相关论文: Hermite-Biehler, Routh-Hurwitz, and total positivi…

Based on the generalized Routh-Hurwitz criterion, we propose a sufficient and necessary criterion for testing the stability of fractional-order linear systems with order {\alpha}{\in}[1,2), called the fractional-order Routh-Hurwitz…

We use Reznick's Theorem for positive homogeneous polynomials to prove an elliptic regularity result for representations of enveloping algebras of Lie algebras. This allows us to relax a technical condition for a sum of squares…

We prove Soergel's conjecture on the characters of indecomposable Soergel bimodules. We deduce that Kazhdan-Lusztig polynomials have positive coefficients for arbitrary Coxeter systems. Using results of Soergel one may deduce an algebraic…

The normalized totally positive bases are widely used in many fields.Based on the generalized Vandermonde determinant, the normalized total positivity of a kind of generalized toric-Bernstein basis is proved, which is defined on a set of…

Quillen proved that, if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares.…

In this paper we give a matrix version of Handelman's Positivstellensatz [1], representing polynomial matrices which are positive definite on convex, compact polyhedra. Moreover, we propose also a procedure to find such a representation. As…

We give a detailed account of various connections between several classes of objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices, Stietjes and Jacobi-type continued fractions, Cauchy indices, moment problems, total…

Log-concavity and almost log-convexity of the cycle index polynomials were proved by Bender and Canfield [J. Combin. Theory Ser. A 74 (1996)]. Schirmacher [J. Combin. Theory Ser. A 85 (1999)] extended them to $q$-log-concavity and almost…

We prove an abstract Birkhoff normal form theorem for Hamiltonian partial differential equations on torus. The normal form is complete up to arbitrary finite order. The proof is based on a valid non-resonant condition and a suitable norm of…

In this paper, we consider matrices whose entries are combinatorial sequences which can be expressed in terms of a convolution of elementary and complete homogeneous symmetric functions. We establish the total positivity of these matrices…

In this paper, we study a certain type of Hurwitz numbers which count branched covers over the Riemann sphere admitting several branch points with fixed ramification types, one branch point with a fixed number of preimages, and one branch…

We settle three problems from the literature on stable and real zero polynomials and their connection to matroid theory. We disprove the weak real zero amalgamation conjecture by Schweighofer and the second author. We disprove a conjecture…

We study the structures of ordinary simple Hurwitz numbers and monotone Hurwitz numbers with varying genus. More precisely, we prove that when the ramification type is fixed and the genus is treated as a variable, the connected monotone…

We present two different proofs that positive polynomials on closed boxes of $\mathbb{R}^2$ can be written as bivariate Bernstein polynomials with strictly positive coefficients. Both strategies can be extended to prove the analogous result…

The paper presents methods of eigenvalue localisation of regular matrix polynomials, in particular, stability of matrix polynomials is investigated. For this aim a stronger notion of hyperstability is introduced and widely discussed. Matrix…

The study of dynamical systems on complex networks is of paramount importance in engineering, given that many natural and artificial systems find a natural embedding on discrete topologies. For instance, power grids, chemical reactors and…

We give an different proof of our result computing the stable homology of dihedral group Hurwitz spaces. This proof employs more elementary methods, instead of higher algebra.

We characterize ratios of permanents of (generalized) submatrices which are bounded on the set of all totally positive matrices. This provides a permanental analog of results of Fallat, Gekhtman, and Johnson [{\em Adv.\ Appl.\ Math.} {\bf…

We generalize a preceding simple proof of the Jamiolkowski criterion to check whether a given linear map between algebras of operators is completely positive or not. The generalization is performed to embrace all algebras of Hilbert-Schmidt…

We prove a version of the Bhargava-Kane-Lenstra-Poonen-Rains heuristics for Selmer groups of quadratic twist families of abelian varieties over global function fields. As a consequence, we derive a result towards the "minimalist conjecture"…