Related papers: Determinantal representations of semi-hyperbolic p…

In a recent paper, Adamchik [V.S. Adamchik, On the Hurwitz function for rational arguments, Appl. Math. Comp. 187 (2007) 3--12] expressed in a closed form symbolic derivatives of four functions belonging to the class of functions whose…

Torsion polynomials connect the genus of a hyperbolic knot (a topological invariant) with the discrete faithful representation (a geometric invariant). Using a new combinatorial structure of an ideal triangulation of a 3-manifold that…

We announce some results towards the classification of partially hyperbolic diffeomorphisms on 3-manifolds, and outline the proofs in the case when the diffeomorphism is dynamically coherent. Detailed proofs are long and technical and will…

The q-Hermite I-Sobolev type polynomials of higher order are consider for their study. Their hypergeometric representation is provided together with further useful properties such as several structure relations which give rise to a…

We develop a method to determine the eigenvalues and eigenfunctions of two-boson Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential…

Our main goal is to develop a representation for finite distributive nearlattices through certain ordered structures. This representation generalizes the well-known representation given by Birkhoff for finite distributive lattices through…

We express Wronskian Hermite polynomials in the Hermite basis and obtain an explicit formula for the coefficients. From this we deduce an upper bound for the modulus of the roots in the case of partitions of length 2. We also derive a…

We demonstrate that a system of bi-orthogonal polynomials and their associated functions corresponding to a regular semi-classical weight on the unit circle constitute a class of general classical solutions to the Garnier systems by…

We construct a class of quadratic irrationals having continued fractions of period $n\geq2$ with "small" partial quotients for which certain integer multiples have continued fractions of period $1$, $2$ or $4$ with "large" partial…

In this note we show that unsatisfiable systems of linear equations with a constant number of variables per equation over prime finite fields have polynomial-size constant-degree semi-algebraic proofs of unsatisfiability. These are proofs…

We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic…

We find the generating set of SL-invariant polynomials in four qubits that are also invariant under permutations of the qubits. The set consists of four polynomials of degrees 2,6,8, and 12, for which we find an elegant expression in the…

We study hyperbolic cohomology classes in the general context of simplicial complexes and prove homological invariance statements for them. We relate the existence of hyperbolic cohomology classes to the non-amenability of the fundamental…

Let $N$ be a manifold of dimension $m$ with a flat vector bundle given by a representation $\rho:\pi_1(N) \rightarrow \mathrm{GL}(n, \mathbf{R})$ where $\pi_1(N)$ is finitely generated. The holonomy group $\rho$ is a $k$-partially…

We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the known bounds for permanents. One of these families is obtained by replacing…

We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.

The paper is mainly devoted to the irreducibility of the polynomial representation of the double affine Hecke algebra for an arbitrary reduced root systems and generic "central charge" q. The technique of intertwiners in the non-semisimple…

The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. Hyperbolic polynomials give rise to a class of (hyperbolic) matroids which properly contains the class of…

The (generalised) Mellin transforms of certain Chebyshev and Gegenbauer functions based upon the Chebyshev and Gegenbauer polynomials, have polynomial factors $p_n(s)$, whose zeros lie all on the `critical line' $\Re\,s=1/2$ or on the real…

We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynomial maps from a finite union of copies of the complex…