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Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result that characterizes properties of an exponential system on a…

Classical Analysis and ODEs · Mathematics 2025-09-30 Oleg Asipchuk , Laura De Carli , Weilin Li

Assume that a projective variety together with a polarization is uniformly K-stable. If the polarization is canonical or anti-canonical, then the projective variety is uniformly K-stable with respects to any polarization sufficiently close…

Algebraic Geometry · Mathematics 2017-09-26 Kento Fujita

We provide a uniform approach to obtain sufficient criteria for a (higher order) fixed point of a given bracket structure on a manifold to be stable under deformations. Examples of bracket structures include Lie algebroids, Lie…

Differential Geometry · Mathematics 2025-03-20 Karandeep J. Singh

The KP-II equation was derived by Kadmotsev and Petviashvili to explain stability of line solitary waves of shallow water. Recently, Mizumachi (Mem. Amer. Math. Soc. 238 (2015)) has proved nonlinear stability of $1$-line solitons for…

Analysis of PDEs · Mathematics 2015-12-29 Tetsu Mizumachi

For the two sixth-order polynomials $a(s)$ and $b(s),$ Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial $c(s)$ such that $c(s)/a(s)$ and $c(s)/b(s)$ are both strictly positive real.…

Optimization and Control · Mathematics 2007-05-23 Long Wang

It is shown by Makai, Martini, and \'Odor that a convex body $K\subset\mathbb{R}^n$, all of whose maximal sections pass through the origin, must be origin-symmetric. We prove a stability version of this result. We also discuss a theorem of…

Metric Geometry · Mathematics 2015-06-16 Matthew Stephen , Vladyslav Yaskin

This paper considers linear delay-difference equations, that is, equations relating the state at a given time with its past values over a given bounded interval. After providing a well-posedness result and recalling Hale--Silkowski…

Dynamical Systems · Mathematics 2025-06-06 Felipe Gonçalves Netto , Yacine Chitour , Guilherme Mazanti

In this paper, we introduce stable multivariate generalizations of Narayana polynomials of type A and type B. We give an insertion algorithm for labeled plane trees and introduce the notion of improper edges. Our polynomials are…

Combinatorics · Mathematics 2024-04-09 Harold R. L. Yang , Philip B. Zhang

We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…

Logic · Mathematics 2023-02-17 Saharon Shelah , Alexander Usvyatsov

Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…

Optimization and Control · Mathematics 2013-12-30 S. Damak , M. Di Loreto , W. Lombardi , V Andrieu

We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all…

Analysis of PDEs · Mathematics 2017-03-08 Anna Geyer , Dmitry E. Pelinovsky

We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that…

Classical Analysis and ODEs · Mathematics 2014-11-05 Lun Zhang , Galina Filipuk

This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…

Optimization and Control · Mathematics 2020-07-23 Zhaobo Liu , Chanying Li

A polynomial $f(x)$ over a field $K$ is said to be stable if all its iterates are irreducible over $K$. L. Danielson and B. Fein have shown that over a large class of fields $K$, if $f(x)$ is an irreducible monic binomial, then it is stable…

Number Theory · Mathematics 2022-12-21 Mohamed Ayad , Boualem Benseba , Mohamed Madi

In this paper, we investigate the geometric properties of complex-valued pluriharmonic mappings defined over convex Reinhardt domains in $\mathbb{C}^n$. We first establish a multidimensional analogue of the Noshiro-Warschawski Theorem,…

Complex Variables · Mathematics 2026-02-03 Molla Basir Ahamed , Sujoy Majumder , Debabrata Pramanik

Determinantal polynomials play a crucial role in semidefinite programming problems. Helton-Vinnikov proved that real zero (RZ) bivariate polynomials are determinantal. However, it leads to a challenging problem to compute such a…

Optimization and Control · Mathematics 2019-02-01 Papri Dey

The estimates of the uniform norm of the Chebyshev polynomial associated with a compact set $K$ consisting of a finite number of continua in the complex plane are established. These estimates are exact (up to a constant factor) in the case…

Complex Variables · Mathematics 2014-04-15 V. V. Andrievskii

We introduce a theory of uniform K-stability for big line bundles on smooth projective varieties. This extends the existing theory both for varieties with ample line bundles, and for varieties with big anticanonical class. Our main result…

Algebraic Geometry · Mathematics 2026-03-27 Ruadhaí Dervan , Rémi Reboulet

This work investigates the stability properties of Lyapunov exponents of transfer operator cocycles from a measure-theoretic perspective. Our results focus on so-called Blaschke product cocycles, a class of random dynamical systems amenable…

Dynamical Systems · Mathematics 2024-08-12 Cecilia González-Tokman , Joshua Peters

The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further…

Combinatorics · Mathematics 2016-11-21 Nima Amini