[email protected] [email protected] Abstract: Consider the events fFn \ Sn 1 k=1 Fk = ;g, n 2 N, where (Fn) 1 n=1 is an i.i.d. sequence of stationary random subsets of a compact group G . A plausible conjecture is that these events will not occur in nitely often with positive probability if PfFi\Fj 6= ; jFjg > 0 a.s. for i 6= j. We present a counterexample to show that this conditio...

A second look at the authors’ ([BDR1], [BDR2]) characterization of the approximation order of a Finitely generated Shift-Invariant subspace S(Φ) of L2(IR) results in a more explicit formulation entirely in terms of the (Fourier transform of the) generators φ ∈ Φ of the subspace. Further, when the generators satisfy a certain technical condition, then, under the mild assumption that the set of 1...

Previous research by J. M. Hinson, T. L. Jameson, and P. Whitney (2003) demonstrated that a secondary task in a delayed discounting paradigm increased subjects' preference for the immediate reward. J. M. Hinson et al. interpreted their findings as evidence that working memory load results in greater impulsivity. The present authors conducted a reanalysis of the data from J. M. Hinson et al.'s E...

In the present paper we analyze Fréchet frame of the form {φ(·−j) | j ∈ Z}. With a known condition on φ, we show that the given sequence constitutes a frame for a test space isomorphic to the space of periodic smooth functions so that its dual is the multiple of the space of periodic distributions by φ̂. AMS Mathematics Subject Classification (2000): 42C15,42C40,42C99,46A35,46B20

For x ∈ [0, 1), let x = [a 1 (x), a 2 (x), · · · ] be its continued fraction expansion with partial quotients {a n (x), n ≥ 1}. E(ψ) := x ∈ [0, 1) : lim n→∞ 1 ψ(n) n j=1 log a j (x) = 1 is completely determined without any extra condition on ψ.

Recall that the Lorentz ideal C− p is the collection of operators A satisfying the condition ‖A‖p = ∑∞ j=1 j sj(A) < ∞. Consider Hankel operators Hf : H(S) → L(S, dσ) H(S), where H(S) is the Hardy space on the unit sphere S in C. In this paper we characterize the membership Hf ∈ C− p , 2n < p <∞.

Several matrix factorizations depend on orthogonal factors, matrices that preserve the Euclidean scalar product. Some of these factorizations can be extended and generalized to (J, J̃)-orthogonal factors, that is, matrices that satisfy H JH = J̃ , where J and J̃ are diagonal with diagonal elements ±1. The purpose of this work is to analyze the perturbation of matrix factorizations that have a (J, ...

Let v : [0, T ] × R → R be the solution of the parabolic backward equation ∂tv + (1/2) ∑ i,j [σσ ]i,j∂xi∂xjv + ∑ i bi∂xiv + kv = 0 with terminal condition g, where the coefficients are timeand state-dependent, and satisfy certain regularity assumptions. Let X = (Xt)t∈[0,T ] be the associated R -valued diffusion process on some appropriate (Ω,F ,Q). For p ∈ [2,∞) and a measure dP = λT dQ, where ...

We prove global existence of weak solutions to two systems of equations which extend the dynamics of the Navier-Stokes equations for incompressible viscous flow with no-slip boundary condition. The systems of equations we consider arise as formal limits of time discrete pressure-Poisson schemes introduced by Johnston & Liu [J. Comput. Phys. 199, 221–259, 2004] and by Shirokoff & Rosales [J. Com...