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Mathematical Modeling of Complex Biological Systems : A Kinetic Theory Approach
This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems—comprised of large populations of interacting cells—whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. The authors propose a new biological model for the analysis of competition between cells of an aggressive host and cells of a corresponding immune system.Because the microscopic description of a biological system is far more complex than that of a physical system of inert matter, a higher level of analysis is needed to deal with such complexity. Mathematical models using kinetic theory may represent a way to deal with such complexity, allowing for an understanding of phenomena of nonequilibrium statistical mechanics not described by the traditional macroscopic approach. The proposed models are related to the generalized Boltzmann equation and describe the population dynamics of several interacting elements (kinetic population models).The particular models proposed by the authors are based on a framework related to a system of integro-differential equations, defining the evolution of the distribution function over the microscopic state of each element in a given system. Macroscopic information on the behavior of the system is obtained from suitable moments of the distribution function over the microscopic states of the elements involved. The book follows a classical research approach applied to modeling real systems, linking the observation of biological phenomena, collection of experimental data, modeling, and computational simulations to validate the proposed models. Qualitative analysis techniques are used to identify the prediction ability of specific models.
Mathematical Modeling of Biological Systems ; Vol. II : Epidemiology, Evolution and Ecology,Immunology, Neural Systems and the Brain, and Innovative Mathematical Methods
This two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout both works are mathematical and computational approaches to examine central problems in the life sciences, ranging from the organizational principles of individual cells to the dynamics of large populations.
Mathematical Modeling of Biological Systems ; Vol. I : Cellular Biophysics, Regulatory Networks, Development, Biomedicine, and Data Analysis
This two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout both works are mathematical and computational approaches to examine central problems in the life sciences, ranging from the organizational principles of individual cells to the dynamics of large populations.
Mathematical methods and modelling in hydrocarbon exploration and production
Hydrocarbon exploration and production incorporate great technology challenges for the oil and gas industry. In order to meet the world's future demand for oil and gas, further technological advance is needed, which in turn requires research across multiple disciplines, including mathematics, geophysics, geology, petroleum engineering, signal processing, and computer science. This book addresses important aspects and fundamental concepts in hydrocarbon exploration and production. Moreover, new developments and recent advances in the relevant research areas are discussed, whereby special emphasis is placed on mathematical methods and modelling. The book reflects the multi-disciplinary character of the hydrocarbon production workflow, ranging from seismic data imaging, seismic analysis and interpretation and geological model building, to numerical reservoir simulation. Various challenges concerning the production workflow are discussed in detail.
Mathematical Masterpieces : Further Chronicles by the Explorers
Experience the discovery of mathematics by reading the original work of some of the greatest minds throughout history. Here are the stories of four mathematical adventures, including the Bernoulli numbers as the passage between discrete and continuous phenomena, the search for numerical solutions to equations throughout time, the discovery of curvature and geometric space, and the quest for patterns in prime numbers. Each story is told through the words of the pioneers of mathematical thought. Particular advantages of the historical approach include providing context to mathematical inquiry, perspective to proposed conceptual solutions, and a glimpse into the direction research has taken.
Mathematical Events of the Twentieth Century
Russian mathematics (later Soviet mathematics, and Russian mathematics once again) occupies a special place in twentieth-century mathematics. In addition to its well-known achievements, Russian mathematics established a unique style of research based on the existence of prominent mathematical schools. These schools were headed by recognized leaders, who became famous due to their talents and outstanding contributions to science. The present collection is intended primarily to gather in one book the t- timonies of the participants in the development of mathematics over the past century. In their articles the authors have expressed their own points of view on the events that took place. The editors have not felt that they had a right to make any changes, other than stylistic ones, or to add any of their own commentary to the text. Naturally, the points of view of the authors should not be construed as those of the editors. The list of mathematicians invited to participate in the present edition was quite long.
Mathematical Control Theory and Finance
This book highlights recent developments in mathematical control theory and its applications to finance. It presents a collection of original contributions by distinguished scholars, addressing a large spectrum of problems and techniques. Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, ranging from "pure" areas of mathematics up to applied sciences like finance. Stochastic optimal control is a well established and important tool of mathematical finance. Other branches of control theory have found comparatively less applications to financial problems, but the exchange of ideas and methods has intensified in recent years. This volume should contribute to establish bridges between these separate fields. The diversity of topics covered as well as the large array of techniques and ideas brought in to obtain the results make this volume a valuable resource for advanced students and researchers.
Mathematical Control Theory : An Introduction
Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems.
Mathematical and Computational Models for Congestion Charging
This book presents rigorous treatments of issues related to congestion pricing. The chapters describe recent advances in areas such as mathematical and computational models for predicting traffic congestion, determining when, where, and how much to levy tolls, and analyzing the impact of tolls on transporation systems. The analyses and methodologies developed in this book provide Mechanisms that aid in determining and comparing congestion pricing schemes; Methodologies for evaluating the efficiency of existing and proposed congestion pricing schemes; A means to predict the impact of pricing on urban transporation systems; and Information essential to the financial and political success of congestion pricing programs.
Mathematical Analysis I
The purpose of the volume is to provide a support for a first course in Mathematical Analysis, along the lines of the recent Programme Specifications for mathematical teaching in European universities. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques.
Mathematical Analysis : Linear and Metric Structures and Continuity
The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.
Mathematica for Theoretical Physics : Electrodynamics, Quantum Mechanics, General Relativity, and Fractals
Mathematica for Theoretical Physics: Electrodynamics, Quantum Mechanics, General Relativity, and Fractals This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A brief glossary of terms and functions is contained in the appendices.
Mathematica for Theoretical Physics : Classical Mechanics and Nonlinear Dynamics
Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A brief glossary of terms and functions is contained in the appendices.
Materials Fundamentals of Gate Dielectrics
This book presents materials fundamentals of novel gate dielectrics that are being introduced into semiconductor manufacturing to ensure the continuous scalling of the CMOS devices. This is a very fast evolving field of research so we choose to focus on the basic understanding of the structure, thermodunamics, and electronic properties of these materials that determine their performance in device applications. Most of these materials are transition metal oxides. Ironically, the d-orbitals responsible for the high dielectric constant cause sever integration difficulties thus intrinsically limiting high-k dielectrics. Though new in the electronics industry many of these materials are wel known in the field of ceramics, and we describe this unique connection. The complexity of the structure-property relations in TM oxides makes the use of the state of the art first-principles calculations necessary. Several chapters give a detailed description of the modern theory of polarization, and heterojunction band discontinuity within the framework of the density functional theory. Experimental methods include oxide melt solution calorimetry and differential scanning calorimetry, Raman scattering and other optical characterization techniques, transmission electron microscopy, and x-ray photoelectron spectroscopy.
Matematica generale con il calcolatore
By introducing mathematical objects, it teaches students how to use a computer to perform numerical and symbolic calculations, define a function and calculate its values, plot and explore graphs, and execute simple algorithms. The course is rich in examples, applications, and models, drawn from economics, physics, biology, statistics, and mathematics itself. The analysis of these models constitutes, in a certain sense, the true purpose of the mathematical theory covered. Automatic calculation tools (mathematics software, spreadsheets) are used extensively to explore and illustrate concepts and properties. Mathcad® software, in particular, was used, both as a calculation tool and as a simple yet powerful programming language. Considerable space is devoted to approximation, emphasizing the distinction between numerical and symbolic calculation; to algorithms as a synthesis of the syntactic and semantic aspects of mathematical objects; and to computer simulation, interpreted as a "physical" experiment and a source of conjecture. The ability to use a calculator marks a sort of "democratization" of mathematics: even complex results, which have always required a broad background of knowledge and laborious calculations, are now quickly accessible to anyone who understands the meaning of mathematical objects and knows how to use the syntax.
Masonry Constructions : Mechanical Models and Numerical Applications
This monograph firstly provides a detailed description of the constitutive equation of masonry-like materials, clearly setting out its most important features. It then goes on to provide a numerical procedure to solve the equilibrium problem of masonry solids.
Martingale Methods in Financial Modelling
This book provides a comprehensive, self-contained and up-to-date treatment of the main topics in the theory of option pricing. The first part of the text starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice.
Maple and Mathematica : A Problem Solving Approach for Mathematics
the history of mathematics there are many situations in which cal- lations were performed incorrectly for important practical applications. the history of computing the number began in Egypt and Babylon about 2000 years BC, since then many mathematicians have calculated (e. g. , Archimedes, Ptolemy, Vi` ete, etc. ). In modern mathematics there exist computers that can perform various mathematical operations for which humans are incapable. Therefore the computers can be used to verify the results obtained by humans, to discovery new results, to - prove the result sthatahumancanobtain without anytechnology
Managing Critical Infrastructure Risks
At the beginning of each year, there is a deluge of top-10 lists on just about every subject you can imagine. A top-10 list of biggest news stories, best-selling books, most popular music and movies, richest companies, and best places to visit or live. It seems everyone has his or her own top-10 list, reflecting, perhaps, differences in regional, national, and cultural values. Companies and governments most often tend to focus their top-10 lists on economic priorities, or priorities related to national defense, security, public health, and new infrastructure. This year, 2007, was no exception. Yet, increasingly, we see governments, private organizations, and companies advocating a new type of prioritization. This framework needs to reach beyond the realms of economics, world trade, and corporate management to include the environment, stakeholders, public preferences, and social goals. Moreover, corporations and individuals are not only interested in generic 10-best lists; they want lists tailored to their values, goals, and current economic and social state. For example, the U. S.
Malliavin Calculus for Lévy Processes with Applications to Finance
While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions to stochastic differential equations, this book has another goal. It portrays the most important and innovative applications in stochastic control and finance, such as hedging in complete and incomplete markets, optimisation in the presence of asymmetric information and also pricing and sensitivity analysis. In a self-contained fashion, both the Malliavin calculus with respect to Brownian motion and general Lévy type of noise are treated. Besides, forward integration is included and indeed extended to general Lévy processes. The forward integration is a recent development within anticipative stochastic calculus that, together with the Malliavin calculus, provides new methods for the study of insider trading problems.
