The change in entropy, S , associated with the quasi-static absorption of a particle of energy ε by a Schwarzschild black hole (ScBH) is approximately (ε/T )− s, where T is the Hawking temperature of the black hole and s is the entropy of the particle. Motivated by the statistical interpretation of entropy, it is proposed here that the absorption should be suppressed, but not forbidden, when S ...

CG, SYMMLQ, and MINRES are Krylóv subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and SYMMLQ’s solution could explode, while MINRES would give a least-squares solution but not necessarily the minimum-length (pseudoinverse) solution. This underst...

A Boolean function is symmetric if it is invariant under all permutations of its arguments; it is quasi-symmetric if it is symmetric with respect to the arguments on which it actually depends. We present a test that accepts every quasi-symmetric function and, except with an error probability at most δ > 0, rejects every function that differs from every quasi-symmetric function on at least a fra...

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...

Radzik (1991) showed that two-player games on compact intervals of the real line have ε – equilibria for all ε > 0, provided that payoff functions are upper semicontinuous and strongly quasi-concave. In an attempt to generalize this theorem, Ziad (1997) stated that the same is true for n-player games on compact, convex subsets of Rm, m ≥ 1 provided that we strengthen the upper semicontinuity co...

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...

We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75 (2006), 1449–1466]. For a given semi-rational polytope p and a rational subspace L, we integrate a given polynomial function h over all lattice slices of the polytope p parallel to the subspace L and sum...

In metallic wires, electron-electron interactions lead to quasi-elastic scattering, which modifies the electron phase-coherence time, and to inelastic scattering, which redistributes energy between electrons. Several recent experiments have shown that these properties can be sampledependent 1,2. We have found furthermore that the low-temperature saturation of the phasecoherence time τφ of quasi...

In this paper, d-dimensional (dD) quasi-periodically forced nonlinear Schrödinger equation with a general nonlinearity iut −∆u+Mξu+ εφ(t)(u+ h(|u| 2)u) = 0, x ∈ T, t ∈ R under periodic boundary conditions is studied, where Mξ is a real Fourier multiplier and ε is a small positive parameter, φ(t) is a real analytic quasi-periodic function in t with frequency vector ω = (ω1,ω2 . . . ,ωm), and h(|...

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...