Mathematical Notes

In this book, a social dilemma with partner selection is introduced and studied with the methods of formal game theory, experimental economics and computer simulations. It allows exploration of simult

This book consists of surveys of high-frequency financial data analysis and econometric forecasting. Some of the chapters were presented as tutorials to an audience in the Econometric Forecasting and

The primary objective of this book is to demonstrate that a firm's financing decisions depend among other things on bargaining power considerations, and to illustrate potential causes for this depende

This volume on the integration of mathematics history into undergraduate teaching provides ideas and materials for immediate adoption in the classroom. Focusing on the developments of the nineteenth a

This monograph is intended for an advanced undergraduate or graduate course as well as for researchers, who want a compilation of developments in this rapidly growing field of operations research. Thi

The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via sev

This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions.Through the rigorous developm

This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological pro

In these notes, first published in 1980, Professor Northcott provides a self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory. The book divides into two parts. The first four chapters contain all the geometry needed for the second half of the book which deals with affine groups. Alternatively the first part provides a sure introduction to the foundations of algebraic geometry. Any affine group has an associated Lie algebra. In the last two chapters, the author studies these algebras and shows how, in certain important cases, their properties can be transferred back to the groups from which they arose. These notes provide a clear and carefully written introduction to algebraic geometry and algebraic groups.

The authors present a new formal framework forfinding the long-run competitive market equilibrium through short-runequilibria by exploiting the operating policies and plant valuations. This“short-run

This volume sheds light on the current state of complex networks and nonlinear dynamics applied to the understanding of economic and social phenomena ranging from geographical economics to macroeco

Most developed economics show the tendency of an increasing importance of modern services such as tourism, logistical services, finance, and others. In many cases, complex optimization problems can be

The four chapters were selected from the tutorials presented at the program Moving Interface Problems and Applications, held at the Institute for Mathematical Sciences at the National University of Si

In a globalized economy logistics has become a crucial area for the success of companies. The performance of each company depends on the performance of its suppliers and of its business partners. The

The growing complexity of many real world problems is one of the biggest challenges of our time. The area of international finance is one prominent example where decision making is often fraud to mist

Optimization problems arising in practice usually contain several random parameters. Hence, in order to obtain optimal solutions being robust with respect to random parameter variations, the mostly av

This book analyzes the impact of quiescent phases on biological models. Quiescence arises, for example, when moving individuals stop moving, hunting predators take a rest, infected individuals are iso

Surveying standard models and including their mathematical foundations, this book explains the methodology at the heuristic level of dynamical systems and the like, as well as detailing common yet vit

Pesin theory consists of the study of the theory of non-uniformly hyperbolic diffeomorphisms. The aim of this book is to provide the reader with a straightforward account of this theory, following the approaches of Katok and Newhouse. The notes are divided into two parts. The first develops the basic theory, starting with general ergodic theory and introducing Liapunov exponents. Part Two deals with the applications of Pesin theory and contains an account of the existence (and distribution) of periodic points. It closes with a look at stable manifolds, and gives some results on absolute continuity. These lecture notes provide a unique introduction to Pesin theory and its applications. The author assumes that the reader has only a good background of undergraduate analysis and nothing further, so making the book accessible to complete newcomers to the field.

Since the days of Lev Pontryagin and his associates, the discipline of Optimal Control has enjoyed a tremendous upswing – not only in terms of its mathematical foundations, but also with regard to num

One might expect that after their identification in the 19th century, all aspects of Giffen goods would have been studied by now. This appears not to be the case. This book contains the latest insight

The book presents new ideas to model and solve the flexible shift planning problem of personnel workers in the service industry. First, a new modeling approach is proposed that requires shifts to be g

"Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparent

This proceedings volume consists of papers presented at the Seventh International Workshop on Computer-Aided Scheduling of Pllblic Transport, which was held at th th the Massachusetts Institute of Tec

This book presents recent advancements of research, new methods and techniques, applications and projects in decision making and decision support systems. It explores expert systems and neural network

Torsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and étale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the étale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the étale homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and homogeneous spaces, rational and K3 surfaces, geometric invariant theory, rational points, descent and the Brauer–Manin obstruction. Together, these give a state-of-the-art view of a broad area at the crossroads of number theory and algebraic geometry.

The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. They are based on lectures given in Tokyo, but also contain new research. It is the first cohesive account of the area and will provide a useful synthesis of recent research for algebraists.

This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and examples are included throughout the notes.

Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges rai

The field of artificial economics (AE) embraces a broad range of methodologies relying on computer simulations in order to model and study the complexity of economic and social phenomena. The overarch

This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dyna

This book is a “How To” guide for modeling population dynamics using Integral Projection Models (IPM) starting from observational data. It is written by a leading research team in this area and includ

?Waves in Neural Media: From Single Neurons to Neural Fields surveys mathematical models of traveling waves in the brain, ranging from intracellular waves in single neurons to waves of activity in lar

Subfactors have been a subject of considerable research activity for about fifteen years and are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. These notes give an introduction to the subject suitable for a student who has only a little familiarity with the theory of Hilbert space. A new pictorial approach to subfactors is presented in a late chapter.

This is the expanded notes of a course intended to introduce students specializing in mathematics to some of the central ideas of traditional economics. The book should be readily accessible to anyone with some training in university mathematics; more advanced mathematical tools are explained in the appendices. Thus this text could be used for undergraduate mathematics courses or as supplementary reading for students of mathematical economics.

These notes derive from a course of lectures delivered at the University of Florida in Gainesville during 1971/2. Dr Gagen presents a simplified treatment of recent work by H. Bender on the classification of non-soluble groups with abelian Sylow 2-subgroups, together with some background material of wide interest. The book is for research students and specialists in group theory and allied subjects such as finite geometries.

These are notes deriving from lecture courses given by the authors in 1973 at Westfield College, London. The lectures described the connection between the theory of t-designs on the one hand, and graph theory on the other. A feature of this book is the discussion of then-recent construction of t-designs from codes. Topics from a wide range of finite combinatorics are covered and the book will interest all scholars of combinatorial theory.

A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves. This approach provides geometers with the opportunity to acquaint themselves with aspects of their subject virtually ignored by other texts. The exposition is clear and logically carries themes from earlier through to later topics. This enthusiastic work of scholarship is made complete with the inclusion of some interesting historical details and a very comprehensive bibliography.

The surreal numbers form a system which includes both the ordinary real numbers and the ordinals. Since their introduction by J. H. Conway, the theory of surreal numbers has seen a rapid development revealing many natural and exciting properties. These notes provide a formal introduction to the theory in a clear and lucid style. The the author is able to lead the reader through to some of the problems in the field. The topics covered include exponentiation and generalized e-numbers.

These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.