By means of numerous examples we call attention to several problems in the theory of inverse limits with upper semi-continuous bonding functions. Along with the problems we present a few partial solutions. Most of the problems we discuss arise from the failure of certain theorems from the theory of inverse limits with mappings to carry over to the setting of inverse limits with set-valued funct...

The G/G gauged supergroup valued WZNW theory is considered. It is shown that for G = OSP (1, 2), the G/G theory tensoring a (b, c, β, γ) system is equivalent to the non-critical fermionic theory. The relation between integral or half integral moded affine superalgebra and its reduced theory, the NS or R superconformal algebra, is discussed in detail. The physical state space, i.e. the BRST semi...

We argue that a semi-infinite D6-brane ending on an NS5-brane can be obtained from the condensation of the tachyon on the unstable D9-brane of type IIA theory. The construction uses a combination of the descriptions of these branes as solitons of the worldvolume theory of the D9-brane. The NS5-brane, in particular, involves a gauge bundle which is operator valued, and hence is better thought of...

We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological bifurcations of minimal invariant sets are discontinuous with respect to the Hausdorff metric, taking the form of lower semi-continuous explosions and instantaneous ap...

For a continuous nonvanishing complex-valued function g on the real line, several notions of a mean winding number are introduced. We give necessary conditions for a Toeplitz operator with matrixvalued symbol G to be semi-Fredholm in terms of mean winding numbers of detG. The matrix function G is assumed to be continuous on the real line, and no other apriori assumptions on it are made. AMS Sub...

In this article, we investigate sufficient conditions for controllability of second-order semi-linear damped neutral functional initial value problem for the class of differential inclusions in Banach spaces using the theory of strongly continuous cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. An example is provided to illustrate the result. This work i...

MRI-scanners enable non-invasive, in vivo quantitation of metabolites in, e.g., the brain of a patient. Among other things, this requires adequate estimation of the unknown temporal decay function of the complex-valued signal emanating from the metabolites. We propose a method to render a current decay estimator more simple, accurate, and robust, and test it on a simulated signal comprising con...

New observable integer-valued numbers of the topological origin were revealed by the present authors studying the conductivity theory of single crystal 3D normal metals in the reasonably strong magnetic field (B ≤ 10 3 T l). Our investigation is based on the study of dynami-cal systems on Fermi surfaces for the motion of semi-classical electron in magnetic field. All possible asymptotic regimes...

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...