Related papers: Universal Walker metrics

Let $r$ and $n$ be positive integers such that $r<n$, and $\mathbb{K}$ be an arbitrary field. In a recent work, we have determined the maximal dimension for a linear subspace of $n$ by $n$ symmetric matrices with rank less than or equal to…

For a metrizable space, we consider the space of all metrics generating the same topology of the metrizable space, and this space of metrics is equipped with the supremum metric. In this paper, for every metrizable space, we establish that…

Family of replica matrices, related to general ultrametric spaces, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed.

We suggest a concept of generalized `angles' in arbitrary real normed vector spaces. We give for each real number a definition of an `angle' by means of the shape of the unit ball. They all yield the well known Euclidean angle in the…

We study the universal properties of distributions of eigenvalues of random matrices in the large $N$ limit. The distributions fall in universality classes characterized entirely by the support of the spectral density.

This paper gives new insights into the class of Generalized Douglas Weyl ($GDW$)-metrics. This projective invariant class of Finsler metrics, contains some well-known Finsler metrics such as Douglas, Weyl and $R$-quadratic metrics. Here,…

The space of four dimensional string and $M$ theory vacua with non-Abelian gauge symmetry, chiral fermions and unbroken supersymmetry beyond the electroweak scale appears to be a disconnected space whose different components represent…

Let US be the class of all ultrametric spaces generated by labeled star graphs. We prove that compact US-spaces are the completions of totally bounded ultrametric spaces generated by decreasingly labeled rays. We characterize the…

We describe some Cartesian products of metric spaces and find conditions under which products of ultrametric spaces are ultrametric.

We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…

There are many problems and configurations in Euclidean geometry that were never extended to the framework of (normed or) finite dimensional real Banach spaces, although their original versions are inspiring for this type of generalization,…

We study a uniform version of the strong diameter two property. In particular, we find a characterisation that does not involve ultrafilters and we use it to provide some examples of spaces with this uniform property that do not follow from…

Metric spaces $(X, d)$ are ubiquitous objects in mathematics and computer science that allow for capturing (pairwise) distance relationships $d(x, y)$ between points $x, y \in X$. Because of this, it is natural to ask what useful…

A special class of (complex) para-Hermite Einstein spaces is analyzed. For this class of spaces the self-dual Weyl tensor is type-[D] in the Petrov-Penrose classification. The anti-self-dual Weyl tensor is algebraically degenerate,…

As was recently observed by M. Xu and J. Wolf, there is a gap in Berard Bergery's classification of odd dimensional positively curved homogeneous spaces. Since this classification has been used in other papers as well, we give a modern,…

In this paper we prove in certain n-dimensional normed spaces X the existence of full-dimensional equilateral simplices of large size inscribed to the unit ball B. This extends the construction of Makeev [Mak] in dimension 4 and we also…

Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…

We give a new short proof for the uniqueness of the universal minimal space. The proof holds for the uniqueness of the universal object in every collection of topological dynamical systems closed under taking projective limits and…

Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…

We find necessary and sufficient conditions under which an arbitrary metric space $X$ has a unique pretangent space at the marked point $a\in X$. Key words: Metric spaces; Tangent spaces to metric spaces; Uniqueness of tangent metric…