相关论文: New geometric constants of isosceles orthogonal ty…

In this paper, we calculate four geometric constants for discrete Morrey spaces. The constants are generalized von Neumann-Jordan constant, modified von Neumann-Jordan constant, von Neumann-Jordan type constant, and Zb\"{a}ganu constant.…

The current paper is devoted to the study of integral curves of constant type in parabolic homogeneous spaces. We construct a canonical moving frame bundle for such curves and give the criterium when it turns out to be a Cartan connection.…

The second Poincar\'e kinematical group serves as one of new ones in addition to the known possible kinematics. The geometries with the second Poincar\'e symmetry is presented and their properties are analyzed. On the geometries, the new…

We establish a family of parametric isoperimetric-type inequalities with multiple geometric quantities for closed convex curves. These inequalities hold under certain parameter conditions. We also prove the equality conditions. Some new…

We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit…

Goyeneche et al recently proposed a notion of orthogonality for quantum Latin squares, and showed that orthogonal quantum Latin squares yield quantum codes. We give a simplified characterization of orthogonality for quantum Latin squares,…

We study the space of orthogonally additive $n$-homogeneous polynomials on $C(K)$. There are two natural norms on this space. First, there is the usual supremum norm of uniform convergence on the closed unit ball. As every orthogonally…

This paper is devoted to the study of isometrically homogeneous spaces from the view point of metric geometry. Mainly we focus on those spaces that are homeomorphic to lines. One can reduce the study to those distances on $\R$ that are…

In this paper we calculate three geometric constants, namely the von Neumann-Jordan constant, the James constant, and the Dunkl-Williams constant, for Morrey spaces and discrete Morrey spaces. These constants measure uniformly nonsquareness…

In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…

We study non-orthogonality of symmetric, regular types and show that it preserves generic stability and is an equivalence relation on the set of all generically stable, regular types. We will also prove that some of the nice properties from…

The space of $G$-invariant metrics on a homogeneous space $G/H$ is in one-to-one correspondence with the set of inner products on the tangent space $\fr{m}\cong T_{{\it o}}(G/H)$, which are invariant under the isotropy representation. When…

Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of…

A geometrical formulation for adjoint-symmetries as 1-forms is studied for general partial differential equations (PDEs), which provides a dual counterpart of the geometrical meaning of symmetries as tangent vector fields on the solution…

The orthogonal projection of a 4-cube onto a uniform random 3-subspace in R^4 is a convex 3-polyhedron P with 14 vertices almost surely. Three numerical characteristics of P -- volume, surface area and mean width -- are studied. These…

We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.

In this paper we consider a new kind of inequality related to fractional integration, motivated by Gressman's paper. Based on it we investigate its multilinear analogue inequalities. Combining with the Gressman's work on multilinear…

The standard definition of cylindrical symmetry in General Relativity is reviewed. Taking the view that axial symmetry is an essential pre-requisite for cylindrical symmetry, it is argued that the requirement of orthogonal transitivity of…

The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…

We introduce the notion of order projections using the order unit property of a positive element in an order unit space and characterize them in terms of (geometric) orthogonality. We describe order projections of the order unit space…