A thorough introduction to tau functions, from the basics through to the most recent results, with applications in mathematical physics.

Tau functions are a central tool in the modern theory of integrable systems. This volume provides a thorough introduction, starting from the basics and extending to recent research results. It covers a wide range of applications, including generating functions for solutions of integrable hierarchies, correlation functions in the spectral theory of random matrices and combinatorial generating functions for enumerative geometrical and topological invariants. A self-contained summary of more advanced topics needed to understand the material is provided, as are solutions and hints for the various exercises and problems that are included throughout the text to enrich the subject matter and engage the reader. Building on knowledge of standard topics in undergraduate mathematics and basic concepts and methods of classical and quantum mechanics, this monograph is ideal for graduate students and researchers who wish to become acquainted with the full range of applications of the theory of tau functions.

Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.

Many developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles. Particular emphasis lies on highlighting the interplay between operator theory and applications from other areas, such as multi-dimensional systems and function theory of several complex variables, distributed parameter systems and control theory, mathematical physics, wavelets, and numerical analysis.

This book focuses on quantum groups, i.e., continuous deformations of Lie groups, and their applications in physics. These algebraic structures have been studied in the last decade by a growing number of mathematicians and physicists, and are found to underlie many physical systems of interest. They do provide, in fact, a sort of common algebraic ground for seemingly very different physical problems. As it has happened for supersymmetry, the q-group symmetries are bound to play a vital role in physics, even in fundamental theories like gauge theory or gravity. In fact q-symmetry can be considered itself as a generalization of supersymmetry, evident in the q-commutator formulation. The hope that field theories on q-groups are naturally reguralized begins to appear founded, and opens new perspectives for quantum gravity. The topics covered in this book include: conformal field theories and quantum groups, gauge theories of quantum groups, anyons, differential calculus on quantum groups and non-commutative geometry, poisson algebras, 2-dimensional statistical models, (2+1) quantum gravity, quantum groups and lattice physics, inhomogeneous q-groups, q-Poincaregroup and deformed gravity and gauging of W-algebras.

Taurine, or 2aminoethanesulfonic acid, is one of the most abundant sulfurcontaining amino acids in the human body. It is found in the heart, brain, retina, and skeletal muscles, and is synthesized in the pancreas. Studies have revealed that taurine is of high physiological importance: it protects against pathologies associated with mitochondrial diseases, and linked processes like aging, metabolic syndrome, cancer, cardiovascular diseases, and neurological disorders. It is also used as a nutritional supplement. Taurine and the Mitochondrion: Applications in the Pharmacotherapy of Human Diseases explores the significance of taurine in the biology of mitochondria. It also explains its role as a pharmacological agent for treating different diseases. Readers will gain an insight into the crucial role it plays in human physiology and the benefits of taurine supplements. Topics covered in this reference include Synthesis of taurine and its dietary sources The Role of taurine in mitochondrial health Taurine as a neurotransmitter Beneficial effects of taurine in physiological systems such as the reproductive system, renal system, and the gastrointestinal tract Hepatoprotective and antiinflammatory properties of taurine The antiaging promise of taurine supplementation Role of taurine supplementation in obesity

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