The main result of this note is a parametrized version of the BorsukUlam theorem. Loosely speaking, it states that for a map X × S → S (with k < n), considered as a family of maps from S to S, the set of solutions to the Borsuk-Ulam problem (i.e. opposite points in S with the same value) depends continuously on X. We actually formuate this for correspondences. The “continuity” is measured by th...

Based on the characteristics of partial discharge (PD) defects in gas insulated switchgear (GIS), four typical single defects were designed for the present paper. PD three-dimensional (3D) patterns were constructed based on the ultra high frequency detection systems. The pulse-coupled neural networks (PCNN) and wavelet packet decomposition (WPD) method were used in PD feature extraction. The re...

We characterize those regular continuous frames for which the least compactification is a perfect compactification. Perfect compactifications are those compactifications of frames for which the right adjoint of the compactification map preserves disjoint binary joins. Essential to our characterization is the construction of the frame analog of the twopoint compactification of a locally compact ...

In this paper we introduce GF-compactifications, which are compactifications of GF-spaces (a new notion introduced by the authors). We study properties of this new kind of compactification and prove that every GF-compactification is of Wallman type. We also prove that every metrizable compactification of a metric space X is a GF-compactification and, as a corollary, that every metric compactifi...

I discuss the correspondence between realistic four dimensional free fermionic models and Z2 × Z2 orbifold compactification. I discuss the properties of the Z2 × Z2 orbifold that are reflected in the realistic free fermionic models. I argue that the properties of the realistic free fermionic models arise due to the underlying Z2×Z2 orbifold compactification with nontrivial background fields. I ...

Let GL(n, C) ⊃ Un be the group of n× n complex valued invertible matrices and the subgroup of unitary matrices respectively. In this paper we study Finsler p-metrics on the homogeneous space Xn = GL(n, C)/Un for p ∈ [1,∞], which are induced by Schatten p-norms on the tangent bundle of Xn and are invariant under the action of GL(n, C). We show that for p ∈ (1,∞) the Busemann p-compactification i...