Fronts, propagating into an unstable state phi=0, whose asymptotic speed v(as) is equal to the linear spreading speed v* of infinitesimal perturbations about that state (so-called pulled fronts), are very sensitive to changes in the growth rate f(phi) for phi<<1. It was recently found that with a small cutoff, f(phi)=0 for phi< epsilon, v(as) converges to v* very slowly from below, as ln(-2) ep...

A method is presented for variational calculation of the energy and the spin densities derived from a single-determinant wavefunction. Sum and difference coordinates [unk]R = (1/2)([unk]r(1) + [unk]r(1)) and [unk]r = [unk]r(1) - [unk]r(1) are introduced, and the density matrix P([unk]r(1),[unk]r(1)) is expanded in partial waves in the new coordinate frame: [Formula: see text] The functions h(L)...

The semantics of determiner phrases, be they definite descriptions, indefinite descriptions or quantified noun phrases, is often assumed to be a fully solved question: common nouns are properties, and determiners are generalised quantifiers that apply to two predicates: the property corresponding to the common noun and the one corresponding to the verb phrase. We first present a criticism of th...

In this article, the relationships between $S$-spectra, $ S$-spectral radius, \epsilon$-$S$-essential pseudospectra, and pseudospectral radius of diagonal block operator matrices in direct sum Banach spaces their coordinate operators are studied. Then, results supported by applications.

‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...