Bücher der Reihe Infosys Science Foundation Series in Mathematical Sciences

This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixed points, essentiality and the Lichnerowicz conjecture. Later chapters focus on the study of conformal vector fields on special Riemannian and Lorentzian manifolds, with a special emphasis on general relativistic spacetimes and the evolution of conformal vector fields in terms of initial data.The book also delves into the realm of Ricci flow and Ricci solitons, starting with motivations and basic results and moving on to more advanced topics within the framework of Riemannian geometry. The main emphasis of the book is on the interplay between conformal vector fields and Ricci solitons, and their applications in contact geometry. The book highlights the fact that Nil-solitons and Sol-solitons naturally arise in the study of Ricci solitons in contact geometry. Finally, the book gives a comprehensive overview of generalized quasi-Einstein structures and Yamabe solitons and their roles in contact geometry. It would serve as a valuable resource for graduate students and researchers in mathematics and physics as well as those interested in the intersection of geometry and physics.

This book is a self-contained advanced monograph on inequalities involving the numerical radius of bounded linear operators acting on complex Hilbert spaces. The study of numerical range and numerical radius has a long and distinguished history starting from the Rayleigh quotients used in the 19th century to nowadays applications in quantum information theory and quantum computing.This monograph is intended for use by both researchers and graduate students of mathematics, physics, and engineering who have a basic background in functional analysis and operator theory. The book provides several challenging problems and detailed arguments for the majority of the results. Each chapter ends with some notes about historical views or further extensions of the topics. It contains a bibliography of about 180 items, so it can be used as a reference book including many classical and modern numerical radius inequalities.

This book provides an insight into the geometric aspects of the spaces of operators studied by using the notion of Birkhoff¿James orthogonality. It studies the norm attainment set of an operator and its properties, the notion of which plays a very important role in the characterization of B-J orthogonality of operators. The structure of the norm attainment set is studied for Hilbert space operators and is yet to be understood completely for operators between Banach spaces. The book explores the interrelation between B-J orthogonality in the ground space and in the space of operators in its fullest generality. The book further explores the concept of approximate B-J orthogonality and investigated its geometry both in the ground space as well as in the space of operators. It highlights important geometric properties like smoothness and k-smoothness of bounded linear operators, extreme contractions and symmetricity of bounded linear operators defined between Hilbert spaces as well as Banach spaces.

This book studies the construction methods for solving one-dimensional and multidimensional inverse dynamical problems for hyperbolic equations with memory. The theorems of uniqueness, stability and existence of solutions of these inverse problems are obtained. This book discusses the processes, by using generalized solutions, the spread of elastic or electromagnetic waves arising from sources of the type of pulsed directional ¿impacts¿ or ¿explosions¿. This book presents new results in the study of local and global solvability of kernel determination problems for a half-space. It describes the problems of reconstructing the coefficients of differential equations and the convolution kernel of hyperbolic integro-differential equations by the method of Dirichlet-to-Neumann. The book will be useful for researchers and students specializing in the field of inverse problems of mathematical physics.

This book contains selected chapters on perfectoid spaces, their introduction and applications, as invented by Peter Scholze in his Fields Medal winning work. These contributions are presented at the conference on "Perfectoid Spaces" held at the International Centre for Theoretical Sciences, Bengaluru, India, from 9-20 September 2019. The objective of the book is to give an advanced introduction to Scholze's theory and understand the relation between perfectoid spaces and some aspects of arithmetic of modular (or, more generally, automorphic) forms such as representations mod p, lifting of modular forms, completed cohomology, local Langlands program, and special values of L-functions. All chapters are contributed by experts in the area of arithmetic geometry that will facilitate future research in the direction.

This edited volume is a collection of selected research articles discussing the analysis of infectious diseases by using mathematical modelling in recent times. The book also includes applications of fractional differential equations as well as ordinary, partial and integrodifferential equations with optimization methods.

The book discusses major topics in complex analysis with applications to number theory. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two and three manifolds and number theory.

Hermann Thorisson, Shift-Coupling and Maximality.- Ashok Krishnan K. S, Vinod Sharma, Diffusion Approximation Analysis of Multihop Wireless Networks: Quality of Service and Convergence of Stationary Distribution.- Liu Mei, Alexander Dudin, Analysis of Retrial Queue with Heterogeneous Servers and Markovian Arrival Process.- Krishna B. Athreya, What is Standard Brownian Motion?.- Srinivas R. Chakravarthy, Busy Period Analysis of multi-server retrial queueing systems.- Alexander Rumyantsev, Garimella Rama Murthy, Steady State and Transient Analysis of a Single Channel Cognitive Radio Model with Impatience and Balking.- Shruti Kapoor, S. Dharmaraja, Applications of Fluid Queues in Rechargeable Batteries.- Souvik Ghosh, A. D. Banik, M. L. Chaudhry, Analysis of BMAP/R/1 Queues under Gated-limited Service with the Server''s Single Vacation Policy.- G. Arivarignan, M. Keerthana, B. Sivakumar, A Production Inventory System with Renewal and Retrial Demands.- U. C. Gupta, Nitin Kumar, F. P. Barbhuiya, A Queueing System with Batch Renewal Input and Negative Arrivals.- Ekaterina Fedorova, Anatoly Nazarov, Alexander Moiseev, Asymptotic Analysis Methods for Multi-sever Retrial Queueing Systems.- Ekaterina Lisovskaya, Michele Pagano, On the Application of Dynamic Screening Method to Resource Queueing System with Infinite Servers.- Ari Arapostathis, Vivek S. Borkar, Controlled Versions of the Collatz-Wielandt and Donsker-Varadhan Formulae.- Malini S, DhanyaShajin, An (s, S) Production Inventory System with State Dependent Production Rate and Lost Sales.- Dibu A. S., M. J. Jacob, Analysis of a MAP Risk Model with Stochastic Incomes, Inter-Dependent Phase-Type Claims and a Constant Barrier.- Salini S.  Nair, K. P. Jose, A PH Distributed Production Inventory Model with Different Modes of Service and Map Arrivals.- Kavya P., M.  Manoharan, On a Generalized Lifetime Model Using DUS Transformation.- V. P. Praveen, M. Manoharan, Analysis of Inventory Control Model for Items Having General Deterioration Rate.- A. Krishnamoorthy, V. Divya, A Two-Server Queueing System with Processing of Service Items by a Sever.- SinuLal T. S, A. Krishnamoorthy, V. C. Joshua, Vladimir Vishnevsky, A Two Stage Tandem Queue with Specialist Servers.- Jomy Punalal, S. Babu, Retrial Queueing System with Self-Generation of Priorities and Customer Induced Interruption.- D. Kannan, Lina Ma, Valuation of Reverse Mortgage.- Rostislav Razumchik, LusineMeykhanadzhyan, Stationary Distribution of Discrete-Time and Finite-Capacity Queue with Resequencing.- ChiranjibMukherjee, S. R. S. Varadhan, The Polaron Measure.- Tuan Phung Duc, Batch Arrival Multiserver Queue with State-Dependent Setup for Energy Saving Data Center.- T. E. Govindan, Weak Convergence of Probability Measures of Trotter-Kato Approximate Solutions of Stochastic Evolution Equations.- Vladimir Vishnevsky, Andrey Larionov, Stochastic Multiphase Models and Their Application for Analysis of End-To-End Delays in Wireless Multihop Networks.- Garimella Rama Murthy, Variance Laplacian: Quadratic Forms in Statistics.- B. Rajeev, On the Feynman-Kac Formula.- Ekaterina Lisovskaya, Svetlana Moiseeva, Michele Pagano, Ekaterina Pankratova, Heterogeneous Resource Queueing System with Renewal Arrival Process.

This book gathers papers on recent advances in the ergodic theory of group actions on homogeneous spaces and on geometrically finite hyperbolic manifolds presented at the workshop "Geometric and Ergodic Aspects of Group Actions," organized by the Tata Institute of Fundamental Research, Mumbai, India, in 2018.

This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics.

One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitly describe quantum isometry groups of most of the noncommutative manifolds studied in the literature.

This book explores certain structures of fuzzy Lie algebras, fuzzy Lie superalgebras and fuzzy n-Lie algebras. Chapter 6 is devoted to the properties of bipolar fuzzy Lie ideals, bipolar fuzzy Lie subsuperalgebras, bipolar fuzzy bracket product, solvable bipolar fuzzy Lie ideals and nilpotent bipolar fuzzy Lie ideals.

This book addresses single-valued neutrosophic graphs and their applications. In addition, it introduces readers to a number of central concepts, including certain types of single-valued neutrosophic graphs, energy of single-valued neutrosophic graphs, bipolar single-valued neutrosophic planar graphs, isomorphism of intuitionistic single-valued neutrosophic soft graphs, and single-valued neutrosophic soft rough graphs.Divided into eight chapters, the book seeks to remedy the lack of a mathematical approach to indeterminate and inconsistent information. Chap. 1 presents a concise review of single-valued neutrosophic sets, while Chap. 2 explains the notion of neutrosophic graph structures and explores selected properties of neutrosophic graph structures. Chap. 3 discusses specific bipolar neutrosophic graphs. Chap. 4 highlights the concept of interval-valued neutrosophic graphs, while Chap. 5 presents certain notions concerning interval-valued neutrosophic graph structures. Chap. 6 addresses the concepts of rough neutrosophic digraphs and neutrosophic rough digraphs. Chap. 7 focuses on the concepts of neutrosophic soft graphs and intuitionistic neutrosophic soft graphs, before Chap. 8 rounds out the book by considering neutrosophic soft rough graphs.