On polynomial symbols for subdivision schemes

Given a dilation matrix A :ℤ^d→ℤ^d, and G a complete set of coset representatives of 2π(A ^−Tℤ^d/ℤ^d), we consider polynomial solutions M to the equation ∑ _g∈G M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices, we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of arbitrary order. Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network.     

Asymptotic densities of Maass newforms

We define the counting function for Maass newforms of Hecke congruence groups and calculate the three main terms of this counting function. We then give necessary and sufficient conditions for this expansion to have the same shape as if it were counting eigenvalues related to cocompact surfaces. We relate the result to classical instances of the Jacquet-Langlands correspondence.     

Multi-Wavelength Optical Packet Routing Technologies Based on Superstructured Fiber Bragg Gratings

A WDM compatible Edge-to-Edge Self-Routed optical packet switched network that simplifies the optical processing is proposed. The system employs all-optical packet label generation and recognition using coded superstructured Fiber Bragg gratings.     

Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.     

Synthesis and X-ray crystal structures of six [TeL4][MF6] salts, where L is ethylene- or trimethylene-thiourea, and M is Si, Ge or Sn. Five Te(II) complexes with a novel type of structure linked together by unusual N–HF hydrogen bonds

The complexes [Te(etu)₄][SiF₆] (1), [Te(etu)₄][SiF₆] · H₂O (2), [Te(trtu)₄][SiF₆] (3), [Te(etu)₄][GeF₆] · H₂O (4), [Te(trtu)₄][GeF₆] (5) and [Te(etu)₄][SnF₆] (6) (etu = ethylenethiourea, trtu = trimethylenethiourea) have been prepared and their crystal structures determined by X-ray crystallographic methods. The crystals of 1, 3 and 5 are tetragonal; space groups P4cc (No. 103) with Z = 4 for 1, P4nc (No. 104) with Z = 2 for 3, and I4 (No. 79) with Z = 2 for 5. The crystals of 2, 4 and 6 are orthorhombic, space group Pccn (No. 56) with Z = 8 for 2 and 4 and Z = 4 for 6; those of 2 and 4 being isomorphous. The cations contain square planar or slightly distorted square planar TeS₄ coordination groups. In 1, 3 and 5 the Te atoms are located on fourfold rotation axes; the cations have fourfold rotational symmetry and the four thiourea ligands extend to the same side of the TeS₄ plane. These are the first examples of [TeL₄]²⁺ conformers of this type. In 2 and 4 the Te atoms lie on general positions; the cations are distorted versions of those in 1, and also in these the four ligands extend to the same side of the TeS₄ plane. In 6 the Te atoms are located on twofold rotation axes, the conformation of the cations corresponds to the point group C₂ with two neighbouring ligands extending to one side of the coordination plane and the remaining two to the opposite side. In 1–5 each of the four ligands forms a N–HF bond to the same F atom in the counter ion. The crystals of 1–5 are red, and those of 6 are yellow. The red colour is attributed to interactions of Te and S lone electron pairs caused by ligand TeS₄/TeSC tilt angles markedly different from 90°.     

3',4'-trans-linked bicyclic nucleosides locked in S-type conformations

A novel class of 3',4'-trans-linked bicyclic nucleosides with locked S-type furanose conformations is introduced by synthesis of two model derivatives; one was obtained by cyclic ether formation and the other by ring-closing metathesis methodology.     

1H detection in MAS solid-state NMR spectroscopy of biomacromolecules employing pulsed field gradients for residual solvent suppression

In this communication, we demonstrate the feasibility of 1H detection in MAS solid-state NMR for a microcrystalline, uniformly 2H,15N-labeled sample of a SH3 domain of chicken alpha-spectrin, using pulsed field gradients for suppression of water magnetization. Today, B0 gradients are employed routinely in solution-state NMR for coherence order selection and solvent suppression. We suggest to use gradients to purge water magnetization which cannot be suppressed using conventional water suppression schemes. The achievable gain in sensitivity for 1H detection is in the order of 5 compared to the 15N detected version of the experiment (at a MAS rotation frequency of 13.5 kHz). We expect that this labeling concept which achieves high sensitivity due to 1H detection, in combination with the possibility to measure long range 1H-1H distances as we have shown previously, to be a useful tool for the determination of protein structures in the solid state.     

SPOCC-194, a new high functional group density PEG-based resin for solid-phase organic synthesis

A novel polymer matrix for solid-phase synthesis, SPOCC(194) resin (1), was designed featuring a backbone of homogeneous tetraethylene glycol (TEG(194)) macromonomer linked by quaternary carbon junctions and terminating in primary alcohol functionality. Beaded SPOCC(194) resin was effectively prepared by suspension polymerization of oxetanylated TEG macromonomer 5 in stirred silicon oil. Mechanically stable and inert to a diverse range of reaction conditions, SPOCC(194) possessed a high hydroxyl group loading (0.9-1.2 mmol/g) for substrate attachment and swelled effectively ( approximately 2-4 mL/g) in a variety of organic and aqueous solvents. Developed for solid-phase synthesis at high reactant concentrations for driving organic and aqueous reactions to completion, SPOCC(194) exhibited high functional group density (mmol/mL) similar to that of low-loaded aminomethylated polystyrene-divinylbenzene copolymer (PS-1%DVB) yet significantly higher than that of PEGA(1900), SPOCC(1500), and TentaGel S. High-resolution MAS NMR spectra of Fmoc-derivatized SPOCC(194) indicate that monitoring of functional group transformation is possible. Moreover, by employment of a nonaromatic resin-linker combination, electrophilic chemistry, such as Lewis acid catalyzed glycosylation and Friedel-Crafts acylation, was selectively performed on substrate bound to SPOCC(194) resin. Such properties make SPOCC(194) resin a promising new polymer matrix for the support-bound construction of small organic molecules by parallel and combinatorial synthesis and the scavenging of solution-phase reactants or byproducts.