Note on B-splines, wavelet scaling functions, and Gabor frames

Let g be a continuous, compactly supported function on such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g,a,b), with window g and time-shift and frequency-shift parameters a,b>0 has no lower frame bound larger than 0 if b=2,3,... and a>0. In particular, (g,a,b) is not a Gabor frame if g is a continuous, compactly supported wavelet scaling function and if b=2,3,... and a>0. We give an example for our result for the case that g=B/sub 1/, the triangle function supported by [-1,1], by showing pictures of the canonical dual corresponding to (g,a,b) where ab=1/4 and b crosses the lines N=2,3,.     

Understanding silica-supported metal catalysts: Pd/silica as a case study

Supported metal catalysts, particularly noble metals supported on SiO₂, have attracted considerable attention due to the importance of the silica–metal interface in heterogeneous catalysis and in electronic device fabrication. Several important issues, e.g., the stability of the metal–oxide interface at working temperatures and pressures, are not well-understood. In this review, the present status of our understanding of the metal–silica interface is reviewed. Recent results of model studies in our laboratories on Pd/SiO₂/Mo(1 1 2) using LEED, AES and STM are reported. In this work, epitaxial, ultrathin, well-ordered SiO₂ films were grown on a Mo(1 1 2) substrate to circumvent complications that frequently arise from the silica–silicon interface present in silica thin films grown on silicon.     

Structure and electrical characteristics of Ce4+-doped Ba2In2O5

The In-site of Ba₂In₂O₅ with Brownmillerite structure was partially substituted for Ce⁴⁺ ions in order to examine the doping effect on the order-disorder transition. Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.1, 0.2, 0.3, 0.5, 1.0, and 1.5) were prepared by solid state reaction. X-Ray diffraction analyses of these powder samples demonstrated that Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.1 and 0.2) possesses Brownmillerite structure. With increasing content of Ce⁴⁺ ion the crystal system of Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.3, 0.5, and 1.0) changed to cubic perovskite structure above the order-disorder transition temperature of Ba₂In₂O₅. Arrhenius plots of the electrical conductivities of Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.2, 0.3, and 1.0) exhibited no discontinuity. These compounds had high transference numbers of oxide ion above 973 k.     

Methods of Verifying Continuous Automatic Belt Weighers: State and Prospects

The basic methods of verifying continuous automatic belt weighers are described. A comparative analysis of these methods on the basis of experimental studies is made and ways of implementing the results in industry are recommended.     

The anisotropic effect of a weak magnetic field on the photoconductivity of C<Subscript>60</Subscript> single crystals

The effect of crystal orientation on the photogeneration of free charge carriers was studied for C₆₀ single crystals in a weak magnetic field. The photoconductivity sharply depends on the orientation of magnetic field with respect to the crystallographic directions, showing a 5–8% increase for seven axes of the C₆₀ crystal.     

State of polarization changes: Classification and measurement

We propose a standardization procedure that provides a convenient, quantitative and reproducible laboratory-based method for measuring the state of polarization (SOP) fluctuations produced by polarization varying devices. This method is based on the SOP distributions generated by commercial polarization scramblers. We show that these devices generate distributions of the maximum change of the SOP (in a given sample time) that follow Rayleigh statistics, which scale linearly with scrambling frequency and the sample time. We use this procedure to measure the SOP fluctuations in a short length of coiled fiber subject to mechanical perturbations.     

Oligo(ethylene oxide) side‐chain steric screening effects on conductimetric properties of grafted poly(4‐vinylpyridinium) salts in aqueous solutions

A set of poly[N‐oligo(ethylene oxide)yl 4‐vinylpyridinium tosylate] (P4VOEOOTs) has been prepared by spontaneous polymerization of 4‐vinylpyridine. This method gives a grafted polyelectrolyte having a positive charge on every backbone pyridinic moiety. The P4VP15Ts, P4VP164Ts, P4VP350Ts and P4VP750Ts aqueous solution conductivities were determined in the concentration range from 6 × 10^?4 to 10^?2 M at 25 °C. The variation of the conductivity versus concentration of the investigated system exhibits typical polyelectrolyte behaviour. The polyelectrolyte mobility was found to be dependent on the oligo(ethylene oxide) (OEO) side‐chain length. Manning's rod‐like model fails to describe these results. A simple steric effect is proposed to explain the influence of the OEO length. Copyright © 2003 Society of Chemical Industry     

Effects of surface charge, micro-bubble size and particle size on removal efficiency of electro-flotation.

Flotation is a water treatment alternative to sedimentation, and uses small bubbles to remove low-density particles from potable water and wastewater. The effect of zeta potential, bubble size and particle size on removal efficiency of the electro-flotation process was investigated because previous model-simulations indicated that these attributes are critical for high collision efficiency between micro-bubbles and particles. Solutions containing Al3+ as the metal ion were subjected to various conditions. The zeta potentials of bubbles and particles were similar under identical conditions, and their charges were influenced by metal ion concentration and pH. Maximum removal efficiency was 98 and 12% in the presence and absence of flocculation, respectively. Removal efficiency was higher when particle size was similar to bubble size. These results agree with modelling simulations and indicate that collision efficiency is greater when the zeta potential of one is negative and that of the other is positive and when their sizes are similar.     

Effect of film thickness on hydrogen content in a-Si : H

The hydrogen content, its depth distribution, and its bonding configuration have been studied in hydrogenated amorphous silicon prepared by plasma-enhanced chemical vapor deposition with hydrogen-diluted silane. Nuclear reaction analysis and infrared spectroscopy were used to determine the total amount of hydrogen and its bonded component, respectively. It has been established that the total concentration of hydrogen does not depend on the film thickness, and has a uniform depth profile. The concentration of bonded hydrogen changes with the film thickness within the measurement accuracy. The data obtained suggest the presence of molecular (non-bonded) hydrogen, uniformly distributed in concentration across the film thickness.     

Unified Systolic-Like Architecture for DCT and DST Using Distributed Arithmetic

A common computing-core representation of the discrete cosine transform and discrete sine transform is derived and a reduced-complexity algorithm is developed for computation of the proposed computing-core. A parallel architecture based on the principle of distributed arithmetic is designed further for the computation of these transforms using the common-core algorithm. The proposed scheme not only leads to a systolic-like regular and modular hardware for computing these transforms, but also offers significant improvement in area-time efficiency over the existing structures. The structure proposed here is devoid of complicated input/output mapping and does not involve any complex control. Unlike the convolution-based structures, it does not restrict the transform length to be a prime or multiple of prime and can be utilized as a reusable core for cost-effective, memory-efficient, high-throughput implementation of either of these transforms