相关论文: Choosing roots of polynomials with symmetries smoo…

We give examples of non-fibered hyperbolic knot complements in homology spheres that are not commensurable to fibered knot complements in homology spheres. In fact, we give many examples of knot complements in homology spheres with the…

We prove that smoothness of nonautonomous linearization is of class $C^2.$ Our approach admits the existence of stable and unstable manifolds determined by a family of nonautonomous hyperbolicities. Moreover, our goal is reached without…

We study the asymptotic distribution of roots of Lommel polynomials as polynomials of the order with a variable and purely imaginary argument. The roots are complex and accumulate on certain curves in the complex plane. We prove existence…

This paper investigates the stratification of the discriminant hypersurface associated with a univariate polynomial via the number of its distinct complex roots. We introduce two novel approaches different from the one based on…

We show in this paper that the roots $x_1$ and $x_2$ of a scalar quadratic polynomial $ax^2+bx+c=0$ with real or complex coefficients $a$, $b$ $c$ can be computed in a element-wise mixed stable manner, measured in a relative sense. We also…

Let $\mathcal{C}$ be a smooth, projective, genus $g\geq 2$ curve, defined over $\mathbb{C}$. Then $\mathcal{C}$ has \emph{many automorphisms} if its corresponding moduli point $p \in \mathcal{M}_g$ has a neighborhood $U$ in the complex…

For a complex polynomial in two variables we study the morphism induced in homology by the embedding of an irregular fiber in a regular neighborhood of it. We give necessary and sufficient conditions for this morphism to be injective,…

We present a sufficient condition for a self-inversive polynomial to have a fixed number of roots on the complex unit circle. We also prove that these roots are simple when that condition is satisfied. This generalizes the condition found…

In this paper, we show that various kinds of integer polynomials with prescribed properties of their roots have positive density. For example, we prove that almost all integer polynomials have exactly one or two roots with maximal modulus.…

Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…

Connectivity problems like k-Path and k-Disjoint Paths relate to many important milestones in parameterized complexity, namely the Graph Minors Project, color coding, and the recent development of techniques for obtaining kernelization…

We compute some numerical invariants of the lines on hyperplane sections of a smooth cubic threefold over complex numbers. We also prove that for any smooth hypersurface $X\subset \mathbb P^{n+1}$ of degree $d$ over an algebraically closed…

In this paper, we study the root distribution of some univariate polynomials satisfying a recurrence of order two with linear polynomial coefficients. We show that the set of non-isolated limits of zeros of the polynomials is either an arc,…

We study here systems of symmetries on $|1|$--graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous $|1|$--graded geometries. We show the existence of an invariant admissible…

Let $f$ be an ordinary polynomial in $\mathbb{C}[z_1,..., z_n]$ with no negative exponents and with no factor of the form $z_1^{\alpha_1}... z_n^{\alpha_n}$ where $\alpha_i$ are non zero natural integer. If we assume in addicting that $f$…

We show that all hyperbolic surfaces admit an ideal triangulation with bounded shear parameters. This upper bound depends logarithmically on the topology of the surface.

We consider boundary value problems for quasilinear first-order one-dimensional hyperbolic systems in a strip. The boundary conditions are supposed to be of a smoothing type, in the sense that the $L^2$-generalized solutions to the…

We establish asymptotic upper bounds on the number of zeros modulo $p$ of certain polynomials with integer coefficients, with $p$ prime numbers arbitrarily large. The polynomials we consider have degree of size $p$ and are obtained by…

Hyperbolic polynomials elegantly encode a rich class of convex cones that includes polyhedral and spectrahedral cones. Hyperbolic polynomials are closed under taking polars and the corresponding cones, the derivative cones, yield…

Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…