相关论文: On Multi-Vector Spaces
We construct a general framework that generates classes of multilinear operators between Banach spaces which encompasses, as particular cases, the several classes of summing type multilinear operators that have been studied individually in…
This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…
An \emph{interval vector} is a $(0,1)$-vector in $\mathbb{R}^n$ for which all the 1's appear consecutively, and an \emph{interval-vector polytope} is the convex hull of a set of interval vectors in $\mathbb{R}^n$. We study three particular…
In this paper I shall consider various possible scalar-vector-tensor field theories which might be used to describe the Universe. After imposing numerous constraints of a physical and mathematical nature on the theories under consideration,…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…
In this talk I will introduces two spaces: the first space is the usual n-dimensional vector space with the unusual feature that n is non-integer, the second space is composed by the linear matrices acting on the previous space (physicists…
We introduce and study properties of certain new multifunctional harmonic spaces in the upper halfspace.We prove several sharp embedding theorems for such multifunctional spaces,these results are new even in the case of a single function.
We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self-interaction potential in the language of jet bundles and extensions of vector fields. In this framework, the Bianchi-scalar…
Retrieval of classical behaviour in quantum cosmology is usually discussed in the framework of minisuperspace models in the presence of scalar fields together with the inhomogeneous modes of gravitational or scalar fields. In this work we…
A complete classification is obtained of continuous, translation invariant, Minkowski valuations on an m-dimensional complex vector space which are covariant under the complex special linear group.
We study multihomogeneous spaces corresponding to ${\mathbb Z}^n$-graded algebras over an algebraically closed field of characteristic 0 and their relation with the description of $T$-varieties.
The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The…
A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of…
The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical properties, such as curvature, density, or entropy. We develop…
In this paper, we give one possible definition for functions of several variables applied to endomorphisms of finite dimensional C-vector spaces. This definition is consistent with the usual notion of a function of a square matrix. Some…
The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this…
The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few…
Harmonic analysis on Hermitian symmetric spaces of tube type is a natural framework for introducing multivariate Meixner-Pollaczek polynomials. Their main properties are established in this setting: generating and determinantal formulae,…
We derive an integral formula for the linking number of two submanifolds of the n-sphere S^n, of the product S^n x R^m, and of other manifolds which appear as "nice" hypersurfaces in Euclidean space. The formulas are geometrically…