Global existence for small data Cauchy problem of semilinear wave equations with scaling invariant damping in 3-D is established this work, assuming that the are radial and constant front belongs to [1.5,2). The proof based on a weighted L2−L2 estimate inhomogeneous equation, which by interpolating between energy Morawetz type estimate.

For a distributive lattice L, we consider the problem of interpolating functions f : D → L defined on a finite set D ⊆ L, by means of lattice polynomial functions of L. Two instances of this problem have already been solved. In the case when L is a distributive lattice with least and greatest elements 0 and 1, Goodstein proved that a function f : {0, 1} → L can be interpolated by a lattice poly...

A multilevel sparse kernel-based interpolation (MLSKI) method, suitable for moderately high-dimensional function interpolation problems has been recently proposed in [15]. The method uses both level-wise and direction-wise multilevel decomposition of structured or mildly unstructured interpolation data sites in conjunction with the application of kernel-based interpolants with different scaling...

Electronic structure calculations are mostly carried out with Coulomb potential singularity adapted basis sets such as STO or contracted GTO. With another for heavy elements, the pseudopotentials may appear a practical alternative. Here, we introduce exact pseudopotential (EPP) to remove and test it orbitals of small atoms interpolating wavelet set. We apply EPP Galerkin method set consisting D...

The interpolating sequences S for H∞(D), the bounded holomorphic functions in the unit disc D of the complex plane C, were characterized by L. Carleson using metric conditions on S. Alternatively, to characterize interpolating sequences we can use the existence in H∞(D) of an infinity of functions {ρa}a∈S , uniformly bounded in D, the function ρa being 1 at the point a ∈ S and 0 at any b ∈ S \ ...

We consider the problem of interpolating functions partially defined over a distributive lattice, by means of lattice polynomial functions. Goodstein’s theorem solves a particular instance of this interpolation problem on a distributive lattice L with least and greatest elements 0 and 1, resp.: Given a function f : {0, 1}n → L, there exists a lattice polynomial function p : Ln → L such that p|{...

In this paper, we characterize multiresolution analysis(MRA) Parseval frame multiwavelets in L^2(R^d) with matrix dilations of the form (D f )(x) = sqrt{2}f (Ax), where A is an arbitrary expanding dtimes d matrix with integer coefficients, such that |detA| =2. We study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of MRA tight frame multiwa...