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.     

Cos degradation by selected co-utilizing bacteria

Applied Biochemistry and Biotechnology - The results of this study support the hypothesis that several organisms that are capable of utilizing CO are also capable of degrading CO-like compounds,...     

Solvothermal synthesis of new metal organic framework structures in the zinc-terephthalic acid-dimethyl formamide system

Two new metal organic framework (MOF) structures have been obtained from the Zn-terephthalic acid (H₂BDC)-dimethyl formamide (DMF) system and examined by single-crystal X-ray diffraction: Zn(C₈H₄O₄)(C₃H₇NO), 1, monoclinic C2/m, a=11.1369(5), b=14.0217(7), , β=106.316(1)°, , , Z=4, R₁=0.060, wR₂=0.169, S=1.27; Zn(HCO₂)₃(C₂H₈N), 2, trigonal , a=8.1818(1), , , , Z=6, R₁=0.014, wR₂=0.039, S=1.11. Contrary to previously published structures in the same system, the crystals were obtained by solvothermal synthesis at 381 K. Structure 1 consists of 2-D layers stacked in an offset manner to accommodate DMF moieties coordinated to Zn²⁺ within voids in adjacent layers. Structure 2 consists of a 3-D network constructed from Zn²⁺ ions bridged by deprotonated formic acid moieties. Over time, the structure of 1 rearranges to Zn(C₈H₄O₄)(C₃H₇NO)(H₂O) [monoclinic P2₁/n, a=6.6456(2), b=15.2232(5), , β=104.110(2)°, , , Z=4, R₁=0.048, wR₂=0.100, S=1.07], which is identical to the known MOF-2 structure, obtained by crystallization at ambient conditions. The three structures were determined from crystals with similar crystal habits picked from a single solvothermal synthesis batch. The study demonstrates that MOF syntheses can give not only multiple crystal structures under different conditions, but also that numerous different structures, including some that are metastable, can be formed under identical conditions.     

Purification of monoclonal antibodies from cell culture supernatants using a modified zirconia based cation-exchange support

A method suitable for the isolation of monoclonal antibodies (Mabs) is described. The protocol utilizes a zirconia based column modified with ethylenediamine-N,N'-tetra(methylenephosphonic) acid to create a novel cation-exchange chromatographic support. Initial experiments using a linear salt gradient demonstrate the ability of this support to efficiently separate Mab from transferrin and bovine serum albumin in a model matrix. Results of the purification of Mab from an actual cell culture supernatant over a range in protein concentrations are also shown. Analyses by enzyme-linked immunosorbent assay and gel electrophoresis demonstrate that Mabs can be recovered from a cell culture supernatant at high yield (92-98%) and high purity (> 95%) in a single chromatographic step.     

Studies on amino acids and peptides-III. 2,4-bis(4-methoxyphenyl)-1,3,2,4-dithiadiphosphetane 2,4-disulfide,LR, as a new racemization free coupling reagent in peptide synthesis

The easily accessible 2,4-bis (4-methoxyphenyl)-1,3,2,4-dithiadiphosphetane 2,4-disulfide, $\text{LR}$, has been reacted with salts of N-protected amino acids $\text{1}$ (Z-Gly-OH, Boc-Gly-OH, Boc-S-Ser(Bzl)-OH, Boc-S-Tyr(Bzl)-OH, Z-S-Arg(Z₂)-OH, and Z-S-Pro-OH), at room temperature in CH₂Cl₂ to give the intermediates $\text{2}$, mixed anhydrides. When $\text{2}$ is treated with two moles of a base and one mole of the salt of an amino acid ester $\text{3}$ (TosOH·H-Gly-OBzl, HCl·H-Gly-OBzl, HCl·H-Gly-OEt, and HCl·H-S-Phe-OtBu) at 0°C, the expected peptide $\text{4}$ is isolated in high yields. LR is also found to be a useful reagent in a fragment coupling between Z-Gly-S-Ala-OH and TosOH·H-S-Leu-OBzl). This tripeptide was tested by means of HPLC (deprotection and amino acid analysis according to Izumiya was not necessary), and no epimerization (<0.7 %) was observed.     

Studies on organophosphorus compounds: Thiation of 3,1-benzoxathian-4-ones. New routes to 1,2-benzisothiazole-3(2H)-thiones and 3H-1,2-benzodithiol-3-imines

3,1-Benzoxathian-4-ones, 2, when heated with 2,4-bis(4-methoxyphenyl)-1,3,2,4-dithiadiphosphetane-2, 4-disulfide, 1, or with P₄S₁₀ give one or more of the following products 3,1-benzoxathian-4-thione, 3, 1,3-benzodithian-4-one, 4, 1,3-benzodithian-4-thione, 5, and 3H-1,2-benzodithiole-3-thione, 6. Compounds 2, when heated with primary and secondary amines and with hydrazines, give 2-mercaptobenzamides, 7, and 2-mercaptobenzohydrazides, 8, or their corresponding disulfides, 7' and 8'. 3H-1, 2-Benzodithiol-3-immes, which are in equilibrium with 1,2-benzisothiazole-3(2H)-thiones, (9A ? 9B), are prepared by two new routes (a) by allowing 3 or 5 to react with primary amines or hydrazines, (b) by allowing 7, 8, 7' or 8' to react with 1.