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.     

Determination of sulfinpyrazone and two of its metabolites in human plasma and urine by gas chromatography and selective detection

A selective and sensitive gas chromatographic method for simultaneous determination of sulfinpyrazone and two of its metabolites (the para-hydroxylated metabolite and the sulfone metabolite) in biological fluids using alkali flame ionization detection (AFID), electron capture detection (ECD) and mass fragmentographic detection is described. The compounds are extracted from the samples, methylated and separated on 2% OV-17 or 3% OV-225 columns. Phenylbutazone is used as internal standard. Standard curves are linear. The coefficient of variation at 10 microgram/ml of sulfinpyrazone in plasma was shown to be 1.8% (AFID), and the detection limits were 0.1 microgram/ml (AFID) and 10 ng/ml (ECD). Mass spectra of the methylated compounds are shown and serum concentration curves after oral administration of 100 mg sulfinpyrazone to two persons are determined together with the excreted amounts of drug and metabolites.     

Refinement of borate structures from 11B MAS NMR spectroscopy and density functional theory calculations of 11B electric field gradients

The refinement of borate structures using DFT calculations combined with experimental (11)B quadrupole coupling parameters from solid-state NMR spectroscopy is presented. The (11)B electric field gradient (EFG) tensors, calculated using the WIEN2k software for trigonal and tetrahedral boron sites in a series of model compounds, exhibit a convincing linear correlation with the quadrupole coupling tensor elements, determined from (11)B MAS NMR spectra of the central or satellite transitions. The model compounds include Li(2)B(4)O(7), Mg(2)B(2)O(5), Mg(3)B(2)O(6), NH(4)B(C(6)H(5))(4), and colemanite (CaB(3)O(4)(OH)(3).H(2)O). The (11)B quadrupole moment, Q = 0.0409 +/- 0.0002 barn, derived from the linear correlation, is in excellent agreement with the accepted value for Q((11)B). This demonstrates that DFT (WIEN2k) calculations can provide precise (11)B quadrupole coupling parameters on an absolute scale. On the other hand, DFT calculations based on the reported crystal structures for datolite (CaBSiO(4)(OH)) and danburite (CaB(2)Si(2)O(8)) cannot reproduce the experimental (11)B quadrupole coupling parameters to the same high precision. However, optimization of these structures by minimization of the forces between the atoms (obtained by DFT) results in a significant improvement between the calculated and experimental (11)B quadrupole coupling parameters, which indicates that reliable refinements of the borate structures are obtained by this method. Finally, the DFT calculations also provide important structural information about the sign and orientation of the EFG tensor elements in the crystal frame, a kind of information that cannot be achieved from (11)B NMR experiments on powdered samples.     

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.     

The complete 51V MAS NMR spectrum of surface vanadia nanoparticles on anatase (TiO2): vanadia surface structure of a DeNOx catalyst

The first observations of the complete manifold of spinning sidebands (ssbs) including both the central and satellite transitions in (51)V MAS NMR spectra of surface vanadia nanoparticles on titania in DeNO(x) catalysts are presented. (51)V quadrupole coupling and chemical shift anisotropy parameters for the dominating vanadia structure are determined from (51)V MAS NMR spectra recorded at 9.4 and 14.1 T. Based on correlations previously established between (51)V NMR parameters and crystal structure data for inorganic vanadates, the NMR data are consistent with vanadium in a distorted octahedral oxygen coordination environment for the so-called strongly bonded vanadia species on the surface. The investigation includes two vanadia-titania model catalysts and six industrial-type DeNO(x) catalysts.