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One of the main applications of semidefinite programming lies in linear systems and control theory. Many problems in this subject, certainly the textbook classics, have matrices as variables, and the formulas naturally contain…
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon…
Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…
Given a square, nonsingular matrix of univariate polynomials $\mathbf{F}\in\mathbb{K}[x]^{n\times n}$ over a field $\mathbb{K}$, we give a deterministic algorithm for finding the determinant of $\mathbf{F}$. The complexity of the algorithm…
We define a two-dimensional noncommutative space as a limit of finite-matrix spaces which have space-time dimension three. We show that on such space the Grosse-Wulkenhaar (renormalizable) action has natural interpretation as the action for…
The data-driven approach to robot control has been gathering pace rapidly, yet generalization to unseen task domains remains a critical challenge. We argue that the key to generalization is representations that are (i) rich enough to…
We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that…
We construct general Wigner rotations for both massive and massless particles in $D$-dimensional spacetime. We work out the explicit expressions of these Wigner rotations for arbitrary Lorentz transformations. We study the relation between…
We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups instead of a product of the general linear groups and by…
The generalized vector is defined on an $n$ dimensional manifold. Interior product, Lie derivative acting on generalized $p$-forms, $-1\le p\le n$ are introduced. Generalized commutator of two generalized vectors are defined. Adding a…
We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and…
Generalized planning is concerned with the characterization and computation of plans that solve many instances at once. In the standard formulation, a generalized plan is a mapping from feature or observation histories into actions,…
We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by…
For a Riemann surface $X$ and the moduli of regularly stable $G$-bundles $M$, there is a naturally occuring "$adjoint$" vector bundle over $X \times M$. One can take the determinant of this vector bundle with respect to the projection map…
The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective…
In this paper, we generalize an elementary real-analysis result to a class of topological vector spaces. We also give an example of a topological vector space to which the result cannot be generalized.
The notion of virtual global generation (VGG) for a vector bundle has multiple possible generalization from the case of curves to higher dimensional normal projective varieties. We study relationship between these notions. All these notions…
Last years a certain attention was attracted to the statement that Hamiltonian formulations of General Relativity, in which different parametrizations of gravitational variables were used, may not be related by a canonical transformation.…
We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows…