A Banach space has the weak fixed point property if its dual space has a weak∗ sequentially compact unit ball and the dual space satisfies the weak∗ uniform Kadec-Klee property; and it has the fixed point property if there exists ε > 0 such that, for every infinite subset A of the unit sphere of the dual space, A ∪ (−A) fails to be (2 − ε)-separated. In particular, E-convex Banach spaces, a cla...

The Arnoldi method is currently a very popular algorithm to solve large-scale eigenvalue problems. The main goal of this paper is to generalize the Arnoldi method to the characteristic equation of a delay-differential equation (DDE), here called a delay eigenvalue problem (DEP). The DDE can equivalently be expressed with a linear infinite dimensional operator whose eigenvalues are the solutions...

Abstract. Let φm be a polynomial satisfying some mild conditions. Given a set R ⊂ C, a continuous function f on R and its best approximation p n−1 from Πn−1 with respect to the maximum norm, we show that p ∗ n−1 ◦φm is a best approximation to f ◦ φm on the inverse polynomial image S of R, i.e. φm(S) = R, where the extremal signature is given explicitly. A similar result is presented for constra...

In this paper an asymptotic numerical method is suggested to solve singularly perturbed weakly coupled system of convectiondiffusion type second order ordinary differential equations with delay (negative shift) terms. An error estimate is derived in the supremum norm and it is found to be of order O(N−1 lnN) provided that ε ≤ CN−1, where ε is small perturbation parameter and N is the discretiza...

We consider the theory of correctors to homogenization in stationary transport equations with rapidly oscillating, random coefficients. Let ε 1 be the ratio of the correlation length in the random medium to the overall distance of propagation. As ε ↓ 0, we show that the heterogeneous transport solution is well-approximated by a homogeneous transport solution. We then show that the rescaled corr...

Folded Reed-Solomon codes are an explicit family of codes that achieve the optimal tradeoff between rate and list error-correction capability: specifically, for any ε > 0, Guruswami and Rudra presented an n time algorithm to list decode appropriate folded RS codes of rateR from a fraction 1−R− ε of errors. The algorithm is based on multivariate polynomial interpolation and root-finding over ext...

Abstract. We consider a billiard in the punctured torus obtained by removing a small disk of radius ε > 0 from the flat torus T, with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity ω only. Let τ̃ε(ω), and respectively R̃ε(ω), denote the first exit time (length of the trajectory), and respectively the number of collisions wit...

Global entropy solutions in BV for a scalar nonlocal conservation law with fading memory are constructed as limits of vanishing viscosity approximate solutions. The uniqueness and stability of entropy solutions in BV are established, which also yield the existence of entropy solutions in L∞ while the initial data is only in L∞. Moreover, if the memory kernel depends on a relaxation parameter ε ...

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A cent...