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Weakly Connected Nonlinear Systems
Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected
Measure and Integral
Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less
The Separable Galois Theory of Commutative Rings
The Separable Galois Theory of Commutative Rings, Second Edition provides a complete and self-contained account of the Galois theory of commutative rings from the viewpoint of categorical classification theorems and using solely the techniques of commutative algebra. Along with updating nearly every result and explanation, this edition contains a n
Strong Nonlinear Oscillators
This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author’s original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear osc...
Stability Theory for Dynamic Equations on Time Scales
This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete ...
Quadratic Irrationals
Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups.T
Algorithms of the Synthesis of Optimal Regulations
This book focuses on methods to solutions regarding matrix equations: algebraic, periodic, and unilateral Riccati equations, Lyapunov equations, Silvester equations, generalized Silvester equations, and factorization of matrix polynomials in continuous and discrete cases. These equations are used to solve problems of the synthesis of optimal controllers. Also presented is the problem of the synthesis of optimal controllers in the frequency domain when measuring part of the phase coordinates. A general parameterization algorithm is proposed for its solution. The well-known parameterizations (Youla–Jabr–Bongiorno (1976) and Desoer–Liu–Murrau–Saeks (1980)) are demonstrated by us to form a special case of the proposed general parameterization algorithm. The obtained results can be applied to solve various problems in oil production by the gas-lift method and rod pump systems, unmanned aerial vehicles, and walking machines. Each section is illustrated by examples. The MATLAB environment is used for numerical solution of the problems. The book is intended for students and experts in applied mathematics and control systems theory.
Classification of Lipschitz Mappings
Classification of Lipschitz Mappings presents a systematic, self-contained treatment of a new classification of Lipschitz mappings and its application in many topics of metric fixed point theory. Suitable for readers interested in metric fixed point theory, differential equations, and dynamical systems, the book only requires a basic background in
