Algebraic Linguistics Analytical Models By Solomon Marcus
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Algebraic Linguistics; Analytical Models by Solomon Marcus
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Mathematics Almost Everywhere: In Memory Of Solomon Marcus
The book is a collection of original papers, research and surveys, dedicated to the memory of the Romanian mathematician Solomon Marcus (1925-2016). Marcus published many papers and books in mathematical analysis, theoretical computer science, mathematical linguistics, poetics, theory of literature, semiotics, and several other fields less strongly connected to mathematics, like cultural anthropology, biology, history and philosophy of science, education. He exemplified an unimaginable richness of ideas.This volume intends to emphasize the mathematical fields in which Solomon Marcus worked, and demonstrate — as he also did — the interconnection between them. The authors who contribute to this volume are well-known experts in their fields. Most of them knew Solomon Marcus well, some even owed him for his decisive impulses for their careers and general development. With articles in so diverse areas, the volume will attract readers who would like to diversify their own knowledge or find unexpected connections with other topics.
Comparison and Oscillation Theory of Linear Differential Equations
Mathematics in Science and Engineering, Volume 48: Comparison and Oscillation Theory of Linear Differential Equations deals primarily with the zeros of solutions of linear differential equations. This volume contains five chapters. Chapter 1 focuses on comparison theorems for second order equations, while Chapter 2 treats oscillation and nonoscillation theorems for second order equations. Separation, comparison, and oscillation theorems for fourth order equations are covered in Chapter 3. In Chapter 4, ordinary equations and systems of differential equations are reviewed. The last chapter discusses the result of the first analog of a Sturm-type comparison theorem for an elliptic partial differential equation. This publication is intended for college seniors or beginning graduate students who are well-acquainted with advanced calculus, complex analysis, linear algebra, and linear differential equations.