A concise outline of the basic facts of potential theory and quasiconformal mappings makes this book an ideal introduction for non-experts who want to get an idea of applications of potential theory and geometric function theory in various fields of construction analysis.
A concise outline of the basic facts of potential theory and quasiconformal mappings makes this book an ideal introduction for non-experts who want to get an idea of applications of potential theory and geometric function theory in various fields of construction analysis.
Over the last thirty years an abundance of papers have been writ ten on adaptive dynamic control systems. Nevertheless, now it may be predicted with confidence that the adaptive mechanics, a new division, new line of inquiry in one of the violently developing fields of cybernetic mechanics, is emerging. The birth process falls far short of being com pleted. There appear new problems and methods of their solution in the framework of adaptive nonlinear dynamics. Therefore, the present work cannot be treated as a certain polished, brought-to-perfection school textbook. More likely, this is an attempt to show a number of well known scientific results in the parametric synthesis of nonlinear systems (this, strictly speaking, accounts for the availability of many reviews), as well as to bring to notice author's developments on this question undoubtedly modern and topical. The nonlinear, and practically La grangian, systems cover a wide class of classical objects in theoretical mechanics, and primarily solid-body (robotic, gyroscopic, rocket-cosmic, and other) systems. And what is rather important, they have a direct trend to practical application. To indicate this discussion, I should like to notice that it does not touch upon the questions concerned with the linear and stochastic con trolobjects. Investigated are only nonlinear deterministic systems being in the conditions when some system parameters are either unknown or beyond the reach of measurement, or they execute an unknown limited and fairly smooth drift in time.
In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.
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