Related papers: Kernel representation formula from complex to real…
We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…
Matrix transformations in terms of triangular matrices is the easiest method of evaluating matrix-variate gamma and beta integrals in the real and complex cases. Here we give several procedures of explicit evaluation of gamma and beta…
A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex…
An explicit form of the generators of quantum and ordinary semisimple algebras for an arbitrary finite-dimensional representation is found. The generators corresponding to the simple roots are obtained in terms of a solution of a system of…
By the theory of elliptic curves, we study the integers representable as the product of the sum of four integers with the sum of their reciprocals and give a sufficient condition for the integers with a positive representation.
We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…
We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by…
The integral representation of the two-parameter Mittag-Leffler function $E_{\rho,\mu}(z)$ is considered in the paper that expresses its value in terms of the contour integral. For this integral representation, the transition is made from…
The paper is an investigation of the analytic properties of a new class of special functions that appear in the kernels of a class of integral operators underlying the dynamics of matter relaxation processes in attractive fields. These…
We construct a relationship between integral and differential representation of second-order Jordan chains. Conditions to obtain regular potentials through the confluent supersymmetry algorithm when working with the differential…
The central object of the quantum algebraic approach to the study of quantum integrable models is the universal $R$-matrix, which is an element of a completed tensor product of two copies of quantum algebra. Various integrability objects…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…
We discuss the Mellin-Barnes representation of complex multidimensional integrals. Experiments frontiered by the High-Luminosity Large Hadron Collider at CERN and future collider projects demand the development of computational methods to…
An exact inversion formula for the Lorentz integral transform (LIT) is provided together with the spectrum of the LIT kernel. The exponential increase of the inverse Fourier transform of the LIT kernel entering the inversion formula…
In this paper, we present a dual representation of the influence functions, whose computational complexity scales with dataset size rather than model size. Both analytically and experimentally, we show that this representation can be an…
We derive a piecewise-linear formula for the rigid representation of a Dynkin quiver of a given dimension vector, and illustrate the formula in several examples.
Explicit expressions for the Temperley-Lieb-Martin algebras, i.e., the quotients of the Hecke algebra that admit only representations corresponding to Young diagrams with a given maximum number of columns (or rows), are obtained, making…
We consider compact matrix quantum groups whose $N$-dimensional fundamental representation decomposes into an $(N-1)$-dimensional and a one-dimensional subrepresentation. Even if we know that the compact matrix quantum group associated to…
The inversion problem for rational B\'ezier curves is addressed by using resultant matrices for polynomials expressed in the Bernstein basis. The aim of the work is not to construct an inversion formula but finding the corresponding value…
We consider a class of domains, generalizing the upper half-plane, and admitting rotational, translational and scaling symmetries, analogous to the half-plane. We prove Paley-Wiener type representations of functions in Bergman spaces of…