Related papers: Dimension in Polynomial Variational Inequalities

We introduce a broad class of equations that are described by a graph, which includes many well-studied systems. For these, we show that the number of solutions (or the dimension of the solution set) can be bounded by studying certain…

Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to…

We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…

Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…

The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…

This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…

We study a general class of nonlinear second-order variational inequalities with interconnected bilateral obstacles, related to a multiple modes switching game. Under rather weak assumptions, using systems of penalized unilateral backward…

The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case…

The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that…

This article proposes a bivariate polynomial problem for finite-order real matrices that endows a \textit{`sufficient condition'} for a map from the standard vector spaces of finite-order real matrices to the same dimensional bivariate…

We study nested variational inequalities, which are variational inequalities whose feasible set is the solution set of another variational inequality. We present a projected averaging Tikhonov algorithm requiring the weakest conditions in…

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

In this paper we determine the region of variability for certain subclasses of univalent functions satisfying differential inequalities. In the final section we graphically illustrate the region of variability for several sets of…

In this paper, we consider modular local polynomials. These functions satisfy modularity while they are locally defined as polynomials outside of an exceptional set. We prove an inequality for the dimension of the space of such forms when…

In this paper, we study the value distribution of zeros of certain nonlinear difference polynomials of entire functions of finite order.

The standard definition of the dimension of a vector space or rank of a module states that dimension or rank is equal to the cardinality of any basis, which requires an understanding of the concepts of basis, generating set, and linear…

In the present paper a new mean value theorem for polynomials of special form is obtained. The case of sums on vertices of a regular polygon is studied. A criterion for a certain equation to be satisfied is obtained.

Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their…

This paper is devoted to dimensional reductions via the norm resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The efficiency of our abstract tool is demonstrated by its…

We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular…