A class of infinite sums and integrals

In this paper closed-form sums are given for various slowly-convergent infinite series which arise essentially from the differentiation of Dirichlet -series. Some associated integrations are also considered. A small number of the results appear in standard tables, but most seem to be new.

     

Analysis of current-voltage characteristics of inhomogeneous Schottky diodes at low temperatures

Two approaches of Gaussian distribution of barrier heights in inhomogeneous Schottky diodes have been analyzed by comparing the results for consistency between the two. For this the current-voltage characteristics of inhomogeneous Schottky diodes have been generated by using analytically solved thermionic-emission diffusion equation incorporating Gaussian distribution of barrier heights and by direct numerical integration over a barrier height range. The differences in the results obtained in two approaches are discussed and it is shown that the two approaches yield current-voltage characteristics with slightly different features. The discrepancies in the results obtained in two approaches are attributed to the same series resistance assumed for all elementary barriers of the distribution. It is shown that assigning same series resistance to all barrier of the distribution in numerical integration approach causes current saturation at low bias and inhibits intersection of current-voltage curves from being observable which otherwise occurs in the curves obtained using analytical equation. The paper deals with these aspects in details.     

Effect of POSS on crystalline transitions and physical properties of polyamide 12

Polyamide 12/Trisilanolphenyl‐POSS (PA 12/POSS) composites were prepared via melt‐compounding. The effect of polyhedral oligomeric silsesquioxane (POSS) on crystalline structure and crystalline transition of PA 12 was investigated by wide‐angle X‐ray diffraction (WAXD) and real time fourier transform infrared spectroscopy (FTIR). WAXD results indicated that PA 12 crystallized into γ‐form as slowly cooling from melt and the presence of POSS did not influence the crystalline structure of PA 12. Both PA 12 and PA 12/POSS composites underwent Brill transitions when they were heated from room temperature to melt point. Real time FTIR patterns showed that an absorption band at 697 cm^?1 ascribed to Amide V (α) mode was emerged along with the disappearance of Amide VI (γ) band at 628 cm^?1 with the increase of the temperature for PA 12 and PA 12/POSS composites, which suggested that the γ‐form crystalline has transformed into α form. The Brill bands were identified and the transformed mechanism was discussed based on the real FTIR results. The addition of POSS enhanced the tensile strength and thermal stability of PA 12. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 121–129, 2009     

An Efficient N‐Arylation of Heterocycles with Aryl‐, Heteroaryl‐, and Vinylboronic Acids Catalyzed by Copper Fluorapatite

N‐Arylation of N‐containing heterocycles, such as pyrazoles, imidazoles, and benzimidazoles with aryl‐, heteroaryl‐, and vinylboronic acids was efficiently carried out by copper fluorapatite (CuFAP) catalyst in MeOH at room temperature under base‐free conditions. The N‐arylated heterocycles were isolated in good‐to‐excellent yields.     

The first total synthesis of the (±)-17-methyl-trans-4,5-methyleneoctadecanoic acid and related analogs with antileishmanial activity

The first total synthesis of the marine cyclopropane fatty acid (±)-17-methyl-trans-4,5-methyleneoctadecanoic acid was accomplished in eight steps and in 9.1% overall yield starting from 1-bromo-12-methyltridecane. The cis analog (±)-17-methyl-cis-4,5-methyleneoctadecanoic acid was also synthesized but in seven steps and in 16.4% overall yield. With the two isomeric cyclopropane fatty acids at hand it was possible to unequivocally corroborate the trans relative configuration of the naturally occurring fatty acid by gas chromatographic co-elution of the corresponding methyl esters. The cis isomer was cytotoxic to Leishmania donovani promastigotes with an IC₅₀ of 300.2 ± 4.2 μM.     

Synthesis, structural and electrical properties of La and Nb modified Bi4Ti3O12 ferroelectric ceramics

Polycrystalline ceramic samples of Bi_4−xLa_xTi₃O₁₂ (x=0.0, 0.5 and 1) and Bi_3.5La_0.5Ti_3−yNb_yO₁₂ (y=0.02 and 0.04) have been synthesized by standard high temperature solid state reaction method using high purity oxides and carbonates. The effect of lanthanum doping on Bi-site and Nb doping on Ti-site on the structural and electrical properties of Bi₄Ti₃O₁₂ powders was investigated by X-ray diffraction, scanning electron microscopy, dc conductivity and dielectric studies. A better agreement between the observed and calculated X-ray diffraction pattern was obtained by performing the Rietveld refinement with a structural model using the non-centrosymmetric space group Fmmm in all the cases. A better agreement between observed and calculated d-values also shows that the lattice parameters calculated using the Rietveld refinement analysis are better. The increase in lanthanum and niobium contents does not lead to any secondary phases. It is found that La³⁺ doping reduces the material grain size and changes its morphology from the plate-like form to a spherical staking like form. The substitution of Nb for Ti ions affected the degree of disorder and modified the dielectric properties leading to more resistive ceramic compounds. The shape and size of the grains are strongly influenced by the addition of niobium to the system. The activation energies of all the compounds were calculated by measuring their dc electrical conductivities. The frequency and temperature dependent dielectric behavior of all the compounds have also been studied and the results are discussed in detail. The substitution of La and Nb on the Bi and Ti sites decreased the T_c and improved the dielectric and ferroelectric behavior.     

Effect of WO3 on EPR, structure and electrical conductivity of vanadyl doped WO3·M2O·B2O3 (M=Li, Na) glasses

Glasses with composition xWO₃·(30−x)M₂O·70B₂O₃ (M=Li, Na; 0≤x≤15) doped with 2 mol% V₂O₅ have been prepared using the melt-quench technique. The electron paramagnetic resonance spectra have been recorded in X-band (ν≈9.14 GHz) at room temperature (RT). The spin Hamiltonian parameters, dipolar hyperfine coupling parameter and Fermi contact interaction parameter have been calculated. It is observed that the resultant resonance spectra contain hyperfine structures (hfs) only due to V⁴⁺ ions, which exist as VO²⁺ ions in octahedral coordination with a tetragonal compression in the present glass system. The tetragonality increases with WO₃:M₂O ratio and also there is an expansion of 3d_xy orbit of unpaired electron in the vanadium ion. The study of IR transmission spectra over a range 400-4000 cm⁻¹ depicts the presence of WO₆ group. The DC conductivity (σ) has been measured in the temperature range 423-623 K and is found to be predominantly ionic.     

High-temperature oxidation studies of cold-sprayed Ni-20Cr and Ni-50Cr coatings on SAE 213-T22 boiler steel

The high-temperature oxidation behavior of cold-sprayed Ni-20Cr and Ni-50Cr coatings on SAE 213-T22 boiler steel has been investigated at 900 °C in air under cyclic heating and cooling conditions for 50 cycles. The kinetics of oxidation of coated and bare boiler steel has been established with the help of weight change measurements. It was observed that all the coated and bare steels obeyed parabolic rate law of oxidation. X-ray diffraction, FE-SEM/EDAX and X-ray mapping techniques were used to analyse the oxidation products of the coated and uncoated boiler steel. The uncoated steel suffered corrosion in the form of intense spalling and peeling of its oxide scale, which was perhaps due to the formation of unprotective Fe₂O₃ oxide scale. Both the coatings showed better resistance to the air oxidation as compared to the uncoated steel. The Ni-50Cr coating was found to be more protective than the Ni-20Cr-coated steel. The formation of oxides and spinels of nickel and chromium may be contributing to the development of air oxidation resistance in the coatings.     

On the power of white pebbles

We construct a family (G _p |p) of directed acyclic graphs such that any black pebble strategy forG _p requiresp ² pebbles whereas 3p+1 pebbles are sufficient when white pebbles are allowed.Supported by the National Science Foundation under contract no. DCR-8407256 and by the office of Naval Research under contract no. N0014-80-0517.