Control Perspectives on Numerical Algorithms and Matrix Problems organizes the analysis and design of iterative numerical methods from a control perspective. The authors discuss a variety of applications, including iterative methods for linear and nonlinear systems of equations, neural networks for linear and quadratic programming problems, support vector machines, integration and shooting methods for ordinary differential equations, matrix preconditioning, matrix stability, and polynomial zero finding. This book opens up a new field of interdisciplinary research that should lead to insights in the areas of both control and numerical analysis and shows that a wide range of applications can be approached from, and benefit from, a control perspective.
This book introduces optimal control methods, formulated as optimization problems, applied to business dynamics problems. Business dynamics refers to a combination of business management and financial objectives embedded in a dynamical system model. The model is subject to a control that optimizes a performance index and takes both management and financial aspects into account. Business Dynamics Models: Optimization-Based One Step Ahead Optimal Control includes solutions that provide a rationale for the use of optimal control and guidelines for further investigation into more complex models, as well as formulations that can also be used in a so-called flight simulator mode to investigate different complex scenarios. The text offers a modern programming environment (Jupyter notebooks in JuMP/Julia) for modeling, simulation, and optimization, and Julia code and notebooks are provided on a website for readers to experiment with their own examples. This book is intended for students majoring in applied mathematics, business, and engineering. The authors use a formulation-algorithm-example approach, rather than the classical definition-theorem-proof, making the material understandable to senior undergraduates and beginning graduates.
This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type" Liapunov functions are ubiquitous in the literature attracted the attention of the authors and led to some natural questions. Why does this happen so often? What are the spe cial virtues of these functions in this context? Do they occur so frequently merely because they belong to the simplest class of Liapunov functions and are thus more convenient, or are there any more specific reasons? This monograph constitutes the authors' synthesis of the work on this subject that has been jointly developed by them, among others, producing and compiling results, properties, and examples for many years, aiming to answer these questions and also to formalize some of the folklore or "cul ture" that has grown around diagonal stability and diagonal-type Liapunov functions. A natural answer to these questions would be that the use of diagonal type Liapunov functions is frequent because of their simplicity within the class of all possible Liapunov functions. This monograph shows that, although this obvious interpretation is often adequate, there are many in stances in which the Liapunov approach is best taken advantage of using diagonal-type Liapunov functions. In fact, they yield necessary and suffi cient stability conditions for some classes of nonlinear dynamical systems.
In Sanskrit, the word “Sutra” means “thread”, “hints” or “guidelines”. The book explains the way to reach the ultimate zenith of human evolution. In this book the ultimate state of Om is adored and expounded. It includes fifty-five Sanskrit verses and their English translation and explanation. This is a book of wisdom for walking on the path of enlightenment. The Sutras provide the techniques and means to clear the mind from the accumulated experiences, conditioning and memories that bind humans to the world of sorrow. As one is established in Om, life is filled with peace, joy and harmony. The book is organized into twelve parts. Each part elaborates steps for breaking free of the limited identification and training the mind to achieve oneness with the universe. Each sutra is presented as Sanskrit text followed by transliteration, precise English translation and authoritative explanation.
Ambitious and encyclopaedic in scope, this is a first-of-its-kind book that presents the history of media and entertainment in India -- from the times of the Indus Valley Civilization right up to the twenty-first century. The book starts with an examination of the origins, looking at a wide array of aspects such as: the state of entertainment during Harappan and Vedic times, including details from the Natyashastra; the early drama, music and dance of Kalidasa; the development of ragas; musical instruments and early folk traditions; the genesis of classical dance forms; developments through the ages, including in the Mughal period, in the southern kingdoms, in the north-east, and under the Marathas and the British. Independence onwards, the book takes a decade-wise look at the evolution of newspapers, cinema, music, television, dance, theatre and radio. The author, himself a film producer, director and lyricist who has worked in the entertainment industry all his life, brings his unique perspective to bear on the subject. This pioneering work is a must-read not just for the students and practitioners of the arts and media but also for their lay consumers.
The importance of Purushartha Chatushtya is well known since time immemorial. It is always necessary that each individual is to be made oriented to fulfill the requirements to accomplish the goals for Purushartha Chatushtya and that is highly dependent upon the healthy status of every human being.1 As it has been enumerated that Ashraya of Vyadhi is Deha and Manas and both are illuminating about the Swastha Sharira. Again it has been advised that keeping everything aside, body is to be concentrated because in absence of body i.e. healthy body nothing there is absence of all bodily entities.2 Hence, the primitive aim of Ayurveda is to maintain the normalcy of health which is followed by prevention of the disease
This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type" Liapunov functions are ubiquitous in the literature attracted the attention of the authors and led to some natural questions. Why does this happen so often? What are the spe cial virtues of these functions in this context? Do they occur so frequently merely because they belong to the simplest class of Liapunov functions and are thus more convenient, or are there any more specific reasons? This monograph constitutes the authors' synthesis of the work on this subject that has been jointly developed by them, among others, producing and compiling results, properties, and examples for many years, aiming to answer these questions and also to formalize some of the folklore or "cul ture" that has grown around diagonal stability and diagonal-type Liapunov functions. A natural answer to these questions would be that the use of diagonal type Liapunov functions is frequent because of their simplicity within the class of all possible Liapunov functions. This monograph shows that, although this obvious interpretation is often adequate, there are many in stances in which the Liapunov approach is best taken advantage of using diagonal-type Liapunov functions. In fact, they yield necessary and suffi cient stability conditions for some classes of nonlinear dynamical systems.
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