相关论文: On Multi-Vector Spaces

We describe all metric spaces that have sufficently many affine functions. As an application we obtain a metric characterization of linear-convex subsets of Banach spaces.

Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…

The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic…

Mutidimensional cosmological models with $n\left( n\geq 2\right) $ Einstein spaces $M_i\left( i=1,\ldots ,n\right) $ are investigated. The cosmological constant and homogeneous minimally coupled scalar field as a matter sources are…

In a polydiagonal subspace of the Euclidean space, certain components of the vectors are equal (synchrony) or opposite (anti-synchrony). Polydiagonal subspaces invariant under a matrix have many applications in graph theory and dynamical…

Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By proper subset one understands a set included in A,…

The Kalman variety of a linear subspace is a vector space consisting of all endomorphisms that have an eigenvector in that subspace. We resolve a conjecture of Ottaviani and Sturmfels and give the minimal defining equations of the Kalman…

We present the MULTIMODAL UNIVERSE, a large-scale multimodal dataset of scientific astronomical data, compiled specifically to facilitate machine learning research. Overall, the MULTIMODAL UNIVERSE contains hundreds of millions of…

In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces.…

We study arrangements of $m$ hyperplanes in the $n$-dimensional real projective space, with a special focus on $m=n+3$ and $n=3$ or $n=4$.

In this paper we present the definitions and some properties of several Samrandache Type Functions that are involved in many solved and unsolved problems and conjectures in number theory and recreational mathematics.

This paper is a modern exposition of old ideas. The setting is a Euclidian space $E$ of dimension $n$ with associated vector space $V$ of dimension $n$. A (non-zero) sliding vector is a vector in $V$ that is free to move, but only within a…

After an overview of general aspects of modelling the pulsation- convection interaction we present reasons why such simulations (in multidimensions) are needed but, at the same time, pose a considerable challenge. We then discuss, for…

We define a monad M on a category of measurable bornological sets, and we show how this monad gives rise to a theory of vector-valued integration that is related to the notion of Pettis integral. We show that an algebra X of this monad is a…

We define the notion of a marked moduli space as the parameter space of a physical theory together with all of its observables. In geometric examples, this coincides with the mathematical notion of Teichm\"uller space. We propose two new…

The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold ($C$-space) consists not…

In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context…

Multinets are certain configurations of lines and points with multiplicities in the complex projective plane P2. They are used in the studies of resonance and characteristic varieties of complex hyperplane arrangement complements and…

The idea of a multiverse -- an ensemble of universes -- has received increasing attention in cosmology, both as the outcome of the originating process that generated our own universe, and as an explanation for why our universe appears to be…

In this paper, we construct a new series of prehomogeneous vector spaces from figures made up of triangles, called triangle arrangements. Our main theorem states that, under suitable assumptions, we are able to construct a prehomogeneous…