
Publisher : Birkhäuser
Page : 509 pages
File Size : 49,8 Mb
Release : 2017-09-16
Category : Computers
ISBN : 9783319661520

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Introductory Statistics and Random Phenomena by Manfred Denker,Wojbor Woyczynski Pdf

This textbook integrates traditional statistical data analysis with new computational experimentation capabilities and concepts of algorithmic complexity and chaotic behavior in nonlinear dynamic systems. This was the first advanced text/reference to bring together such a comprehensive variety of tools for the study of random phenomena occurring in engineering and the natural, life, and social sciences. The crucial computer experiments are conducted using the readily available computer program Mathematica® Uncertain Virtual WorldsTM software packages which optimize and facilitate the simulation environment. Brief tutorials are included that explain how to use the Mathematica® programs for effective simulation and computer experiments. Large and original real-life data sets are introduced and analyzed as a model for independent study. This is an excellent classroom tool and self-study guide. The material is presented in a clear and accessible style providing numerous exercises and bibliographical notes suggesting further reading. Topics and Features Comprehensive and integrated treatment of uncertainty arising in engineering and scientific phenomena – algorithmic complexity, statistical independence, and nonlinear chaotic behavior Extensive exercise sets, examples, and Mathematica® computer experiments that reinforce concepts and algorithmic methods Thorough presentation of methods of data compression and representation Algorithmic approach to model selection and design of experiments Large data sets and 13 Mathematica®-based Uncertain Virtual WorldsTM programs and code This text is an excellent resource for all applied statisticians, engineers, and scientists who need to use modern statistical analysis methods to investigate and model their data. The present, softcover reprint is designed to make this classic textbook available to a wider audience.

The Natural Axiom System of Probability Theory

Daguo Xiong
The Natural Axiom System of Probability Theory Book PDF

Author : Daguo Xiong
Publisher : World Scientific
Page : 200 pages
File Size : 52,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812384089

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The Natural Axiom System of Probability Theory by Daguo Xiong Pdf

The causation space established in this book is a mathematical model of the random universe and a ?living house? of all random tests and probability spaces. By using this space, one can introduce the mathematical calculation methods related to probability spaces and random tests. The book also points out that the basic unit to be studied in the probability theory is the random test, and not a stand-alone event.

Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms

Dmitri Koroliouk,Igor Samoilenko
Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms Book PDF

Author : Dmitri Koroliouk,Igor Samoilenko
Publisher : John Wiley & Sons
Page : 276 pages
File Size : 49,6 Mb
Release : 2023-08-29
Category : Mathematics
ISBN : 9781786309112

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Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms by Dmitri Koroliouk,Igor Samoilenko Pdf

This book illustrates a number of asymptotic and analytic approaches applied for the study of random evolutionary systems, and considers typical problems for specific examples. In this case, constructive mathematical models of natural processes are used, which more realistically describe the trajectories of diffusion-type processes, rather than those of the Wiener process. We examine models where particles have some free distance between two consecutive collisions. At the same time, we investigate two cases: the Markov evolutionary system, where the time during which the particle moves towards some direction is distributed exponentially with intensity parameter λ; and the semi-Markov evolutionary system, with arbitrary distribution of the switching process. Thus, the models investigated here describe the motion of particles with a finite speed and the proposed random evolutionary process with characteristics of a natural physical process: free run and finite propagation speed. In the proposed models, the number of possible directions of evolution can be finite or infinite.