Related papers: Supersolvable resolutions of line arrangements
We study about order of growth and hyper order of growth of non trivial solutions of second order linear differential equations, having restrictions in the coefficients. These restrictions involve notions of Yang's inequality, Borel…
Since the beginning of the quest of hypercomplex numbers in the late eighteenth century, many hypercomplex number systems have been proposed but none of them succeeded in extending the concept of complex numbers to higher dimensions. This…
The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
We introduce a direct numerical treatment of nonlinear higher-index differential-algebraic equations by means of overdetermined polynomial least-squares collocation. The procedure is not much more computationally expensive than standard…
This paper is concerned with supersolutions to parabolic equations of the form \begin{equation} \partial_t U (x,t)-D(x)\Delta U(x,t)=0, \quad (x,t)\in \mathbb{R}^N \times (0,\infty), \end{equation} where $D\in C(\mathbb{R}^N)$ is positive.…
We compute the second and third levels of the Lasserre hierarchy for the spherical finite distance problem. A connection is used between invariants in representations of the orthogonal group and representations of the general linear group,…
We give an improved polynomial bound on the complexity of the equation solvability problem, or more generally, of finding the value sets of polynomials over finite nilpotent rings. Our proof depends on a result in additive combinatorics,…
The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity…
In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic…
This manuscript explores novel complexity results for the feasibility problem over $p$-order cones, extending the foundational work of Porkolab and Khachiyan. By leveraging the intrinsic structure of $p$-order cones, we derive refined…
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
Criteria are given for determining whether an irreducible sextic equation with rational coefficients is algebraically solvable over the complex numbers.
By using computer assistance, we prove that the fundamental group of the complement of a real complexified line arrangement is not determined by its intersection lattice, providing a counter-example for a problem of Falk and Randell. We…
Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…
Equations over linearly ordered semilattices are studied. For any equation $t(X)=s(X)$ we find irreducible components of its solution set and compute the average number of irreducible components of all equations in $n$ variables.
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
In arrangements of pseudocircles (Jordan curves) the weight of a vertex (intersection point) is the number of pseudocircles that contain the vertex in its interior. We give improved upper bounds on the number of vertices of weight <=k in…