Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov functions with variable sign, expressed in quadratic forms, to the solution of this problem. The authors explore the preservation of invariant tori of dynamic systems under perturbation. This volume is a classic contribution to the literature on stability theory and provides a useful source of reference for postgraduates and researchers.
Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov func
First published in 1991. This volume presents a brief description of the natural conditions of the permafrost regions, the properties of the permafrost and the processes occurring in it, the fundamentals of the heat transfer processes during drilling and the service temperature conditions of the tool. Methods and devices for cooling the flushing media, principles of quality control of flushing agents and the technology and commercial viability of their use during drilling in the permafrost have been considered. The main emphasis in this book is on the drilling technology which uses a variety of flushing agents. The text also includes a description of the technology of utilizing grouting solutions, the theory and practice of drilling with simultaneous freezing of weakly cohesive, moist ground as well as jdrilling holes in the ice-sheets of the circumpolar regions. This book is intended for engineers and technical personnel engaged in drilling for exploratory geological works.
This book presents a modified method, based on multidimensionalresidue theory, for the elimination of unknowns from a system ofnonlinear algebraic equations. An algorithm is given for constructingthe resultant of the system, and a computer implementation making useof formula manipulation software is carried out. Programmes in MAPLEare available. The algorithms and programmes are then applied toquestions from the theory of chemical kinetics, such as the search forall stationary solutions of kinetic equations and the construction ofkinetic polynomials. The subject of this book is closely connectedwith a wide range of current problems in the analysis of nonlinearsystems."Audience: " This volume will be of interest to graduate studentsand researchers whose work involves multidimensional theory ofresidues, mathematical kinetics, computer algebra, and symboliccomputation.
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