In this short note on my talk I want to point out the mathematical difficulties that arise in the study of the relation of Wightman and Euclidean quantum field theory, i.e., the relation between the hierarchies of Wightman and Schwinger functions. The two extreme cases where the reconstructed Wightman functions are either tempered distributions — the wellknown Osterwalder-Schrader reconstructio...

We prove that a metric measure space equipped with Dirichlet form admitting an Euclidean heat kernel is necessarily isometric to the space. This helps us providing alternative proof of Colding’s celebrated almost rigidity volume theorem via quantitative version our main result. also discuss case spherical kernel.

In this paper a study of the influence of luminance L* at the CIE L* a* b* color space during color segmentation in highly saturated color images is presented. A comparative study is made between the behavior of segmentation in color images using (1) the Euclidean metric of the RGB channels (2) the Euclidean metric of a* and b* in CIE L*a*b* color space and (3) an adaptive color similarity func...

A metric space has doubling dimension d if for every ρ > 0, every ball of radius ρ can be covered by at most 2d balls of radius ρ/2. This generalizes the Euclidean dimension, because the doubling dimension of Euclidean space Rd is proportional to d. The following results are shown, for any d ≥ 1 and any metric space of size n and doubling dimension d: First, the maximum number of diametral pair...

We study the information metric on instanton moduli spaces in two-dimensional nonlinear sigma models. In the CP1 model, the information metric on the moduli space of one instanton with the topological charge Q=k(k > or =1) is a three-dimensional hyperbolic metric, which corresponds to Euclidean anti-de Sitter space-time metric in three dimensions, and the overall scale factor of the information...

Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in R in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated...

We express any Courant algebroid bracket by means of a metric connection, and construct a Courant algebroid structure on any orthogonal, Whitney sum E⊕C where E is a given Courant algebroid and C is a flat, pseudo-Euclidean vector bundle. Then, we establish the general expression of the bracket of a transitive Courant algebroid, that is, a Courant algebroid with a surjective anchor, and describ...

We study the information metric on instanton moduli spaces in two-dimensional nonlinear σ models. In the CP 1 model, the information metric on the moduli space of one instanton with the topological charge Q = k (k ≥ 1) is a three-dimensional hyperbolic metric, which corresponds to Euclidean anti–de Sitter space-time metric in three dimensions, and the overall scale factor of the information met...