Bounded function

About: Bounded function is a research topic. Over the lifetime, 77295 publications have been published within this topic receiving 1321552 citations.

Parameterized complexity theory

Abstract: Fixed-Parameter Tractability.- Reductions and Parameterized Intractability.- The Class W[P].- Logic and Complexity.- Two Fundamental Hierarchies.- The First Level of the Hierarchies.- The W-Hierarchy.- The A- Hierarchy.- Kernelization and Linear Programming Techniques.- The Automata-Theoretic Approach.- Tree Width.- Planarity and Bounded Local Tree Width.- Homomorphisms and Embeddings.- Parameterized Counting Problems.- Bounded Fixed-Parameter Tractability.- Subexponential Fixed-Parameter Tractability.- Appendix, Background from Complexity Theory.- References.- Notation.- Index.

Homogenization and two-scale convergence

Abstract: Following an idea of G. Nguetseng, the author defines a notion of “two-scale” convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in $L^2 (\Omega )$ are proven to be relatively compact with respect to this new type of convergence. A corrector-type theorem (i.e., which permits, in some cases, replacing a sequence by its “two-scale” limit, up to a strongly convergent remainder in $L^2 (\Omega )$) is also established. These results are especially useful for the homogenization of partial differential equations with periodically oscillating coefficients. In particular, a new method for proving the convergence of homogenization processes is proposed, which is an alternative to the so-called energy method of Tartar. The power and simplicity of the two-scale convergence method is demonstrated on several examples, including the homogenization of both linear and nonlinear second-order elliptic equations.

Foundations of Optimal Control Theory

Abstract: : This complete and authoritative presentation of the current status of control theory offers a useful foundation for both study and research. With emphasis on general nonlinear differential systems, the book is carefully and systematically developed from elementary motivating examples, through the most comprehensive theory, to the final numerical solution of serious scientific and engineering control problems. The book features reviews of the most recent researches on processes described by partial differential equations, functional- differential, and delay-differential equations; the most recent treatment of impulse controllers, bounded rate controllers, feedback controllers, and bounded phase problems; and many unpublished new research results of the authors. In addition to an exhaustive treatment of the quantitative problems of optimal control, the qualitative concepts of stability, controllability, observability, and plant recognition receive a complete exposition. (Author)

First order quasilinear equations in several independent variables

Abstract: In this paper we construct a theory of generalized solutions in the large of Cauchy's problem for the equations in the class of bounded measurable functions. We define the generalized solution and prove existence, uniqueness and stability theorems for this solution. To prove the existence theorem we apply the "vanishing viscosity method"; in this connection, we first study Cauchy's problem for the corresponding parabolic equation, and we derive a priori estimates of the modulus of continuity in of the solution of this problem which do not depend on small viscosity.Bibliography: 22 items.