The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.

This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Polynomials are well known for their ability to improve their properties and for their applicability in the interdisciplinary fields of engineering and science. Many problems arising in engineering and physics are mathematically constructed by differential equations. Most of these problems can only be solved using special polynomials. Special polynomials and orthonormal polynomials provide a new way to analyze solutions of various equations often encountered in engineering and physical problems. In particular, special polynomials play a fundamental and important role in mathematics and applied mathematics. Until now, research on polynomials has been done in mathematics and applied mathematics only. This book is based on recent results in all areas related to polynomials. Divided into sections on theory and application, this book provides an overview of the current research in the field of polynomials. Topics include cyclotomic and Littlewood polynomials; Descartes' rule of signs; obtaining explicit formulas and identities for polynomials defined by generating functions; polynomials with symmetric zeros; numerical investigation on the structure of the zeros of the q-tangent polynomials; investigation and synthesis of robust polynomials in uncertainty on the basis of the root locus theory; pricing basket options by polynomial approximations; and orthogonal expansion in time domain method for solving Maxwell's equations using paralleling-in-order scheme.

This volume contains 41 original papers and 22 abstracts of research in linear algebra and applications currently conducted by many of the leading experts in the field. More than a dozen of the papers are survey articles, while several propose open problems. The applications range from control to probability theory, with strong emphasis on matrix polynomials, Schur complements, permanents, numerical computation, combinatorics, and core linear algebra.

This book is a printed edition of the Special Issue "Decomposability of Tensors" that was published in Mathematics

This unique volume surveys the current state of research in matrix theory and applied linear algebra. It provides information on matrix approximation and factorization, matrices in optimization theory, the theory of sparse matrices, and matrix theory in statistics, with careful attention to numerical computation and the impact of parallelism of matrix computations. This comprehensive work is an invaluable reference for researchers in all areas of applied mathematics.