Continuity of separately continuous mappings

By means of a topological game, a class of topological spaces which contains compact spaces, q-spaces and W-spaces was defined in [BOUZIAD, A.: The Ellis theorem and continuity in groups, Topology Appl. 50 (1993), 73–80]. We will show that if Y belongs to this class, every separately continuous function f: X × Y → Z is jointly continuous on a dense subset of X × Y provided that X is σ-β-unfavorable and Z is a regular weakly developable space.     

Joint continuity of separately continuous mappings on topological groups

The main theorem of this paper is somewhat stronger than the following statement: Let be a Baire semitopological group, let be a first countable one and let be a first countable topological group; then each separately continuous bi-homomorphism from into is jointly continuous. This theorem has some consequences on joint continuity of separately continuous multiplication of rings and scalar multiplication of modules.

     

Extremal problems in the theory of quasiconformal mappings

Kemerovo. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 1, pp. 202–204, January–February, 1990.     

Fixed-point theory for weakly sequentially continuous mappings

Some fixed-point theorems are established for weakly contractive operators. These results will then be used to establish existence principles for functional, differential, and integral equations.     

Diagonals of separately pointwise Lipschitz mappings

It is proved that, for a metric space X and a normed space Z, the diagonals of pointwise Lipschitz mappings f : X ²? →?Z are exactly stable pointwise limits of pointwise Lipschitz mappings. The joint Lipschitz property of separately pointwise Lipschitz mappings f : X?×?Y?→?Z, where X, Y, and Z are metric spaces, is investigated.     

Inverse problems of optimal control in creep theory

The statement of the inverse quasistatic problems of creep theory is given in the form of a variational principle and optimal control with the restrictions on displacements and stresses. Also the necessary conditions of optimality are presented. While solving some certain examples, we obtain a continuous function of optimal loading which depends on two parameters. Some method of determining the parameters from the given conditions of the problem is constructed and numerically realized.     

On the continuity of separately continuous bihomomorphisms

Separately continuous bihomomorphisms on a product of convergence or topological groups occur with great frequency. Of course, in general, these need not be jointly continuous. In this paper, we exhibit some results of Banach-Steinhaus type and use these to derive joint continuity from separate continuity. The setting of convergence groups offers two advantages. First, the continuous convergence structure is a powerful tool in many duality arguments. Second, local compactness and first countability, the usual requirements for joint continuity, are available in much greater abundance for convergence groups.     

Inverse problems in queueing theory and Internet probing

Queueing theory is typically concerned with the solution of direct problems, where the trajectory of the queueing system, and laws thereof, are derived based on a complete specification of the system, its inputs and initial conditions. In this paper we point out the importance of inverse problems in queueing theory, which aim to deduce unknown parameters of the system based on partially observed trajectories. We focus on the class of problems stemming from probing based methods for packet switched telecommunications networks, which have become a central tool in the measurement of the structure and performance of the Internet. We provide a general definition of the inverse problems in this class and map out the key variants: the analytical methods, the statistical methods and the design of experiments. We also contribute to the theory in each of these subdomains. Accordingly, a particular inverse problem based on product-form queueing network theory is tackled in detail, and a number of other examples are given. We also show how this inverse problem viewpoint translates to the design of concrete Internet probing applications.     

Inverse acoustic problems: theory and numerical methods

We study the inverse problem for the acoustic equation. The several numerical methods are considered and investigated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generating continuous mappings with Lipschitz mappings

If is a metric space, then and denote the semigroups of continuous and Lipschitz mappings, respectively, from to itself. The relative rank of modulo is the least cardinality of any set where generates . For a large class of separable metric spaces we prove that the relative rank of modulo is uncountable. When is the Baire space , this rank is . A large part of the paper emerged from discussions about the necessity of the assumptions imposed on the class of spaces from the aforementioned results.

     

Inverse boundary value problems at the boundary—continuous dependence

We use the methods of microlocal analysis to give a new proof of a theorem of Kohn and Vogelius, showing that the boundary values of a continuous isotropic conductivity can be recovered from voltage and current measurements at the boundary. Moreover, we prove sharp estimates to establish the continuous dependence of the boundary values of the conductivity on the voltage to current maps.     

A new method of solving variational problems in the theory of quasiconformal mappings

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 2, pp. 105–114, March–April, 1988.     

On the homeomorphism of continuous mappings

Denote by C(X) the partially ordered (PO) set of all continuous epimorphisms of a space X under the natural identification of homeomorphic epimorphisms. The following homeomorphism theorem for bicompacta is implicitly contained in Magill’s 1968 paper: two bicompacta X and Y are homeomorphic if and only if the PO sets C(X) and C(Y) are isomorphic. In the present paper, Magill’s theorem is extended to the category of mappings in which the role of bicompacta is played by perfect mappings. The results are obtained in two versions, namely, in the category TOP _Z (of triangular commutative diagrams) and in the category MAP (of quadrangular commutative diagrams).     

Inverse spectral theory for Sturm-Liouville problems with finite spectrum

For any positive integer and any given distinct real numbers we construct a Sturm-Liouville problem whose spectrum is precisely the given set of numbers. Such problems are of Atkinson type in the sense that the weight function or the reciprocal of the leading coefficient is identically zero on at least one subinterval.