Related papers: Embedding and Duality of Matrix-Weighted Modulatio…

We introduced the concept of a metric value set (MVS) in an earlier paper \cite{GM} and developed the idea further in \cite{AS}. In this paper we study locally $M$-metrizable spaces and the products of $M$-metrizable spaces. Finally we…

We consider the space $\mathcal{M}_{2,1}$ --- the open moduli space of complex curves of genus 2 with one marked point. Using language of chord diagrams we describe the cell structure of $\mathcal{M}_{2,1}$ and cell adjacency. This allows…

We show that under minimal assumptions, the intrinsic metric induced by a strongly local Dirichlet form induces a length space. A main input is a dual characterization of length spaces in terms of the property that the 1-Lipschitz functions…

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…

We introduce the notion of tiling spaces for metric spaces. The class of tiling spaces contains the Euclidean spaces, the middle-third Cantor set, and various self-similar spaces appearing in fractal geometry. For doubling tiling spaces, we…

Given a metric measure space $X$, we consider a scale of function spaces $T^{p,q}_s(X)$, called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on…

This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper we focus on the description of the…

An embedding is a function that maps entities from one algebraic structure into another while preserving certain characteristics. Embeddings are being used successfully for mapping relational data or text into vector spaces where they can…

Matlis duals of local cohomology modules are investigated with respect to many different topics (see section 0 - Introduction). One of these topics are complete intersections - see Corollary 1.1.4.

The present article studies holomorphic isometric embeddings of the complex two--plane Grassmannnian into quadrics. We discuss the moduli space of these embeddings up to gauge and image equivalence using a generalisation of do…

Deep neural network has recently shown very promising applications in different research directions and attracted the industry attention as well. Although the idea was introduced in the past but just recently the main limitation of using…

One of the major drawbacks of deep learning models for computer vision has been their inability to retain multiple sources of information in a modular fashion. For instance, given a network that has been trained on a source task, we would…

For bounded domains, eigenvalues and eigenfunctions of double layer potentials are considered. The aim of this paper is to establish some relationships between eigenvalues, eigenfunctions and the geometry of domain boundaries.

This is the sequel to our first paper concerning the balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. We prove the uniqueness of such an embedding. The proof relies on fine estimates of the…

We establish an isomorphism between certain complex-valued and vector-valued modular form spaces of half-integral weight, generalizing the well-known isomorphism between modular forms for $\Gamma_0(4)$ with Kohnen's plus condition and…

We give the mathematical theory of duality computer in the density matrix formalism. This result complements the mathematical theory of duality computer of Gudder in the pure state formalism.

In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…

In this paper, a strong variant for multivalued mappings of the well-known property of openness at a linear rate is studied. Among other examples, a simply characterized class of closed convex processes between Banach spaces, which…

We begin a systematic study of unitary representations of minimal $W$-algebras. In particular, we classify unitary minimal $W$-algebras and make substantial progress in classification of their unitary irreducible highest weight modules. We…