Arithmetically Cohen-Macaulay bundles on complete intersection varieties of sufficiently high multidegree

Recently it has been proved that any arithmetically Cohen-Macaulay (ACM) bundle of rank two on a general, smooth hypersurface of degree at least three and dimension at least four is a sum of line bundles. When the dimension of the hypersurface is three, a similar result is true provided the degree of the hypersurface is at least six. We extend these results to complete intersection subvarieties by proving that any ACM bundle of rank two on a general, smooth complete intersection subvariety of sufficiently high multi-degree and dimension at least four splits. We also obtain partial results in the case of threefolds.

A probabilistic approach to the problem of electron localization in disordered systems and sharpness of the mobility edge

By applying the theory of the asymptotic distribution of extremes and a certain stability criterion to the question of the domain of convergence in the probability sense, of the renormalized perturbation expansion (RPE) for the site self-energy in a cellularly disordered system, an expression has been obtained in closed form for the probability of nonconvergence of the RPE on the real-energy axis. Hence, the intrinsic mobility mu (E) as a function of the carrier energy E is deduced to be given by mu (E)= mu 0exp(-exp( mod E mod -Ec) Delta ), where Ec is a nominal 'mobility edge' and Delta is the width of the random site-energy distribution. Thus mobility falls off sharply but continuously for mod E mod >Ec, in contradistinction with the notion of an abrupt 'mobility edge' proposed by Cohen et al. and Mott. Also, the calculated electrical conductivity shows a temperature dependence in qualitative agreement with experiments on disordered semiconductors.

Stereospecific photodimerization of coumarins in crystalline inclusion complexes. Molecular and crystal structure of 1:2 complex of (S,S)-(-)-1,6-bis(o-chlorophenyl)-1,6-diphenyl-hexa-2,4-diyne-1,6-diol and coumarin

Proximity of molecules is a crucial factor in many solid- state photochemical processes.'S2 The biomolecular photodimerization reactions in the solid state depend on the relative geometry of reactant molecules in the crystal lattice with center-to-center distance of nearest neighbor double bonds of the order of ca. 4 A. This fact emanates from the incisive studies of Schmidt and Cohen.2 One of the two approaches to achieve this distance requirement is the so-called "Crystal-Engineering" of structures, which essentially involves the introduction of certain functional groups that display in-plane interstacking interactions (Cl...Cl, C-He-0, etc.) in the crystal The chloro group is by far the most successful in promoting the /3- packing m ~ d e ,th~o,u~gh recent studies have shown its limitations? Another approach involves the use of constrained media in which the reactants could hopefully be aligned.

From the {Cu(μ2-S)N}4 butterfly architecture to the {Cu(μ3-S)N}12 double wheel

Copper(I) complexes with {Cu(μ2-S)N}4 and {Cu(μ3-S)N}12 core portions of butterfly-shaped or double wheel architectures have been isolated in the reaction of Cu(I) with the Schiff base ligand C6H4(CHNC6H4S)2, aiso-abtâ, under different conditions. View the MathML source containing the tetranuclear electroneutral complex View the MathML source is formed by the reaction of CuI in acetonitrilic solution and recrystallization from DMF, whereas View the MathML source containing dodecanuclear View the MathML source wheels is accessible starting from CuBF4. Complexes 2 and 4 represent the first examples of cyclic complexes with the same overall stoichiometry but different ring sizes. The ligand induces two different coordination environments around copper(I) by switching between μ2- and μ3-sulfur bridging modes.

Experimental studies and phase field modeling of microstructure evolution during solidification with electromagnetic stirring

Thixocasting requires manufacturing of billets with non-dendritic microstructure. Aluminum alloy A356 billets were produced by rheocasting in a mould placed inside a linear electromagnetic stirrer. Subsequent heat treatment was used to produce a transition from rosette to globular microstructure. The current and the duration of stirring were explored as control parameters. Simultaneous induction heating of the billet during stirring was quantified using experimentally determined thermal profiles. The effect of processing parameters on the dendrite fragmentation was discussed. Corresponding computational modeling of the process was performed using phase-field modeling of alloy solidification in order to gain insight into the process of morphological changes of a solid during this process. A non-isothermal alloy solidification model was used for simulations. The morphological evolution under such imposed thermal cycles was simulated and compared with experimentally determined one. Suitable scaling using the thermosolutal diffusion distances was used to overcome computational difficulties in quantitative comparison at system scale. The results were interpreted in the light of existing theories of microstructure refinement and globularisation.

Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Both Surface Proteins (VP4 and VP7) of an Asymptomatic Neonatal Rotavirus Strain (1321) Have High Levels of Sequence Identity with the Homologous Proteins of a Serotype 10 Bovine Rotavirus

The nucleotide sequence of genes 4 and 9, encoding the outer capsid proteins VP4 and VP7 of a serotype 10 tissue culture-adapted strain, 1321, representative of asymptomatic neonatal rotaviruses isolated from neonates in Bangalore, India, were determined. Comparison of nucleotide and deduced amino acid sequences of 1321 VP4 and VP7 with previously published sequences of various serotypes revealed that both genes were highly homologous to the respective genes of serotype 10 bovine rotavirus, B223. The VP4 of 1321 represents a new human P serotype and the 1321 and related strains represent the first description of neonatal rotaviruses that appear to derive both surface proteins from an animal rotavirus.

Size dependence of the bulk modulus of semiconductor nanocrystals from first-principles calculations

The variation in the bulk modulus of semiconductor nanoparticles has been studied within first-principles electronic-structure calculations using the local density approximation (LDA) for the exchange correlation. Quantum Monte Carlo calculations carried out for a silicon nanocrystal Si87H76 provided reasonable agreement with the LDA results. An enhancement was observed in the bulk modulus as the size of the nanoparticle was decreased, with modest enhancements being predicted for the largest nanoparticles studied here, a size just accessible in experiments. To access larger sizes, we fit our calculated bulk moduli to the same empirical law for all materials, the asymptote of which is the bulk value of the modulus. This was found to be within 2-10% of the independently calculated value. The origin of the enhancement has been discussed in terms of Cohen's empirical law M.L. Cohen, Phys. Rev. B 32, 7988 (1985)] as well as other possible scenarios.

CM defect and Hilbert functions of monomial curves

In this article we consider a semigroup ring R = KGamma] of a numerical semigroup Gamma and study the Cohen- Macaulayness of the associated graded ring G(Gamma) := gr(m), (R) := circle plus(n is an element of N) m(n)/m(n+1) and the behaviour of the Hilbert function H-R of R. We define a certain (finite) subset B(Gamma) subset of F and prove that G(Gamma) is Cohen-Macaulay if and only if B(Gamma) = empty set. Therefore the subset B(Gamma) is called the Cohen-Macaulay defect of G(Gamma). Further, we prove that if the degree sequence of elements of the standard basis of is non-decreasing, then B(F) = empty set and hence G(Gamma) is Cohen-Macaulay. We consider a class of numerical semigroups Gamma = Sigma(3)(i=0) Nm(i) generated by 4 elements m(0), m(1), m(2), m(3) such that m(1) + m(2) = mo m3-so called ``balanced semigroups''. We study the structure of the Cohen-Macaulay defect B(Gamma) of Gamma and particularly we give an estimate on the cardinality |B(Gamma, r)| for every r is an element of N. We use these estimates to prove that the Hilbert function of R is non-decreasing. Further, we prove that every balanced ``unitary'' semigroup Gamma is ``2-good'' and is not ``1-good'', in particular, in this case, c(r) is not Cohen-Macaulay. We consider a certain special subclass of balanced semigroups Gamma. For this subclass we try to determine the Cohen-Macaulay defect B(Gamma) using the explicit description of the standard basis of Gamma; in particular, we prove that these balanced semigroups are 2-good and determine when exactly G(Gamma) is Cohen-Macaulay. (C) 2011 Published by Elsevier B.V.

Line clipping revisited: Two efficient algorithms based on simple geometric observations

Two new line clipping algorithms, the opposite-corner algorithm and the perpendicular-distance algorithm, that are based on simple geometric observations are presented. These algorithms do not require computation of outcodes nor do they depend on the parametric representations of the lines. It is shown that the opposite-corner algorithm perform consistently better than an algorithm due to Nicholl, Lee, and Nicholl which is claimed to be better than the classic algorithm due to Cohen-Sutherland and the more recent Liang-Barsky algorithm. The pseudo-code of the opposite-corner algorithm is provided in the Appendix.

Molecular structure and reactions of 1,1 '-bi(acenaphthen-1-ylidene)-2,2 '-dione

The molecular structure of 1,1'-bi(acenaphthen-1-ylidene)-2,2'-dione 1, a potential building-block for the synthesis of fullerene fragments, has been investigated by X-ray crystallography and semi-empirical (AM1 and PM3) calculations. There is a good agreement between the calculated and crystal structure which is essentially planar and has E-configuration. In the solid state, molecules of 1 pack in an interesting manner as corrugated sheets sustained by a network of C-H ... O hydrogen bonds and resulting in the formation of tetrameric loops. While steric factors limit the reactivity of the carbonyl groups in 1, the ene double bond of the ene-dione moiety present in it exhibits propensity toward [4 + 2]-cycloadditions to furnish novel and highly compressed polycycles 8-10.

Acyclic Edge-Coloring of Planar Graphs

A proper edge-coloring with the property that every cycle contains edges of at least three distinct colors is called an acyclic edge-coloring. The acyclic chromatic index of a graph G, denoted. chi'(alpha)(G), is the minimum k such that G admits an acyclic edge-coloring with k colors. We conjecture that if G is planar and Delta(G) is large enough, then chi'(alpha) (G) = Delta (G). We settle this conjecture for planar graphs with girth at least 5. We also show that chi'(alpha) (G) <= Delta (G) + 12 for all planar G, which improves a previous result by Fiedorowicz, Haluszczak, and Narayan Inform. Process. Lett., 108 (2008), pp. 412-417].

The Untouchable Soldier: Caste, Politics, and the Indian Army

Military establishments are omnipresent if not everywhere omnipotent. While these costly bureaucracies are the bane of finance ministers around the world, they do provide an important opportunity for comparative analysis. This paper examines a military system—the Indian one—through time, and attempts to demonstrate the changing relationship of that system to Indian politics and society in general, and to the low-caste communities of India in particular. We select the low-caste untouchables because they represent an extreme challenge to the integrative capacity of both political and social systems, and because they have recently been the subject of intensive political and academic concern.Stephen P. Cohen is Assistant Professor of Political Science in Asian Studies at the University of Illinois. Research for this paper was supported by a fellowship from the American Institute of Indian Studies in 1964–65.

Shear banding in a yield stress bearing Langmuir monolayer

We examine the shear-thinning behaviour of a two dimensional yield stress bearing monolayer of sorbitan tristearate at air/water interface. The flow curve consists of a linear region at low shear stresses/shear rates, followed by a stress plateau at higher values. The velocity profile obtained from particle imaging velocimetry indicates that shear banding occurs, showing coexistence of the fluidized region near the rotor and solid region with vanishing shear-rate away from the rotor. In the fluidized region, the velocity profile, which is linear at low shear rates, becomes exponential at the onset of shear-thinning, followed by a time varying velocity profile in the plateau region. At low values of constant applied shear rates, the viscosity of the film increases with time, thus showing aging behaviour like in soft glassy three-dimensional (3D) systems. Further, at the low values of the applied stress in the yield stress regime, the shear-rate fluctuations in time show both positive and negative values, similar to that observed in sheared 3D jammed systems. By carrying out a statistical analysis of these shear-rate fluctuations, we estimate the effective temperature of the soft glassy monolayer using the Galavatti-Cohen steady state fluctuation relation.

Reduced Rate Ultra Low Delay Audio Coder using Multistage Vector Quantization

Communication applications are usually delay restricted, especially for the instance of musicians playing over the Internet. This requires a one-way delay of maximum 25 msec and also a high audio quality is desired at feasible bit rates. The ultra low delay (ULD) audio coding structure is well suited to this application and we investigate further the application of multistage vector quantization (MSVQ) to reach a bit rate range below 64 Kb/s, in a scalable manner. Results at 32 Kb/s and 64 Kb/s show that the trained codebook MSVQ performs best, better than KLT normalization followed by a simulated Gaussian MSVQ or simulated Gaussian MSVQ alone. The results also show that there is only a weak dependence on the training data, and that we indeed converge to the perceptual quality of our previous ULD coder at 64 Kb/s.