We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric structures. To represent both aspect of uncertainty, we choose an expected distance function as a measure of uncertainty. A formal logical system is constructed for the reasoning about expected distance. Soundness and completeness are shown f...

Recall that a metric space M is said to be complete if every Cauchy sequence in M converges to a limit in M . Not all metric spaces are complete, but it is a fact that all metric spaces can be “completed”, in a way that preserves the essential structure of the metric space. If the space in question is a normed linear space this process completes the space to a Banach space, and an inner product...

We derive and study necessary and sufficient conditions for an S-bundle to admit an invariant metric of positive or nonnegative sectional curvature. In case the total space has an invariant metric of nonnegative curvature and the base space is odd dimensional, we prove that the total space contains a flat totally geodesic immersed cylinder. We provide several examples, including a connection me...

for a symmetric group $g:=sym(n)$ and a conjugacy class $mathcal{x}$ of involutions in $g$, it is known that if the class of involutions does not have a unique fixed point, then - with a few small exceptions - given two elements $a,x in mathcal{x}$, either $angbrac{a,x}$ is isomorphic to the dihedral group $d_{8}$, or there is a further element $y in mathcal{x}$ such that $angbrac{a,y} cong ang...

The Pauli-Fierz Hamiltonian describes an interaction between a low energy electron and photons. Existence of ground states has been established. The purpose of this talk is to show that its ground states is exactly two-fold in a weak coupling region. 1 The Pauli-Fierz Hamiltonian This is a joint work with Herbert Spohn . The Hamiltonian in question is the PauliFierz Hamiltonian in nonrelativisi...

We determine the gluino condensate 〈 Trλ2 〉 in the pure N = 1 super YangMills theory (SYM) for the classical gauge groups SU(r+1), SO(2r+1), USp(2r) and SO(2r), by deforming the pure N = 2 SYM theory with the adjoint scalar multiplet mass, following the work by Finnell and Pouliot, and Ritz and Vainshtein. The value of the gluino condensate agrees in all cases with what was found in the weak co...

This document presents software product metrics we usually use to build software defect prediction models. 1 Software product metrics This document presents software product metrics we usually use to build software defect prediction models, especially those built by Madeyski and Jureczko [6, 5, 4]. • The metrics suite suggested by Chidamber and Kemerer [2]: Weighted Methods per Class (WMC). The...