A Note on nonautonomous klein-gordon-schrödinger equations with homogeneous dirichlet boundary condition

This note discusses the long time behavior of solutions for nonautonomous weakly dissipative Klein-Gordon-Schrodinger equations with homogeneous Dirichlet boundary condition.The authors prove the existence of compact kernel sections for the associated process by using a suitable decomposition of the equations.     

Fiberwise absolute neighborhood extensors for a class of metrizable spaces

In the paper we study fiberwise absolute neighborhood extensors with respect to some classes of metrizable spaces by means of the local extension properties and the lifting properties of the underlying spaces.     

The genus and the category of configuration spaces

In this paper configuration spaces of smooth manifolds are considered. The accent is made on actions of certain groups (mostly p-tori) on this spaces by permuting their points. For such spaces the cohomological index, the genus in the sense of Krasnosel'skii-Schwarz, and the equivariant Lyusternik-Schnirelmann category are estimated from below, and some corollaries for functions on configuration spaces are deduced.     

The emergence of open sets,closed sets,and limit points in analysis and topology

General topology has its roots in real and complex analysis, which made important uses of the interrelated concepts of open set, of closed set, and of a limit point of a set. This article examines how those three concepts emerged and evolved during the late 19th and early 20th centuries, thanks especially to Weierstrass, Cantor, and Lebesgue. Particular attention is paid to the different forms of the Bolzano–Weierstrass Theorem found in the latter's unpublished lectures. An abortive early, unpublished introduction of open sets by Dedekind is examined, as well as how Peano and Jordan almost introduced that concept. At the same time we study the interplay of those three concepts (together with those of the closure of a set and of the derived set of a set) in the struggle to determine the ultimate foundations on which general topology was built, during the first half of the 20th century.     

Decomposition of the curvature tensor of hyper-Kähler manifolds

We give the decomposition into irreducible components of the curvature tensor of a hyper-Kähler manifold.     

Evolutionary weighted p-Laplacian with boundary degeneracy

The paper concerns the well-posedness problem of an evolutionary weighted p-Laplacian with boundary degeneracy. Different from the classical theory for linear equations, it is shown that the degenerate portion of the boundary should be decomposed into two parts: the strongly degenerate boundary on which the equation exhibits hyperbolic characteristics and the weakly degenerate boundary on which the equation still exhibits parabolic characteristics. We formulate reasonably the boundary value condition and establish the existence and uniqueness theorems.     

Equivariant strong shape

In this paper we propose a construction of the equivariant strong shape for compact metrizable G-spaces using an equivariant version of so-called cotelescopes and the concept of a fibrant G-space.