This monograph considers the mathematical modeling of cellular adhesion, a key interaction force in cell biology. While deeply grounded in the biological application of cell adhesion and tissue formation, this monograph focuses on the mathematical analysis of non-local adhesion models. The novel aspect is the non-local term (an integral operator), which accounts for forces generated by long ranged cell interactions. The analysis of non-local models has started only recently, and it has become a vibrant area of applied mathematics. This monograph contributes a systematic analysis of steady...
This monograph considers the mathematical modeling of cellular adhesion, a key interaction force in cell biology. While deeply grounded in the biol...
This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. The text begins by developing the basics of atomic theories and implicational theories in languages that may, or may not, contain equality. Subquasivariety lattices are represented as lattices of closed algebraic subsets of a lattice with operators, which yields new restrictions on the equaclosure operator. As an application of this new approach, it is shown that completely distributive lattices with a dually compact least element are subquasivariety lattices. The book contains many examples to...
This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. The text begins by developing the basics of atomic theor...
This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field. The text collects and synthesizes a number of works on Bernstein’s theorem of counting solutions of generic systems, ultimately presenting the theorem, commentary, and extensions in a comprehensive and coherent manner. It begins with Bernstein’s original theorem expressing solutions of generic systems in terms of the mixed volume of their Newton...
This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate mu...
This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. The text begins by developing the basics of atomic theories and implicational theories in languages that may, or may not, contain equality. Subquasivariety lattices are represented as lattices of closed algebraic subsets of a lattice with operators, which yields new restrictions on the equaclosure operator. As an application of this new approach, it is shown that completely distributive lattices with a dually compact least element are subquasivariety lattices. The book contains many examples to...
This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. The text begins by developing the basics of atomic theor...
This book is the culmination of the authors’ industry-academic collaboration in the past several years. The investigation is largely motivated by bank balance sheet management problems. The main difference between a bank balance sheet management problem and a typical portfolio optimization problem is that the former involves multiple risks. The related theoretical investigation leads to a significant extension of the scope of portfolio theories.
The book combines practitioners’ perspectives and mathematical rigor. For example, to guide the bank managers to trade off...
This book is the culmination of the authors’ industry-academic collaboration in the past several years. The investigation is largely motivated by...
This graduate textbook provides an alternative to discrete event simulation. It describes how to formulate discrete event systems, how to convert them into Markov chains, and how to calculate their transient and equilibrium probabilities. The most appropriate methods for finding these probabilities are described in some detail, and templates for efficient algorithms are provided. These algorithms can be executed on any laptop, even in cases where the Markov chain has hundreds of thousands of states. This book features the probabilistic interpretation of Gaussian elimination, a...
This graduate textbook provides an alternative to discrete event simulation. It describes how to formulate discrete event systems, how to con...
This book aims to introduce graduate students to the many applications of numerical computation, explaining in detail both how and why the included methods work in practice. The text addresses numerical analysis as a middle ground between practice and theory, addressing both the abstract mathematical analysis and applied computation and programming models instrumental to the field. While the text uses pseudocode, Matlab and Julia codes are available online for students to use, and to demonstrate implementation techniques. The textbook also emphasizes multivariate problems...
This book aims to introduce graduate students to the many applications of numerical computation, explaining in detail both how and why the included...
Although the Lucas sequences were known to earlier investigators such as Lagrange, Legendre and Genocchi, it is because of the enormous number and variety of results involving them, revealed by Édouard Lucas between 1876 and 1880, that they are now named after him. Since Lucas’ early work, much more has been discovered concerning these remarkable mathematical objects, and the objective of this book is to provide a much more thorough discussion of them than is available in existing monographs. In order to do this a large variety of results, currently scattered throughout...
Although the Lucas sequences were known to earlier investigators such as Lagrange, Legendre and Genocchi, it is because of the enormous number an...
This book provides a short introduction to partial differential equations (PDEs). It is primarily addressed to graduate students and researchers, who are new to PDEs. The book offers a user-friendly approach to the analysis of PDEs, by combining elementary techniques and fundamental modern methods.
The author focuses the analysis on four prototypes of PDEs, and presents two approaches for each of them. The first approach consists of the method of analytical and classical solutions, and the second approach consists of the method of weak (variational)...
This book provides a short introduction to partial differential equations (PDEs). It is primarily addressed to graduate students and researchers, w...
