Cardinal hermite interpolation with box splines II

Summary In the present work we extent the results in [RS] on CHIP, i.e. Cardinal Hermite Interpolation by the span of translates of directional derivatives of a box spline. These directional derivatives are that ones which define the type of the Hermite Interpolation. We admit here several (linearly independent) directions with multiplicities instead of one direction as in [RS]. Under the same assumptions on the smoothness of the box spline and its defining matrixT we can prove as in [RS]: CHIP has a system of fundamental solutions which are inL L ² together with its directional derivatives mentioned above. Moreover, for data sequences inl ^p ( ^d ), 1p2, there is a spline function inL ^p, 1/p+1/p=1, which solves CHIP.Research supported in part by NSERC Canada under Grant # A7687. This research was completed while this author was supported by a grant from the Deutscher Akademischer Austauschdienst     

DDFSGEN

This paper presents a functional compiler for the automatic design of Direct Digital Frequency Synthesizer (DDFS) integrated circuits (ICs) using a ROM based table look-up architecture. The compiler allows the user to specify high-level specifications such as the acceptable spurious response and it generates the IC architecture, floorplan, and layout. To construct the layout for different specifications, a library of parameterized macrocells has been developed in 1.2 m CMOS technology.A test chip with a quadrature DDFS module has been generated, using the compiler, and fabricated. The chip has two input signals: one is for frequency control while the other is for phase initialization. Input and output word lengths are 16 bits and 6 bits respectively. The chip complexity is approximately 12,000 transistors (DDFS core) and the die size is 4.8×2.9mm ². A maximum sample rate of 80 MHz has been attained implying a maximum sine (cosine) output frequency of 40 MHz and a frequency resolution of 1.22 kHz. The maximum spurious level measured is –46 dB.     

Biosynthesis of desosamine: construction of a new macrolide carrying a genetically designed sugar moiety

[formula: see text] The appended sugars in macrolide antibiotics are indispensable to the biological activities of these important drugs. In an effort to generate a set of novel macrolide derivatives, we have created a new analogue of methymycin and neomethymycin, antibiotics produced by Streptomyces venezuelae. This analogue 15 carrying a different sugar, D-quinovose, instead of D-desosamine, was constructed by taking advantage of targeted gene deletion combined with a specific pathway-independent C-3 reduction capability of the wild type S. venezuelae.     

The exterior Dirichlet problem for quasi-linear elliptic equations with small boundary data

It is shown that if the order of non-uniformity of a quasi-linear elliptic equation is h,10,2(h–1)/h norm. For 0h1,existence of a bounded solution is guaranteed without any smallness assumption on the given boundary data.More precise information is given for the special case of the minimal surface equation.     

Single-photon vacuum-ultraviolet laser-pulsed-field ionization-photoelectron studies of trans- and cis-1-bromopropenes

The vacuum-ultraviolet (VUV) pulsed-field ionization-photoelectron (VUV-PFI-PE) spectra of trans-1-bromopropene (trans-CH(3)CH[Double Bond]CHBr) and cis-1-bromopropene (cis-CH(3)CH[Double Bond]CHBr) have been measured in the energy region of 74 720-76 840 cm(-1). The simulation of fine structures observed in the origin VUV-PFI-PE vibrational bands of these molecules has provided the ionization energies (IEs) of trans-1-bromopropene and cis-1-bromopropene to be 74 779.3+/-2.0 cm(-1) (9.2715+/-0.0002 eV) and 75 140.2+/-2.0 cm(-1) (9.3162+/-0.0002 eV), respectively. The vibrational bands resolved in these VUV-PFI-PE spectra at energies 0-1700 cm(-1) above the IEs of trans-1-bromopropene and cis-1-bromopropene have been assigned based on theoretical vibrational frequencies and calculated Franck-Condon factors for the ionization transitions.     

Excess partial molar enthalpies,entropies, Gibbs energies,and volumes in aqueous dimethylsulfoxide

The excess partial molar enthalpies, the vapor pressures, and the densities of dimethylsulfoxide (DMSO)–H₂O mixtures were measured and the excess partial molar Gibbs energies and the partial molar volumes were calculated for DMSO and for H₂O. The values of the excess partial molar Gibbs energies for both DMSO and H₂O are negative over the entire composition range. The results for the water-rich region indicated that the presence of DMSO enhances the hydrogen bond network of H₂O. Unlike monohydric alcohols, however, the solute-solute interaction is repulsive in terms of the Gibbs energy. This was a result of the fact that the repulsion among solutes in terms of enthalpy surpassed the attraction in terms of entropy. The data in the DMSO-rich region suggest that DMSO molecules form clusters which protect H₂O molecules from exposure to the nonpolar alkyl groups of DMSO.