Related papers: Angular equivalence of normed spaces

Given a locally convex vector space with a topology induced by Hilbert seminorms and a continuous bilinear form on it we construct a topology on its symmetric algebra such that the usual star product of exponential type becomes continuous.…

The equivalence principle is treated on a mathematically rigorous base on sufficiently general subsets of a differentiable manifold. This is carried out using the basis of derivations of the tensor algebra over that manifold. Necessary…

In this paper we study some geometric properties like parallelism, orthogonality and semi-rotundity in the space of bounded linear operators. We completely characterize parallelism of two compact linear operators between normed linear…

Let $E$ be a $(\mathrm{IV})$-polyhedral Banach space. We show that, for each $\epsilon>0$, $E$ admits an $\epsilon$-equivalent $\mathrm{(V)}$-polyhedral norm such that the corresponding closed unit ball is the closed convex hull of its…

The Erd\H{o}s-Anning theorem states that every point set in the Euclidean plane with integer distances must be either collinear or finite. More strongly, for any (non-degenerate) triangle of diameter~$\delta$, at most $O(\delta^2)$ points…

Two matrices $A$ and $B$ are called unitary (resp. orthogonal) equivalent if $AU=VB$ for two unitary (resp. orthogonal) matrices $U$ and $V$. Using trace identities, criteria are given for simultaneous unitary, orthogonal or complex…

Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…

Critical points of an invariant function may or may not be symmetric. We prove, however, that if a symmetric critical point exists, those adjacent to it are generically symmetry breaking. This mathematical mechanism is shown to carry…

In this work, we introduce a new geometry based on the difference angle, an angle defined as the difference of slopes of two lines, together with an axiomatic system for angles. This framework provides a constructive approach to the…

A quandle is an algebraic system whose axioms generalize the algebraic structure of the point symmetries of symmetric spaces. In this paper, we give a definition of Euler characteristics for quandles. In particular, the quandle Euler…

The apparent discrepancy between the bending of light predicted by the equivalence principle and its corresponding value in general relativity is resolved by evaluating the deflection of light with respect to a direction that is parallel…

Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of…

We introduce a bulging triangle like the generalization of the Reuleaux triangle. We may be able to propose various ways to bulge a triangle, but this paper presents the way so that its vertices are the same as them of the original…

In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and we study the notion of $D$-compactness and $D$-boundedness in probabilistic normed spaces.

Congruent polygons are congruent in angles as well as in edge lengths. We concentrate on the angle aspect, and investigate how tilings of the sphere by congruent pentagons can be determined by the angle information only. We also investigate…

The deformation principle admits one to obtain a very broad class of nonuniform geometries as a result of deformation of the proper Euclidean geometry. The Riemannian geometry is also obtained by means of a deformation of the Euclidean…

Symplectic and Finsler geometry are used to settle a conjecture of Sch\"affer stating that the girth of a normed space--the infimum of the lengths of all closed, rectifiable, centrally symmetric curves on its unit sphere--equals the girth…

It is argued that the standard quantum mechanical description of the Bell correlations between entangled subsystems is in conflict with relativistic space-time symmetry. Proposals to abandon relativistic symmetry, in the sense of explicitly…

For every finite collection of curves on a surface, we define an associated (semi-)norm on the first homology group of the surface. The unit ball of the dual norm is the convex hull of its integer points. We give an interpretation of these…

We study the algebraic and geometric structure related to tensor nuclear norms. We show that the unit ball of the nuclear norm is the convex hull of an irreducible real variety and give an explicit description of its real vanishing ideal.…