Elements Of Stochastic Dynamics
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Elements Of Stochastic Dynamics
Author: Guo-qiang Cai
language: en
Publisher: World Scientific Publishing Company
Release Date: 2016-08-11
Stochastic dynamics has been a subject of interest since the early 20th Century. Since then, much progress has been made in this field of study, and many modern applications for it have been found in fields such as physics, chemistry, biology, ecology, economy, finance, and many branches of engineering including Mechanical, Ocean, Civil, Bio, and Earthquake Engineering.Elements of Stochastic Dynamics aims to meet the growing need to understand and master the subject by introducing fundamentals to researchers who want to explore stochastic dynamics in their fields and serving as a textbook for graduate students in various areas involving stochastic uncertainties. All topics within are presented from an application approach, and may thus be more appealing to users without a background in pure Mathematics. The book describes the basic concepts and theories of random variables and stochastic processes in detail; provides various solution procedures for systems subjected to stochastic excitations; introduces stochastic stability and bifurcation; and explores failures of stochastic systems. The book also incorporates some latest research results in modeling stochastic processes; in reducing the system degrees of freedom; and in solving nonlinear problems. The book also provides numerical simulation procedures of widely-used random variables and stochastic processes.A large number of exercise problems are included in the book to aid the understanding of the concepts and theories, and may be used for as course homework.
Probabilistic Methods In The Theory Of Structures: Strength Of Materials, Random Vibrations, And Random Buckling
Author: Isaac E Elishakoff
language: en
Publisher: World Scientific
Release Date: 2017-03-23
The first edition of this book appeared over three decades ago (Wiley-Interscience, 1983), whereas the second one saw light on the verge of new millennium (Dover, 1999). This is third, corrected and expanded edition that appears in conjunction with its companion volume .Thus, the reader is able to both get acquainted with the theoretical material and be able to master some of the problems, following Chinese dictum: I hear and I forget. I see and I remember. I do and I understand — Confucius.The main idea of the book lies in the fact that three topics: probabilistic strength of materials, random vibrations, and probabilistic buckling are presented in a single package allowing one to see the forest in between the trees. Indeed, these three topics usually are presented in separate manners, in different specialized books. Here, the reader gets a feeling of true unity of the subject at large in order to appreciate that in the end what one wants is reliability of the structure, in conjunction with its operating conditions.As the author describes in the Preface of the second edition, this book was not conceived ab initio, as a book that author strived to compose. Rather, it was forced, as it were, upon me due to two reasons. One was rather a surprising but understandable requirement in the venerable Delft University of Technology, The Netherlands to prepare the lecture notes for students with the view of reducing skyrocketing costs of acquisition of textbooks by the students. The other one was an unusually warm acceptance of the notes that the author prepared while at Delft University of Technology and later in Haifa, at the Technion-Israel Institute of Technology by the legendary engineering scientist Warner Tjardus Koiter (1914-1997). The energy necessary to prepare the second and third editions came from enthusiastic reviews that appeared in various sources. Author embraced the simplicity of exposition as the main virtue following Isaac Newton's view that 'Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.'
The Elements and Dynamic Systems of Economic Growth and Trade Models
This updated and expanded book examines the fundamentals of economic growth models as expressed by dynamic systems of nonlinear differential equations. With homogeneous dynamic systems as the unifying mathematical framework, the time paths and long-run stability properties of the solutions to classical, neoclassical, and modern macroeconomic growth models are analyzed. The general structure and solutions of two-sector and multi-sector growth models are also explored, with special attention given to the evolution of output compositions and sectoral factor allocations involved in Walrasian general equilibrium dynamics. Ramsey optimal growth (saving) models with variable intertemporal substitution (non-homothetic utility) are discussed to demonstrate the ability to generate a realistic historically observed evolution of economic per capita growth rates and saving rates. The book aims to highlight how basic economic growth models can be extended widely, including international trading economies, world market prices, commodity trade patterns, and issues related to globalization, migrations, and international factor movements. It will be relevant to students and researchers interested in economic growth and trade policy.