Spline prewavelets for non-uniform knots

Summary In this paper, we develop a framework suitable for performing a multiresolution analysis using univariate spline spaces of arbitrary degree and with non-uniform knot-sequences. To this end, we show, among other things, the existence of compactly supported prewavelets and of prewavelets that are globally supported, but decay exponentially. In each case we obtain a decomposition of a fine spline space as a sum of a coarse spline space plus a spline space spanned by prewavelets.     

Mode beating in spot-size converter lasers

An anomalous modulation in the wavelength spectrum has been observed in lasers with spot-size converters. This intensity modulation is shown to be caused by beating between the fundamental lasing mode and radiation modes in the taper. This results in a periodic modulation in the net gain spectrum, which causes wavelength jumps between adjacent net gain maxima, and a drive current dependent spectral width that is expected to affect system performance. The amplitude of this spectral modulation is reduced significantly by either using an angled rear-facet which reflects the beating radiation modes away from the laser axis, or by using a nonlinear, adiabatic taper.     

Facile preparation of new unsymmetrical curcumin derivatives by solid-phase synthesis strategy

Seventeen unsymmetrical curcumin derivatives were synthesized in good yield and purity by a facile solid phase synthesis strategy.     

Characterization of NOx species in dehydrated and hydrated Na- and Ba-Y, FAU zeolites formed in NO2 adsorption

Adsorbed ionic NO_x species formed upon the interaction of NO₂ with dehydrated or hydrated Na- and Ba-Y, FAU zeolites were characterized using FT-IR/TPD, solid state NMR, and XANES techniques. NO₂ disproportionates on both dehydrated catalyst materials forming NO⁺ and NO₃⁻ species. These ionic species are stabilized by their interactions with the negatively charged zeolite framework and the charge compensating cations (Na⁺ and Ba²⁺), respectively. Although the nature of the adsorbed NO_x species formed on the two catalysts is similar, their thermal stabilities are strongly dependent on the charge compensating cations. In the presence of water in the channels of these zeolite materials new paths open for reactions between NO⁺ and H₂O, and NO₂ and H₂O, resulting in significant changes in the adsorbed ionic species observed. These combined spectroscopic investigations afforded the understanding of the interactions between water and NO₂ on these zeolite catalysts.     

On the number of full levels in tries

We study the asymptotic distribution of the fill‐up level in a binary trie built over n independent strings generated by a biased memoryless source. The fill‐up level is the number of full levels in a tree. A level is full if it contains the maximum allowable number of nodes (e.g., in a binary tree level k can have up to 2^k nodes). The fill‐up level finds many interesting applications, e.g., in the internet IP lookup problem and in the analysis of level compressed tries (LC tries). In this paper, we present a complete asymptotic characterization of the fill‐up distribution. In particular, we prove that this distribution concentrates on one or two points around the most probably value k = ?log_1/qn ? log log log n + 1 + log log(p/q)?, where p > q = 1 ? p is the probability of generating the more likely symbol (while q = 1 ? p is the probability of the less likely symbol). We derive our results by analytic methods such as generating functions, Mellin transform, the saddle point method, and analytic depoissonization. We also present some numerical verification of our results. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Concerning seven and eight mutually orthogonal Latin squares

In this paper, three new direct Mutually Orthogonal Latin Squares (MOLS) constructions are presented for 7 MOLS(24), 7 MOLS(75) and 8 MOLS(36); then using recursive methods, several new constructions for 7 and 8 MOLS are obtained. These reduce the largest value for which 7 MOLS are unknown from 780 to 570, and the largest odd value for which 8 MOLS are unknown from 1935 to 419. © 2003 Wiley Periodicals, Inc.     

The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption

In this paper we prove some new equivalences between convergence of the Ishikawa and Mann iteration sequences with errors in two schemes by Xu [Y.G. Xu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998) 91-101] and Liu [L.S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995) 114-125], respectively, for strongly successively pseudocontractive mappings. Our main results improve and extend the corresponding results of the all references listed in this article.     

Comment on “smooth and discontinuous signature change in general relativity”

Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weaker formulation is possible, in which less restrictive smoothness assumptions are made, and (a slightly different form of) the Einstein field equations are satisfied. In particular, in this formulation it is possible to have a bounded energy-momentum tensor at a change of signature without satisfying their condition that the extrinsic curvature vanish.