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Matsuzoe Hiroshi: Differential
Geometrical Foundations Of Information

Differential Geometrical Foundations Of Information Geometry: Geometry Of Statistical Manifolds And Divergences

This book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks.

This book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks.

Theory, Applications and Algorithms

Classical and Discrete Differential Geometry

This book provides an accessible introduction to using the tools of differential geometry to tackle a wide range of topics in physics, with the concepts developed through numerous examples to help the reader become familiar with the techniques.

This book provides an accessible introduction to using the tools of differential geometry to tackle a wide range of topics in physics, with the concepts developed through numerous examples to help the reader become familiar with the techniques.

A Geometrical Approach to Physics

The author introduces the main conceptions for multiplicative surfaces: multiplicative first fundamental form, the main multiplicative rules for differentiations on multiplicative surfaces, and the main multiplicative regularity conditions for multiplicative surfaces. Many examples and problems are included.

The author introduces the main conceptions for multiplicative surfaces: multiplicative first fundamental form, the main multiplicative rules for differentiations on multiplicative surfaces, and the main multiplicative regularity conditions for multiplicative surfaces. Many examples and problems are included.

Multiplicative Differential Geometry

Textbooks in Mathematics

This text is designed to update the Differential Geometry course by making it more relevant to today's students. It is intended for mathematics students, applied scientists, and engineers who attempt to integrate differential geometry techniques in their work or research.

Lectures on Differential Geometry with Maple

New Mathematical Monographs

"The second of two volumes builds on the foundational material on ergodic theory and geometric measure theory provided in Volume I, and applies all the techniques discussed to describe the beautiful and rich dynamics of elliptic functions. The text begins with an introduction to topological dynamics of transcendental meromorphic functions, before progressing to elliptic functions, discussing at length their classical properties, measurable dynamics and fractal geometry. The authors then look in depth at compactly non-recurrent elliptic functions. Much of this material is appearing for the first time in book or paper form. Both senior and junior researchers working in ergodic theory and dynamical systems will appreciate what is sure to be an indispensable reference"--

This text, the second of two volumes, provides a comprehensive and self-contained approach to the rich dynamics of elliptic functions on the complex plane, with an emphasis on ergodic aspects. The first monograph on the subject, it is an indispensable reference for any researchers interested in low-dimensional dynamics.

Elliptic Functions with an Introduction to the Dynamics of Meromorphic Functions

Meromorphic Dynamics: Volume 2

This book is devoted to multiplicative analytic geometry. The book is intended for senior undergraduate students and beginning graduate students of engineering and science courses &amp; reflects some recent investigations in multiplicative analytic geometry. The multiplicative differential calculus has applications in biology, chemistry, finance.

This book is devoted to multiplicative analytic geometry. The book is intended for senior undergraduate students and beginning graduate students of engineering and science courses &amp; reflects some recent investigations in multiplicative analytic geometry. The multiplicative differential calculus has applications in biology, chemistry, finance.

Multiplicative Analytic Geometry

This book provides a better understanding of mutant strains and their pathogenicity by performing genomic sequences of samples. The book will benefit clinicians, educators, scientists, industrialists and policymakers in handling the crisis of the outbreak.

This book provides a better understanding of mutant strains and their pathogenicity by performing genomic sequences of samples. The book will benefit clinicians, educators, scientists, industrialists and policymakers in handling the crisis of the outbreak.

Recent Advances and Challenges

Frontiers of Fractal Analysis

The book explains the reasons for various definitions. The interactive applets offer motivation for definitions, allowing students to explore examples, and give a visual explanation of complicated theorems. More elementary exercises are added and some challenging problems are moved later in exercise sets to assure more graduated progress.

The book explains the reasons for various definitions. The interactive applets offer motivation for definitions, allowing students to explore examples, and give a visual explanation of complicated theorems. More elementary exercises are added and some challenging problems are moved later in exercise sets to assure more graduated progress.

Differential Geometry of Curves and Surfaces

This book offers a captivating journey through the world of elliptic partial differential equations (PDEs) and their surprising appearances across science, engineering, and even everyday life. Blending mathematical rigor with an accessible and engaging style, it introduces the Laplace operator and elliptic PDEs through diverse real-world phenomena, from physics and biology to artificial intelligence and image processing.Readers will explore fundamental topics such as diffusion, wave propagation, and fluid dynamics, alongside unexpected applications -- including pattern formation in nature, traffic jams, quantum mechanics, and even the mathematics behind fighting pandemics and cancer. With a focus on both intuition and formalism, the book provides a wealth of examples, historical insights, and thought-provoking problems that make the subject come alive.Awarded the prestigious Book Prize of the Unione Matematica Italiana, this work has been praised as 'a remarkable journey through delightful applications of elliptic PDEs, all while maintaining the highest standards of mathematical rigor.' Whether you are a student, researcher, or simply curious about how mathematics shapes the world around us, this book will challenge and inspire you.

Elliptic Partial Differential Equations From An Elementary Viewpoint: What The Laplacian Is Good For

The K-stability of Fano varieties has been a major area of research over the last decade, ever since the Yau-Tian-Donaldson conjecture was resolved. This is the first book to give a comprehensive algebraic treatment of this emerging field. It introduces all the notions of K-stability that have been used over the development of the subject, proves their equivalence, and discusses newly developed theory, including several new proofs for existing theorems. Aiming to be as self-contained as possible, the text begins with a chapter covering essential background knowledge, and includes exercises throughout to test understanding. Written by an author at the forefront of developments in the area, it will be a source of inspiration for graduate students and researchers who work in algebraic geometry.

K-stability of Fano Varieties

The author presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together classical and modern formulations. The goal is to introduce manifolds in a both streamlined and mathematically rigorous way.

The author presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together classical and modern formulations. The goal is to introduce manifolds in a both streamlined and mathematically rigorous way.

Differential Geometry of Manifolds

Differential Geometrical Foundations Of Information Geometry: ...

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