The paper is devoted to complete proofs of theorems on consistency on cubic lattices for 3 × 3 determinants. The discrete nonlinear equations on Z defined by the condition that the determinants of all 3×3 matrices of values of the scalar field at the points of the lattice Z that form elementary 3 × 3 squares vanish are considered; some explicit concrete conditions of general position on initial...

By making the connection between four-dimensional lattice Green functions (LGFs) and Picard–Fuchs ordinary differential equations of Calabi–Yau manifolds, we have given explicit forms for the coefficients of the fourdimensional LGFs on the simple-cubic and body-centred cubic lattices, in terms of finite sums of products of binomial coefficients, and have shown that the corresponding four-dimens...

1. INTRODUCTION. There is something fascinating about procedures for solving low degree polynomial equations. On one hand, we all know that while general solutions (using radicals) are impossible beyond the fourth degree, they have been found for quadratics, cubics, and quartics. On the other hand, the standard solutions for the the cubic and quartic are complicated, and the methods seem ad hoc...

Darvishi and Barati [M.T. Darvishi, A. Barati, Super cubic iterative methods to solve systems of nonlinear equations, Appl. Math. Comput., 2006, 10.1016/j.amc.2006.11.022] derived a Super cubic method from the Adomian decomposition method to solve systems of nonlinear equations. The authors showed that the method is third-order convergent using classical Taylor expansion but the numerical exper...

In this paper we obtain conditions on the coefficients of a cubic Lotka–Volterra system of the form _ x 1⁄4 xð2 a20x a11xy a02yÞ; _ y 1⁄4 yð 3þ b20x þ b11xyþ b02yÞ; ð1Þ which fulfillment yields the existence in a neighborhood of the origin of a first integral of the form /ðx; yÞ 1⁄4 x3y2 þ h:o:t:, in which case the origin is termed a 2 : 3 resonant center. This system was studied in [13], where...

In this article, we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients. We focus on the case where those coefficients vanish on vacuum. We prove the stability of weak solutions for periodic domain Ω = T as well as the whole space Ω = R , when N = 2 and N = 3. The pressure is given by p = ρ , and our result holds for any γ > 1. In particular, we prove ...

n-th order with n 2 has not yet been well established; its local aspect is clari ed under the assumption that the discriminant of the characteristic equation is of simple zeros ([AKT, Theorem 1.4 and Theorem 1.6]), but its global aspect is far from complete understanding ([BNR], [AKT, Section 2]). The purpose of this paper is to examine the validity of our Ansatz concerning the Stokes geometry ...

Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. A real inflection point is also required for transforming projectively a planar cubic algebraic curve to the normal form, in order to facilitate further analysis of the curve. However, the naive method for computing the inf...

We extend Chen, Wei, and Yan’s constructions of families of solutions with unbounded energies ([5]) to the case of cubic nonlinear Schrödinger equations in the optimal dimension four.

We give a complete solution to a system of Diophantine equations related to a problem on the fundamental unit of a family of cubic fields.