Related papers: Multi-dimensional vector product
Let X_R be a geometrically irreducible smooth projective curve, defined over R, such that X_R does not have any real points. Let X= X_R\times_R C be the complex curve. We show that there is a universal real algebraic line bundle over X_R x…
We study one extremal problem on the product of power of generalized inner radii of non-overlapping domains in $\mathbb{C}^{n}$.
Consider the following toy problem. There are $m$ rectangles and $n$ points on the plane. Each rectangle $R$ is a consumer with budget $B_R$, who is interested in purchasing the cheapest item (point) inside R, given that she has enough…
We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…
What is a good vector representation of an object? We believe that it should be generative in 3D, in the sense that it can produce new 3D objects; as well as be predictable from 2D, in the sense that it can be perceived from 2D images. We…
Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…
The gauge coupling constant unification at the low ($O$(TeV)) scale can be obtained just in four dimensions, without help of the power like renormalization group evolution in extra dimensions, due to the presence of some extra particle…
We prove a connectedness result for products of weighted projective spaces.
We characterize all logarithmic, holomorphic vector-valued modular forms which can be analytically continued to a region strictly larger than the upper half-plane.
26 different concrete representations of the space of vector valued distributions on a smooth manifold of dimension n are presented systematically, most of them new. In the particular case of representations as module homomorphisms acting…
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.
The conditions for a generalized Burgers equation which a priori involves nine arbitrary functions of one, or two variables to allow an infinite dimensional symmetry algebra are determined. Though this algebra can involve up to two…
In computer vision, image datasets used for classification are naturally associated with multiple labels and comprised of multiple views, because each image may contain several objects (e.g. pedestrian, bicycle and tree) and is properly…
We establish some bounds on the number of higher-dimensional partitions by volume. In particular, we give bounds via vector partitions and MacMahon's numbers.
The goal of this paper is to generalize the theory of triangularizing matrices to linear transformations of an arbitrary vector space, without placing any restrictions on the dimension of the space or on the base field. We define a…
We show that the Cartesian product of three hereditarily infinite dimensional compact metric spaces is never hereditarily infinite dimensional. It is quite surprising that the proof of this fact (and this is the only proof known to the…
Some aspects of the multidimensional soliton geometry are considered.
We prove a generalization of the topological Tverberg theorem. One special instance of our general theorem is the following: Let $\Delta$ denote the 8-dimensional simplex viewed as an abstract simplicial complex, and suppose that its…
In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved (\cite{Sa}, \cite{CaSoA}). However, the question for multidimensional Lorentz spaces is still open. In this paper,…