Related papers: On a diagonal quadric in dense variables

A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of…

In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.

In strongly coupled field theories, perturbation theory cannot be employed to study the low-energy spectrum. Thus, non-perturbative techniques are required. We employ the variational method, a rigorous, non-perturbative approach which…

This paper studies the derivation of the quadratic porous medium equation and a class of cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a nonlocal interaction equation, resp. system, to solutions of…

We investigate a generalized Hele-Shaw equation with a source and drift terms where the density is constrained by an upper-bound density constraint that varies in space and time. By using a generalized porous medium equation approximation,…

We consider certain respondent-driven sampling procedures on dense graphs. We show that if the sequence of the vertex-sets is ergodic then the limiting graph can be expressed in terms of the original dense graph via a transformation related…

In the area of symbolic-numerical computation within computer algebra, an interesting question is how "close" a random input is to the "critical" ones, like the singular matrices in linear algebra or the polynomials with multiple roots for…

Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its…

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…

For non-singular intersections of pairs of quadrics in 11 or more variables, we prove an asymptotic for the number of rational points in an expanding box.

In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and nondecreasing initial data. Moreover, we show…

We consider the flow of a viscous incompressible fluid through a porous medium. We allow the permeability of the medium to depend exponentially on the pressure and provide an analysis for this model. We study a splitting formulation where a…

In this paper we present a new method of solving certain quartic and higher degree homogeneous polynomial diophantine equations in four variables. The method can also be extended to solve simultaneous homogeneous polynomial diophantine…

In this article we consider the action of affine group and time rescaling on planar quadratic differential systems. We construct a system of representatives of the orbits of systems with at least five invariant lines, including the line at…

We give a specific method to solve with quadratic complexity the linear systems arising in known algorithms to deal with the sign determination problem. In particular, this enable us to improve the complexity bound for sign determination in…

We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…

In a recent work [1, 2] Sjoberg remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this note we have attempted to provide this generalization to…

This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…

In this paper, we bound the number of solutions to a quadratic Vinogradov system of equations in which the variables are required to satisfy digital restrictions in a given base. Certain sets of permitted digits, namely those giving rise to…