Vijay Gupta Livres

Well-entrenched in Hinduism is the belief that God sometimes descends to earth as an avatar, the manifestation of a deity that has assumed human form for some divine purpose. We may also define an avatar as an incarnate divine teacher. Haidakhan Baba qualifies as an avatar on both counts. He appeared out of a cave in 1970 at the Haidakhan village, seemingly out of nowhere, and went on to touch and transform the lives of millions of devotees. As a teenager, Vijay Gupta spent some years with Haidakhan Baba as his closest disciple. Peppered with innumerable gripping, often funny and always meaningful anecdotes, this book is a detailed, personal account of Vijay Gupta's spiritual journey serving Haidakhan Baba. Tightly interwoven into the narrative, is his unwavering, unshaken bond with Babaji, to which he remained true, even when he was at odds with Him.

The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. ​​This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using well- known operators. The presentation is systematic and the authors include a brief summary of the notations and basic definitions of q-calculus before delving into more advanced material. The many applications of q-calculus in the theory of approximation, especially on various operators, which includes convergence of operators to functions in real and complex domain​ forms the gist of the book. This book is suitable for researchers and students in mathematics, physics and engineering, and for professionals who would enjoy exploring the host of mathematical techniques and ideas that are collected and discussed in the book.

Focusing on convergence in real and complex domains, this book presents advanced findings that are essential for graduate students and researchers. It delves into innovative and efficient applications crafted by the authors, enhancing the study of optimization and analysis.

This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian–Ivanov for linear combinations of Bernstein and Bernstein–Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduateand postgraduate courses as well as a basis for future study and development.

Rapid advances in information processing, communication, and sensing technologies have enabled devices to incorporate embedded processors, networking capabilities, and sensors. This evolution allows for an architecture where numerous simple components communicate and cooperate to achieve a collective goal. Such a distributed architecture offers enhanced performance, reliability, and design simplicity. However, it necessitates an extension of traditional control, communication, and computation theories, advocating for a unified understanding of these fields. From an estimation and control standpoint, real communication channels can introduce non-classical information patterns, leading to significant performance losses. This text addresses new design principles to mitigate such degradation, focusing on the joint design of information flow and control laws. Unlike traditional control design, which assumes a specific information flow to calculate optimal control inputs, this approach synthesizes optimal information flow alongside control laws that meet the constraints of that flow. Consequently, it prompts critical questions: What actions should an agent take? Who should they communicate with? What information should be shared? When should communication occur? This joint design of information flow and control input represents a crucial degree of freedom for system designers, yielding substantial performance improvements over conve