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We introduce regular sequences and associated Koszul resolutions for monoids in the category of functors over an essentially small linear symmetric monoidal category. Next we define polynomials over such monoids. We compute the Hochschild…
We consider polynomials with integer coefficients and discuss their factorization properties in Z[[x]], the ring of formal power series over Z. We treat polynomials of arbitrary degree and give sufficient conditions for their reducibility…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
Polynomials related to rational solutions of Painleve' equations satisfy certain difference equations. Conditions are given to acertain that all solutions really are polynomials.
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
We give a combinatorial algorithm for equivariant embedded resolution of singularities of a toric variety defined over a perfect field. The algorithm is realized by a finite succession of blowings-up with smooth invariant centres that…
Polynomial algebra offers a standard approach to handle several problems in geometric modeling. A key tool is the discriminant of a univariate polynomial, or of a well-constrained system of polynomial equations, which expresses the…
This paper develops the theory of Macdonald-Koornwinder polynomials in parallel analogy with the work done for the $GL_n$ case in [CR22]. In the context of the type $CC_n$ affine root system the Macdonald polynomials of other root systems…
When studying families in the moduli space of dynamical systems, choosing an appropriate representative function for a conjugacy class can be a delicate task. The most delicate questions surround rationality of the conjugacy class compared…
Recent work on the use of dimensional reduction for the regularisation of non--supersymmetric theories is reviewed. It is then shown that there exists a class of theories for which a universal form of the soft supersymmetry breaking terms…
A (conjecturally complete) list of components of complements of discriminant varieties of parabolic singularities of smooth real functions is given. We also promote a combinatorial program that enumerates possible topological types of…
Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries. The structure of the generalized spectral function is described in terms of…
We study a wide class of solvable PT symmetric potentials in order to identify conditions under which these potentials have regular solutions with complex energy. Besides confirming previous findings for two potentials, most of our results…
We define and study a homological version of Sullivan's rational de Rham complex for simplicial sets. This new functor can be generalised to simplicial symmetric spectra and in that context it has excellent categorical properties which…
A formula is presented for the determinant of the second additive compound of a square matrix in terms of coefficients of its characteristic polynomial. This formula can be used to make claims about the eigenvalues of polynomial matrices,…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.