相关论文: Non Standard Metric Products

Metric algebras are metric variants of $\Sigma$-algebras. They are first introduced in the field of universal algebra to deal with algebras equipped with metric structures such as normed vector spaces. Recently a similar notion of…

A. Derdzinki [D] gave examples of Riemannian metrics with harmonic curvature and non parallel Ricci tensor on some compact manifolds $(M,g]$ . We examine their existence as well as their number wich naturally depends on the geometry of the…

We prove that rationally essential manifolds with suitably large fundamental groups do not admit any maps of non-zero degree from products of closed manifolds of positive dimension. Particular examples include all manifolds of non-positive…

For a surface immersed in a three-dimensional space endowed with a norm instead of an inner product, one can define analogous concepts of curvature and metric. With these concepts in mind, various questions immediately appear. The aim of…

Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming…

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. To represent both aspect of uncertainty, we choose an expected distance function as…

By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local…

The paper studies a generalized von Neumann-Jordan constant of non-normable metrics on vector spaces. To the best of our knowledge, all existing results of the von Neumann-Jordan constant and its generalizations have been established only…

We consider a general class of non-linear Bellman equations. These open up a design space of algorithms that have interesting properties, which has two potential advantages. First, we can perhaps better model natural phenomena. For…

For a class of wreath-like product groups with property (T), we describe explicitly all the embeddings between their von Neumann algebras. This allows us to provide a continuum of ICC groups with property (T) whose von Neumann algebras are…

Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.

This is the second part of the paper (the first part is published in Jour. of AMS, vol.9, 1135--1170, q-alg/9508017). In the first part, we defined for every modular tensor category (MTC) inner products on the spaces of morphisms and proved…

For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…

The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…

In this paper we review $G_2$ and $Spin(7)$ geometries in relation with a special type of metric structure which we call warped-like product metric. We present a general ansatz of warped-like product metric as a definition of warped-like…

We consider finite point subsets (distributions) in compact metric spaces. Non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in metric balls are given in the case of general…

Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, but not actually…

We demonstrate --- using the case of the two-dimensional quantum systems --- that the "natural measure on the space of density matrices describing N-dimensional quantum systems" proposed by Zyczkowski et al (quant-ph/9804024) does not…

A 4-dimensional Riemannian manifold equipped with an additional tensor structure, whose fourth power is the identity, is considered. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant, and it…

We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the…