On a Ratio of Functions of Exponential Random Variables and Some Applications

Consider L independent and identically distributed exponential random variables (r.vs) X-1, X-2 ,..., X-L and positive scalars b(1), b(2) ,..., b(L). In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Sigma(L)(j=1) X-j)(2) / (Sigma(L)(j=1) b(j)X(j)). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii)M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.

A2MoTiO7−x (Atriple bond; length as m-dashrare earth or Y): a new series of oxide pyrochlores prepared by topochemical reduction of A2MoTiO8 scheelites

A series of anion-deficient pyrochlore oxides of the formula A2MoTiO7−x (xless-than-or-equals, slant0.5), where Atriple bond; length as m-dashSm, Gd, Tb, Dy, Ho, Er, Lu and Y, has been prepared by reduction of A2MoTiO8 scheelites. The scheelite-to-pyrochlore conversion is reversible, indicating that the reaction is likely to be topochemical. The oxidation states of molybdenum and titanium are most probably Mo(III) and Ti(IV) for the limiting composition of the pyrochlores A2MoTiO6.5. The new pyrochlores are non-metallic and paramagnetic as expected.

Total synthesis of substituted (±)-6,6-dimethyl-B-norestra-1,3,5(10)-trien-17?-ols and their 9?-isomers

Total syntheses of (±)-1,4-dimethoxy-6,6-dimethyl-B-norestra-1,3,5(10)-trien-17?-ol(11a), (±)-2,3-dimethoxy-6,6-dimethyl-B-norestra-1,3,5(10)-trien-17?-ol (11b), and (±)-3-methoxy-6,6-dimethyl-B-norestra-1,3,5(10)trien-17?-ol (11c), have been carried out starting from 4,7-dimethoxy-3,3-dimethylindan-1-one (1), 5,6-dimethoxy-3,3-dimethylindan-1-one (2), and 4?-methoxy-3-methylbut-2-enophenone (4), respectively. Generally, it is found that the intermediate 6,6-dimethyl-B-norestra-1,3,5(10),8-tetraen-17?-ols (10), on lithium�liquid ammonia reduction, yield a mixture of 8?,9?- and 8?,9?-trienols, (11) and (12) respectively, in the ratio 1 : 1. This is due to the comparable stabilities of these two isomers. However, the reduction carried out in presence of aniline affords a higher percentage of the 8?,9?-trienol (11). The assignment of configurations is made by chemical and 1H n.m.r. analysis. Catalytic hydrogenation of the tetraenols (10) is shown to proceed via initial isomerisation to the corresponding 6,6-dimethyl-B-norestra-1,3,5(10),9(11)-tetraen-17?-ols (26), followed by hydrogenation from the ?-side to give, exclusively, the 8?,9?-trienols (12).

A Convenient Methodology for the Selective Reduction of Carboxylic Acids With Benzyltriethyl-Ammonium Borohydride—Chlorotrimethylsilane

A combination of benzyltriethylammonium borohydride and chlorotrimethylsilane (1:1) in dichloromethane (0-25°C) has been found to be a convenient reagent system for the selective reduction of carboxylic acids to alcohols.

A new approach to the kinetics of size reduction in ball milling

The rate of breakage of feed in ball milling is usually represented in the form of a first-order rate equation. The equation was developed by treating a simple batch test mill as a well mixed reactor. Several case of deviation from the rule have been reported in the literature. This is attributed to the fact that accumulated fines interfere with the feed material and breaking events are masked by these fines. In the present paper, a new rate equation is proposed which takes into account the retarding effect of fines during milling. For this purpose the analogy of diffusion of ions through permeable membranes is adopted, with suitable modifications. The validity of the model is cross checked with the data obtained in batch grinding of ?850/+600 ?m size quartz. The proposed equation enables calculation of the rate of breakage of the feed at any instant of time.

An optimal parallel algorithm for sparse matrix bandwidth reduction on a linear array

A simple and efficient algorithm for the bandwidth reduction of sparse symmetric matrices is proposed. It involves column-row permutations and is well-suited to map onto the linear array topology of the SIMD architectures. The efficiency of the algorithm is compared with the other existing algorithms. The interconnectivity and the memory requirement of the linear array are discussed and the complexity of its layout area is derived. The parallel version of the algorithm mapped onto the linear array is then introduced and is explained with the help of an example. The optimality of the parallel algorithm is proved by deriving the time complexities of the algorithm on a single processor and the linear array.

Effect of thiocarbamate, urea, and uracil herbicides on lipid metabolism in groundnut (Arachis hypogaea) leaves

The effect of thiocarbamates (S-ethyldipropylthiocarbamate and diallate), substituted ureas (monuron and diuron), and uracils (bromacil and terbacil) on lipid metabolism in groundnut (Arachis hypogaea) leaves was investigated under nonphotosynthetic conditions. The uptake of [1-14C]acetate by leaf disks was inhibited by the thiocarbamates and marginally by the substituted ureas, but not by the uracil herbicides. The uptake of [methyl-14C]choline was inhibited to a lesser extent by thiocarbamates, while the other herbicides showed a slight stimulation. The thiocarbamates almost completely inhibited uptake of [32P]orthophosphate at 1.0 mM concentration, while diuron and terbacil showed significant inhibition. [1-14C]Acetate incorporation into lipids was inhibited only by diallate. [methyl-14C]Choline incorporation into the choline phosphoglycerides was inhibited by diallate, diuron, and bromacil. The incorporation of [32P]orthophosphate into phospholipids was substantially inhibited (over 90% at 1.0 mM) by the thiocarbamates, but not by the other herbicides. [35S]Sulfate incorporation into sulfoquinovosyl diglycerides was markedly inhibited only by the thiocarbamates. Fatty acid synthesis by isolated chloroplasts was inhibited 40–85% by thiocarbamates, substituted ureas, and bromacil, but not by terbacil. The inhibitory effect of the urea derivatives was reversible, but that of thiocarbamates was irreversible. sn-Glycerol-3-phosphate acyltransferase(s) of the chloroplast and microsomal fractions were profoundly inhibited by thiocarbamates, but not by the other two groups of herbicides. Phosphatidic acid phosphatase was insensitive to all the herbicides tested.

Combustion synthesis and properties of fine-particle rare-earth-metal zirconates, Ln2Zr2O7

Fine-particle rare-earth-metal zirconates, Ln2Zr2O7, where Ln = La, Ce, Pr, Nd, Sm, Gd and Dy having the pyrochlore structure have been prepared using a novel combustion process. The process employs aqueous solutions of the corresponding rare-earth-metal nitrate, zirconium nitrate and carbohydrazide/urea in the required molar ratio. When the solution is rapidly heated to 350–500 °C it boils, foams and burns autocatalytically to yield voluminous oxides. The formation of single-phase Ln2Zr2O7 has been confirmed by powder X-ray diffraction, infrared and fluorescence spectroscopy. The solid combustion products are fine, having surface areas in the range 6–20 m2 g–1. The cold-pressed Pr2Zr2O7 compact when sintered at 1500 °C, 4 h in air, achieved 99% theoretical density.

Differential reproductive success in Cassia fistula in different habitants-A case of pollinator limitations?

Differences in flower success patterns in two habitat types that differed drastically with respect to rainfall, tree density and species composition were studied at Mudumalai wildlife sanctuary, India. Observations on phenological patterns of two species, Cassia fistula and Gmelina arborea, were made from April 1988 through June 1990. Quantitative data on flower-fruit ratio, insect visitation rates, pollen grain per stigma and the number of fruits per tree were recorded. Data were also collected on the number of pollen deposited on the stigma after different types of bees visited the flower. The data suggested that only carpenter bees (Xylocopa spp) effect pollination in C. fistula. The differences in fruit-flower ratios were attributed to the differences in insect visitation rates to inflorescences between sites. The low pollen number per stigma and the resultant reduction in reproductive success in C. fistula are attributed to the competing species G. arborea receiving more visitations from pollinators in the wetter site. These results suggest that pollinator limitation is another constraint in reproductive success of plants.

Molecular expression for dielectric friction on a rotating dipole: Reduction to the continuum theory

Recently we presented a microscopic expression for dielectric friction on a rotating dipole. This expression has a rather curious structure, involving the contributions of the transverse polarization modes of the solvent and also of the molecular length scale processes. It is shown here that under proper limiting conditions, this expression reduces exactly to the classical continuum model expression of Nee and Zwanzig [J. Chem. Phys. 52, 6353 (1970)]. The derivation requires the use of the asymptotic form of the orientation‐dependent total pair correlation function, the neglect of the contributions of translational modes of the solvent, and also the use of the limit that the size of the solvent molecules goes to zero. Thus, the derivation can be important in understanding the validity of the continuum model and can also help in explaining the results of a recent computer simulation study of dielectric relaxation in a Brownian dipolar lattice.

Nafion®-bound carbon electrodes containing transitionmetal phthalocyanines for oxygen reduction in solid-polymer-electrolyte fuel cells

Catalytic activities of some transition metal-phthalocyanine complexes towards electroreduction of molecular oxygen are examined on Nafion®-bound and bare porous carbon electrodes in 2.5 M H2SO4 electrolyte. It is found that these metal complexes exhibit better catalytic activities towards oxygen reduction with the Nafion®-bound electrodes.