Recall that a continuous function $fcolon Xto Y$ between Tychonoff spaces is proper if and only if the Stone extension $f^{beta}colon beta Xtobeta Y$ takes remainder to remainder, in the sense that $f^{beta}[beta X-X]subseteq beta Y-Y$. We introduce the notion of ``taking remainder to remainder" to frames, and, using it, we define a frame homomorphism $hcolon Lto M$ to be $beta$-proper, $lambd...

Objective: To present a multidimensional scale for identifying strategic thinkers and profiling strategists. Research Design & Methods: The multi-method approach used included systematic literature review, qualitative studies (biographical IDI’s), quantitative research (a survey). Findings: First, the review conceptualised operationalised multi-dimensional construct of thinking. Second, bio...

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...

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 ...

Necessary and sufficient conditions are given (in terms of monodromy) for extending a family of smooth curves over an open subset U ⊂ S to a family of stable curves over S. More precisely, we introduce the abelian monodromy extension (AME) property and show that the standard Deligne-Mumford compactification is the unique, maximal AME compactification of the moduli space of curves. We also show ...

We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics. We explain how this work implies that there is a “landscape” of string/M theory vacua, perhaps containing many candidates for describing r...