Related papers: Free basis consisting of strictly small sections

An effective upper bound is established for the least non-trivial integer solution to the system of cubic forms \[ \begin{cases} F = c_{1}x_1^3 + c_{2}x_2^3 + \cdots + c_{n}x_n^3 = 0, \\ G = d_{1}x_1^3 + d_{2}x_2^3 + \cdots + d_{n}x_n^3 =…

In this paper we study ascending chain conditions in a free Baxter algebra by making use of explicit constructions of free Baxter algebras that were obtained recently. We investigate ascending chain conditions both for ideals and for Baxter…

A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the…

Criterion for a companion matrix to have a certain number of flat portions on the boundary of its numerical range is given. The criterion is specialized to the cases of 3-by-3 and 4-by-4 matrices. In the latter case, it is proved that a…

In the present paper, a robust approach to a special class of convex feasibility problems is considered. By techniques of convex and variational analysis, conditions for the existence of robust feasible solutions and related error bounds…

We derive a formula for expressing free cumulants whose entries are products of random variables in terms of the lattice structure of non-crossing partitions. We show the usefulness of that result by giving direct and conceptually simple…

We consider an oscillatory obstacle problem where the coincidence set and free boundary are also highly oscillatory. We establish a rate of convergence for a regularized notion of free boundary to the free boundary of a corresponding…

We consider the problem of conditional independence testing of $X$ and $Y$ given $Z$ where $X,Y$ and $Z$ are three real random variables and $Z$ is continuous. We focus on two main cases - when $X$ and $Y$ are both discrete, and when $X$…

The purpose of this paper is to give new examples of families of free singularities. We first show that a generic equidimensional subspace arrangement is free. Furthermore, we show that a product of two reduced Cohen-Macaulay subspaces is…

In this paper, we show that a compact real surface embedded in a complex surface has a regular Stein neighborhood basis, provided that there are only finitely many complex points on the surface, and that they are all flat and hyperbolic. An…

This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those…

A new version of a strong law of large numbers for a ``good'' pairwise independent sequence of random variables (r.v.'s) with a small part of ``bad'' dependent r.v.'s is proposed. The main goal is to relax the assumption on the existence of…

We prove necessary optimality conditions for problems of the calculus of variations on time scales with a Lagrangian depending on the free end-point.

We prove a local minimizing property for strictly stable free-boundary minimal hypersurfaces in the relative current setting. Let $\Sigma^n$ be a compact, two-sided, properly embedded free-boundary minimal hypersurface in a compact…

We establish a boundary maximum principle for free boundary minimal submanifolds in a Riemannian manifold with boundary, in any dimension and codimension. Our result holds more generally in the context of varifolds.

We employ min-max techniques to show that the unit ball in $\mathbb{R}^3$ contains embedded free boundary minimal surfaces with connected boundary and arbitrary genus.

In this paper we study algebras of modular forms on unitary groups of signature $(n,1)$. We give a necessary and sufficient condition for an algebra of unitary modular forms to be free in terms of the modular Jacobian. As a corollary we…

In terms of initial data, a sufficient condition for the smoothness of the solution to the Cauchy problem for one-dimensional relativistic cold plasma equations over any given time interval is found. Unlike the non-relativistic case, such…

The aim of this paper is to give a simple construction of the free skew-brace over a set $X$.

We construct free boundary minimal disc stackings, with any number of strata, in the three-dimensional Euclidean unit ball, and prove uniform, linear lower and upper bounds on the Morse index of all such surfaces. Among other things, our…