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Convolutional calculus
178
Book Reviews
networks and other technical systems which use an allocation of resources of a central processor among many users. These models are characterized by nonclassical service disciplines such as round-robin, egalitarian or foreground-background processor-sharing, etc. The main purpose is to present the author's own research results and recent developments in exact solutions for the problems of determination of the sojourn-time and queue-length distributions as well as another performance measure for basic processor-sharing queueing models. Special attention is devoted to the background of the novel analytic methods for analysis of the random processes in nonclassical queues. The book is also concerned with various aspects of the sojourn-time and queue-length problems in queueing networks with particular emphasis on the cases of a Poisson output process for a broad class of service disciplines. The results include computational-convenient formulae for some performance measures. Some numerical examples are presented. The book is addressed to scientists in the field of queueing theory and its computer applications. It also can be recommended to specialists in computer science, in particular, to operating systems designers as well as to senior and post-graduate students. (WFA)
I.H. Dimovski, Convolutional Calculus, Mathematics and its Applications (East European Series). Kluwer, Dordrecht, 1990. 184 pp., Dfl.150, US$79, UK£53, ISBN 0-7923-0623-6. This volume presents the development of a method based on the notion of the convultion of a linear operator. This unifies approaches from operational calculus, multiplier theory, algebraic analysis and spectral theory. The starting point is Mikusinski's approach to the Heaviside operational calculus and this is extended to local and nonlocal boundary value problems for first- and second-order linear differential operators. The basic tool employed for new developments is the transmutation method. This is used for obtaining explicit convolutons for the Sturm-Liouville and Hankel finite integral transforms. The most important application of the convolutional method is the extension of the Duhamel method for space-variables of problems of mathematical physics in rectangular domains. Duhamel representations are obtained for a large class of nonlocal boundary value problems for the diffusion, wave and Poisson equations. The book should be of interest to engineers, mathematicians, and mathemafcal physicists interested in applied analysis. (WFA)
V,M. G 6 | ' ~ t z :~ and Yu.G. Reshetnyak, Quasiconformal Mappings and Sobolev Spaces, Mathe-
matics and its Applications (Soviet Series). Kluwer, Dordrecht. Dfl.260, US$133, UK£85, ISBN 0-7923-0543-4. Here we find a study of the interconnection between Sobolev spaces, geometric classes of mappings (quasiconformal and quasi-isometric) and nonlinear capacity. Chapter 1 introduces the terminology and auxiliary results which will be used later. Chapter 2 deals with the foundations of the theory of classes of functions with generalized derivatives, and discusses in detail methods of constructing special integral representations of functions. Chapter 3 is concerned with the theory of nonlinear capacity which, in certain respects, fulfils a role similar to that of measure in
Book Reviews
networks and other technical systems which use an allocation of resources of a central processor among many users. These models are characterized by nonclassical service disciplines such as round-robin, egalitarian or foreground-background processor-sharing, etc. The main purpose is to present the author's own research results and recent developments in exact solutions for the problems of determination of the sojourn-time and queue-length distributions as well as another performance measure for basic processor-sharing queueing models. Special attention is devoted to the background of the novel analytic methods for analysis of the random processes in nonclassical queues. The book is also concerned with various aspects of the sojourn-time and queue-length problems in queueing networks with particular emphasis on the cases of a Poisson output process for a broad class of service disciplines. The results include computational-convenient formulae for some performance measures. Some numerical examples are presented. The book is addressed to scientists in the field of queueing theory and its computer applications. It also can be recommended to specialists in computer science, in particular, to operating systems designers as well as to senior and post-graduate students. (WFA)
I.H. Dimovski, Convolutional Calculus, Mathematics and its Applications (East European Series). Kluwer, Dordrecht, 1990. 184 pp., Dfl.150, US$79, UK£53, ISBN 0-7923-0623-6. This volume presents the development of a method based on the notion of the convultion of a linear operator. This unifies approaches from operational calculus, multiplier theory, algebraic analysis and spectral theory. The starting point is Mikusinski's approach to the Heaviside operational calculus and this is extended to local and nonlocal boundary value problems for first- and second-order linear differential operators. The basic tool employed for new developments is the transmutation method. This is used for obtaining explicit convolutons for the Sturm-Liouville and Hankel finite integral transforms. The most important application of the convolutional method is the extension of the Duhamel method for space-variables of problems of mathematical physics in rectangular domains. Duhamel representations are obtained for a large class of nonlocal boundary value problems for the diffusion, wave and Poisson equations. The book should be of interest to engineers, mathematicians, and mathemafcal physicists interested in applied analysis. (WFA)
V,M. G 6 | ' ~ t z :~ and Yu.G. Reshetnyak, Quasiconformal Mappings and Sobolev Spaces, Mathe-
matics and its Applications (Soviet Series). Kluwer, Dordrecht. Dfl.260, US$133, UK£85, ISBN 0-7923-0543-4. Here we find a study of the interconnection between Sobolev spaces, geometric classes of mappings (quasiconformal and quasi-isometric) and nonlinear capacity. Chapter 1 introduces the terminology and auxiliary results which will be used later. Chapter 2 deals with the foundations of the theory of classes of functions with generalized derivatives, and discusses in detail methods of constructing special integral representations of functions. Chapter 3 is concerned with the theory of nonlinear capacity which, in certain respects, fulfils a role similar to that of measure in