Improving the convergence rate of the inverse iteration method

Solution of generalized eigenproblem, K phi = lambda M phi, by the classical inverse iteration method exhibits slow convergence for some eigenproblems. In this paper, a modified inverse iteration algorithm is presented for improving the convergence rate. At every iteration, an optimal linear combination of the latest and the preceding iteration vectors is used as the input vector for the next iteration. The effectiveness of the proposed algorithm is demonstrated for three typical eigenproblems, i.e. eigenproblems with distinct, close and repeated eigenvalues. The algorithm yields 29, 96 and 23% savings in computational time, respectively, for these problems. The algorithm is simple and easy to implement, and this renders the algorithm even more attractive.

On Walkup's class K (d) and a minimal triangulation of (S-3 (sic) S-1)(#3)

For d >= 2, Walkup's class K (d) consists of the d-dimensional simplicial complexes all whose vertex-links are stacked (d - 1)-spheres. Kalai showed that for d >= 4, all connected members of K (d) are obtained from stacked d-spheres by finitely many elementary handle additions. According to a result of Walkup, the face vector of any triangulated 4-manifold X with Euler characteristic chi satisfies f(1) >= 5f(0) - 15/2 chi, with equality only for X is an element of K(4). Kuhnel observed that this implies f(0)(f(0) - 11) >= -15 chi, with equality only for 2-neighborly members of K(4). Kuhnel also asked if there is a triangulated 4-manifold with f(0) = 15, chi = -4 (attaining equality in his lower bound). In this paper, guided by Kalai's theorem, we show that indeed there is such a triangulation. It triangulates the connected sum of three copies of the twisted sphere product S-3 (sic) S-1. Because of Kuhnel's inequality, the given triangulation of this manifold is a vertex-minimal triangulation. By a recent result of Effenberger, the triangulation constructed here is tight. Apart from the neighborly 2-manifolds and the infinite family of (2d + 3)-vertex sphere products Sd-1 X S-1 (twisted for d odd), only fourteen tight triangulated manifolds were known so far. The present construction yields a new member of this sporadic family. We also present a self-contained proof of Kalai's result. (C) 2011 Elsevier B.V. All rights reserved.

Liquid alloy semiconductors revisited - Discussion

In 1990 Enderby and Barnes reviewed the electrical properties of liquid alloys which show features associated with semiconducting behaviour. They proposed an empirical classification scheme based on the notion that some liquid semiconductors are characterized by a finite gap in σ (E), the energy-dependent conductivity (narrow definition), whereas in others σ (E) is continuous (broad definition). Interesting behaviour occurs for systems at the narrow/broad boundary and further analysis of these liquid alloys will form the subject matter of this paper. Particular attention will be focused on liquid silver chalcogenides as these offer a severe test of current theories.

Metal-billed and hollow carbon nanotubes obtained by the decomposition of metal-containing free precursor molecules

Vapor-phase pyrolysis of Fe(CO)(5) in the presence of another carbon source such as CO or Ca He yields iron-filled or hollow nanotubes depending on the relative concentration of the carbon source. Essentially single-walled nanotubes are obtained when the C6H6/Fe(CO)(5) ratio is high. Pyrolysis of metallocenes yields metal-filled nanotubes and hollow nanotubes are obtained when metallocenes are pyrolyzed along with benzene. Metal-decorated nanotubes are also obtained by this method.

Microwave assisted preparation and sintering of Al2O3, ZrO2 and their composites from metalorganics

Controlled pyrolysis of Al(OBus)(3), Zr(OPrn)(4) and their mixtures in ethyl acetate induced using microwaves of 2.45 GHz frequency has been carried out. Microwave irradiation yields second-stage precursors for the preparation of respective oxides and their composites. It is observed that the microwave irradiation has a directive influence on the morphology of the ultimate oxide products. Al2O3, ZrO2 and the two composites 90% Al2O3-10% ZrO2 and 90% ZrO2-10% Al2O3 are also found to be sintered to very high densities within 35 min of microwave irradiation by the use of beta-SiC as a secondary susceptor.

Nitrogen-containing carbon nanotubes

Carbon nanotubes containing small amounts of nitrogen are produced by the pyrolysis of aza-aromatics such as pyridine, methylpyrimidine and triazine over cobalt nanoparticles in an Ar atmosphere; good yields of such nanotubes are obtained by carrying out the pyrolysis of a mixture of pyridine and Fe(CO)(5) in flowing Ar + H-2.

Potential herblayer production and grazing effects in anthropogenic savanna-grasslands in the moist tropical forests of the Western Ghats of India

The moist tropical forests of the Western Ghats of India are pockmarked with savanna-grasslands created and managed by local agricultural communities. A sample of such savanna-grasslands with differing growing conditions was studied in terms of peak above-ground biomass, monthly growth, and cumulative production under different clipping treatments. The herblayer was found to be dominated by perennial C4 grasses, with Eulalia trispicata, Arundinella metzii and Themeda triandra being common to all sites. Peak biomass ranged between 3.3-5.9 t/ha at sites most favourable for grass production. Across these sites, peak biomass was found to be inversely related to the number of rainy days during the growing season, suggesting that growth may be light-limited. This hypothesis is supported by the observation that growth is most rapid immediately after the easing of the monsoon. Single clips early in the growing season had no negative or a slightly positive effect on production, but mid-season single clips or continuous frequent clipping reduced production by as much as 40%. The results suggest that, while indiscriminate grazing may certainly be deleterious, it is possible to obtain sustained high yields from forest lands managed for grass production without totally excluding grazing.

Selective deprotection of propargyl ethers using tetrathiomolybdate

Benzyltriethylammonium tetrathiomolybdate, [PhCH2NEt3](2)MoS4, 1 deprotects propargyl ethers of alcohols and phenols in a selective manner in high yields. Easily reducible groups like nitro, aldehyde, keto and allyl are not affected.

Stability and throughput analysis of unslotted CDMA-ALOHA with finite number of users and code sharing

We consider a system comprising a finite number of nodes, with infinite packet buffers, that use unslotted ALOHA with Code Division Multiple Access (CDMA) to share a channel for transmitting packetised data. We propose a simple model for packet transmission and retransmission at each node, and show that saturation throughput in this model yields a sufficient condition for the stability of the packet buffers; we interpret this as the capacity of the access method. We calculate and compare the capacities of CDMA-ALOHA (with and without code sharing) and TDMA-ALOHA; we also consider carrier sensing and collision detection versions of these protocols. In each case, saturation throughput can be obtained via analysis pf a continuous time Markov chain. Our results show how saturation throughput degrades with code-sharing. Finally, we also present some simulation results for mean packet delay. Our work is motivated by optical CDMA in which "chips" can be optically generated, and hence the achievable chip rate can exceed the achievable TDMA bit rate which is limited by electronics. Code sharing may be useful in the optical CDMA context as it reduces the number of optical correlators at the receivers. Our throughput results help to quantify by how much the CDMA chip rate should exceed the TDMA bit rate so that CDMA-ALOHA yields better capacity than TDMA-ALOHA.

Stereospecific and regioselective catalytic epoxidation of alkenes by a novel ruthenium(II) complex under aerobic conditions

Epoxidation of alkenes by molecular oxygen is effected in high yields by catalysis of RuCl2(biox)(2) using isobutyraldehyde as the co-reductant: the reaction is stereospecific and regioselective.

Sulfur transfer reactions of tetrathiomolybdate in water: Synthesis of alkyl disulfides from alkyl halides

Reaction of a number of alkyl halides with tetrathiomolybdate in water as the solvent affords the corresponding disulfides in good yields.

Synthesis and properties of nanodispersed granular materials

Nanometric granular materials represent a new class of materials with significant promise. We shall discuss in this paper two phase granular materials where one of the phases having nanometric dimension is embedded in a matrix of larger dimension. These materials show many interesting properties which include structural, magnetic and transport properties, The phase transformation of the embedded particles shows distinctive behavior and yields new insight. We shall first highlight the strategy of synthesis of these materials through rapid solidification. This will be followed by three examples where the nanoscale dimension of the embedded particles play a unique role. These are melting and solidification of the nanodispersed embedded particles and the superconducting transition. (C) 1997 Elsevier Science S.A.

Synthesis and reactivity of chiral tellurium azomethines: Pseudopolymorphism of [o-((((1S,2R)-2-hydroxy-2-phenyl-1-methylethyl)amino)methinyl)phenyl] tellurium(IV) bromide

A range of novel chiral tellurium compounds having an azomethine functional group in the position ortho to tellurium has been synthesized by the reaction of the tellurium-containing aldehydes bis(o-formylphenyl) telluride (1) and o-(butyltelluro)benzaldehyde (4) with chiral amines (R)-(+)-(1-pheylethylamine) and (1R,2S)-(-)-norephedrine, respectively. The precursor aldehydes were prepared by using a reported procedure with slight but advantageous modifications. During the preparation of o-(butyltelluro)benzaldehyde, interesting side products, namely bis(o-formylphenyl) ditelluride ethylene acetal 5, bis(o-formylphenyl) tritelluride (6), and bis(o-formylphenyl) ditelluride (7) were isolated in moderate yields. The ditelluride 7 has been characterized by single-crystal X-ray diffraction studies. The liquid Schiff bases 10 and 11 were further characterized by derivatizing with liquid bromine. The title compound was obtained in excellent yield by reacting the Schiff base 11 with elemental bromine. Detailed NMR studies indicated the presence of a rigid environment for the hydroxyl group. Single-crystal X-ray determinations of the crystals obtained from the different batches indicated. the presence of the two pseudopolymorphic forms 13a and 13b, respectively. In the case of 13a there is one molecule of CH3CN as solvent of crystallization, whereas in 13b half a molecule of CH3CN per molecule of the title compound lies along the 2-fold axis. In 13a the hydroxyl hydrogen is hydrogen-bonded to the nitrogen of the solvent molecule, whereas in 13b it is hydrogen-bonded to the bromine of the neighboring molecule.