Let L = −∆+ V be a Schrödinger operator on R, d ≥ 3, where V is a nonnegative function, V 6= 0, and belongs to the reverse Hölder class RHd/2. The purpose of this paper is three-fold. First, we prove a version of the classical theorem of Jones and Journé on weak∗-convergence in H L(R ). Secondly, we give a bilinear decomposition for the product space H L(R )×BMOL(R). Finally, we study the commu...

We study perturbations of a stochastic program with a probabilistic constraint and r-concave original probability distribution. First we improve our earlier results substantially and provide conditions implying Hölder continuity properties of the solution sets w.r.t. the Kolmogorov distance of probability distributions. Secondly, we derive an upper Lipschitz continuity property for solution set...

In this paper, first we prove fixed point theorems for different variant of compatible maps, satisfying a contractive condition of integral type in fuzzy metric spaces, which improve the results of Branciari [2], Rhoades [33], Kumar et al. [23], Subramanyam [35] and results of various authors cited in the literature of ”Fixed Point Theory and Applications”. Secondly, we introduce the notion of ...

The problem of density estimation on R is concerned. Adopting the maxiset point of view, the aim of this paper is threefold. Firstly, we prove that the maxiset of any elitist rule is contained in the intersection of a Besov space and a weak Besov space. Secondly, we provide an adaptive procedure for which the maxiset is the largest one among elitist rules (ideal maxiset). Thirdly, we point out ...

This paper proposes a complete scheme of a ratedistortion optimal progressive fine granularity scalable (PFGS) video codec. Firstly, it introduces the use of multiple enhancement layer references and a modified mode decision algorithm based on the analysis of the unique characteristic of the residue data of the enhancement layer. Secondly, the rate-distortion optimal method to select the enhanc...

We are interested in the homogenization of energy like quantities for electromagnetic waves in the high frequency limit for Maxwell's equations with various boundary conditions. We use a scaled variant of H-measures known as semi classical measures or Wigner measures. Firstly, we consider this system in the half space of R 3 in the time harmonic and with conductor boundary condition at the flat...

and socio-political aspects. Secondly, few explanations of the crisis take account of evidence from the local and regional levels. Thirdly and most seriously, theories of the crisis have ignored Germany, while historians of Germany have ignored the crisis debate. This article seeks tojill these gaps. It puts Germany at the centre of a comprehensive theory of the crisis that takes existing crisi...

We say that a tree T is an S-Steiner if S⊆V(T) and hypergraph hypertree it can be trimmed to tree. prove NP-complete decide, given H some S⊆V(H), whether there subhypergraph of which hypertree. As corollaries, we give two negative results for Steiner orientation problems in hypergraphs. Firstly, show H, r∈V(H) this has every vertex S reachable from r. Secondly, any vertices are mutually each ot...

Let Sβ := {z ∈ C : |Imz| < β} be a strip in complex plane. H̃r ∞,β denotes those 2π-periodic, real-valued functions on R which are analytic in the strip Sβ and satisfy the condition |f (r)(z)| ≤ 1, z ∈ Sβ . Osipenko and Wilderotter obtained the exact values of the Kolmogorov, linear, Gel′fand, and information n-widths of H̃r ∞,β in L∞[0, 2π], r = 0, 1, 2, . . ., and 2n-widths of H̃r ∞,β in Lq [0, ...

We are not aware of functions or packages in R that implement the Infomax algorithm (Bell and Sejnowski 1995). We offer an alternative to Matlab code (http://cnl.salk. edu/~tewon/ICA/code.html), but with a few modifications that decrease computation time. First, we use the full data (the so-called offline algorithm) in each iteration rather than an online algorithm with batches. Secondly, we us...