Session 1. 8:40 10:15 AM. Melamed Benjamin Rutgers University, Chair Berge’s Maximum Theorem for Non-compact Image Sets and Its Applications. Pavlo Kasyanov, Kyiv Polytechnic Institute & World Data Center, Ukraine and Eugene A. Feinberg, Stony Brook University. For an upper semi-continuous set-valued mapping from one topological space to another and for a lower semi-continuous function defined ...

A class of skew products over irrational rotations of the circle is defined which contains some systems which have strange nonchaotic attractors. The global attractor of these systems is characterized: it lies between an upper semi-continuous curve and a lower semi-continuous curve. With additional assumptions on the class of maps considered more detail of the attractor can be given. Mathematic...

Let S be a smooth projective curve over the complex numbers and X → S a semi-stable projective family of curves. Assume that both S and the generic fiber of X over S have genus at least two. Then the sheaf of absolute differentials ΩX defines a vector bundle on X which is semi-stable in the sense of Mumford-Nakano with respect to the canonical line bundle on X . The Bogomolov inequality c1(Ω 1 ...

In this paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps. These extend earlier results for real-valued Locally functions.

In this note we analyse an anisotropic, two-dimensional bootstrap percolationmodel introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced by Duarte.

We characterize finite-dimensional normed linear spaces as strongly proximinal subspaces in all their superspaces. A connection between upper Hausdorff semi-continuity of metric projection and finite dimensionality of subspace is given.

We provide simpler proofs of several boundedness theorems, contained in in articles [2], [3], for log surfaces of general type with semi log canonical singularities. At the same time, we make these proofs e ective, with explicit upper bounds.

An upper bound of the basis number of the semi-strong product of cycles with bipartite graphs is given. Also, an example is presented where the bound is achieved.

We derive an improved upper bound for the VC-dimension of neural networks with polynomial activation functions. This improved bound is based on a result of Rojas [Roj00] on the number of connected components of a semi-algebraic set.

We prove the existence of a compact, finite dimensional, global attractor for a coupled PDE system comprising a nonlinearly damped semilinear wave equation and a nonlinear system of thermoelastic plate equations, without any mechanical (viscous or structural) dissipation in the plate component. The plate dynamics is modelled following Berger’s approach; we investigate both cases when rotational...