Related papers: Zonal polynomials and hypergeometric functions of …
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
In this paper we introduce two definitions for algebraic and geometric multiplicities of a quaternion right eigenvalue. This definitions are equivalent to the classical ones. However, differently from the usual definitions, the notions of…
Orthogonal polynomials with respect to a weight function defined on a wedge in the plane are studied. A basis of orthogonal polynomials is explicitly constructed for two large class of weight functions and the convergence of Fourier…
Quadratically optimized polynomials are described which are useful in multi-bosonic algorithms for Monte Carlo simulations of quantum field theories with fermions. Algorithms for the computation of the coefficients and roots of these…
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…
We consider solvable matrix models. We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one…
We introduce families of rational functions that are biorthogonal with respect to the $q$-hypergeometric distribution. A triplet of $q$-difference operators $X$, $Y$, $Z$ is shown to play a role analogous to the pair of bispectral operators…
We extend the $L^4$-square function estimates for the parabola and the half-cone to quadratic manifolds in higher dimensions and their conical extensions. To this end, we require transversality for the tangent spaces of the quadratic…
The local minima of a quadratic functional depending on binary variables are discussed. An arbitrary connection matrix can be presented in the form of quasi-Hebbian expansion where each pattern is supplied with its own individual weight.…
In a recent work, H.Narita presented problems concerning the strict positivity of central values of certain automorphic $L$-functions in the form of questions regarding special values of the hypergeometric series. In this paper, we present…
We introduce a polynomial zeta function $\zeta^{(p)}_{P_n}$, related to certain problems of mathematical physics, and compute its value and the value of its first derivative at the origin $s=0$, by means of a very simple technique. As an…
The local minima of a quadratic functional depending on binary variables are discussed. An arbitrary connection matrix can be presented in the form of quasi-Hebbian expansion where each pattern is supplied with its own individual weight.…
In this paper we express the eigenvalues of a sort of real heptadiagonal symmetric matrices as the zeros of explicit rational functions establishing upper and lower bounds for each of them. From these prescribed eigenvalues we compute also…
We provide several properties of the geometric polynomials discussed in earlier works of the authors. Further, the geometric polynomials are used to obtain a closed form evaluation of certain series involving Riemann's zeta function.
We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…
Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2j. The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of biorthogonal systems is a useful…
The eigenvalue distribution is investigated for matrix models related via the localization to Chern-Simons-matter theories. An integral representation of the planar resolvent is used to derive the positions of the branch points of the…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
It has been known since 2007 that the Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere,…