相关论文: Structural Properties of ${\cal R}_2$ Part II

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

A simplified calculation of the structure constants of the diffeomorphism group of the two-sphere is presented

This paper is devoted to a discussion of specific properties of invariants in the theory of forms.

We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincar\'e duality and hard Lefschetz theorem), and their relations and applications to integral…

This is the second part of two parts, titled " cone construction". In this part we prove the Lefschetz cohomologicity of the cone operator $Con$.

Two main topics are considered: The characterisation of finite homomorphism dualities for relational structures, and the splitting property of maximal antichains in the homomorphism order.

We present the structural constants of low dimensional pseudo $H$-type algebras.

In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.

In this paper we give the functional characteristics of the Rothberger and Menger properties.

We briefly review the structure and properties of self-dual field actions.

We study $GL(2)$-structures on differential manifolds. The structures play a fundamental role in the geometric theory of ordinary differential equations. We prove that any $GL(2)$-structure on an even dimensional manifold give rise to a…

The Poisson structures on two-dimensional Galilei group, classified in the author previous paper are quantized. The dual quantum Galilei Lie algebras are found.

These largely expository notes describe the properties of the function ${\cal R}$ which assigns a number to a $4$-tuple of distinct fixed points of an orientation preserving homeomorphism or diffeomorphism of $S^2$.

Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral…

In this paper, we will introduce two generalizations of second submodules of a module over a commutative ring and explore some basic properties of these classes of modules.

This is the direct continuation of the paper "Mapping properties of Fourier transforms" (arXiv:2112.04896) using the same notation as there without further explanations. It deals with continuous and compact mappings of the Fourier transform…

In the first part of this note, we review results concerning analytic characterization of convexity for planar sets. The second part is devoted to results valid for arbitrary $m \ge 2$.

By using the concept of duality between direct channel resonances and Regge exchanges we relate the small- and large-$x$ behavior of the structure functions. We show that even a single resonance exhibits Bjorken scaling at large $Q^2$.

We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane…

This paper continues the study of highest weight categorical sl_2-actions started in part I. We start by refining the definition given there and showing that all examples considered in part I are also highest weight categorifications in the…