We prove that, for every $$k\ge 4$$ , the sets M(k) and L(k), which are Markov Lagrange dynamical spectra related to conservative horseshoes associated continued fractions with coefficients bounded by k coincide intersections of classical $$(-\infty ,\sqrt{k^2+4k}]$$ . also observe despite corresponding statement is true $$k=2$$ it false $$k=3$$

The gyroscopic force acting on a ferromagnetic soliton reflects the tendency of spins to precess. Its components increase linearly with (generalized) velocities soliton. proportionality coefficients form tensor, generalization Thiele's gyrovector. Originally introduced as an auxiliary quantity, tensor turns out be mathematical object fundamental importance long history going back Lagrange. We r...

This article considers the backward error of the solution of polynomial eigenvalue problems expressed as Lagrange interpolants. One of the most common strategies to solve polynomial eigenvalue problems is to linearize, which is to say that the polynomial eigenvalue problem is transformed into an equivalent larger linear eigenvalue problem, and solved using any appropriate eigensolver. Much of t...

Iterative substructuring methods with Lagrange multipliers for the elliptic system of linear elasticity are considered. The algorithms belong to the family of dual-primal FETI methods which was introduced for linear elasticity problems in the plane by Farhat et al. [2001] and then extended to three dimensional elasticity problems by Farhat et al. [2000]. In dual-primal FETI methods, some contin...

The paper is mainly concerned with an approximate three-ball inequality for solutions in elliptic periodic homogenization. We consider a family of second order operators $\mathcal{L}_\epsilon$ divergence form rapidly oscillating and coefficients. It the first time such homogenization theory obtained. implies quantitative propagation smallness. proof relies on representation solution by Poisson ...

A new method to fit specific types of conics to scattered data points is introduced. Direct, specific fitting of ellipses and hyperbolae is achieved by imposing a quadratic constraint on the conic coefficients, whereby an improved partitioning of the design matrix is devised so as to improve computational efficiency and numerical stability by eliminating redundant aspects of the fitting procedu...

We aim at proposing novel stable finite element methods for the mixed Darcy equation with heterogeneous coefficients within a space splitting framework. We start from the primal hybrid formulation of the elliptic model for the pressure. Localization of this infinite-dimensional problem leads to element-level boundary value problems which embed multiscale and high-contrast features in a natural ...

We present a Singular Function Boundary Integral Method (SFBIM) for solving elliptic problems with a boundary singularity. In this method the solution is approximated by the leading terms of the asymptotic solution expansion, which exists near the singular point and is known for many benchmark problems. The unknowns to be calculated are the singular coefficients, i.e. the coefficients in the as...

Although the issues of routing and scheduling in packet radio networks are highly interdependent, few studies have addressed their interactions. In this paper, we address the problem of routing for the minimization of congestion as a first step toward the solution of the joint routing-scheduling problem. We formulate this as a combinatorial-optimization problem, and we develop a Hopfield neural...