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.

A Survey on Cascaded Multilevel Inverters

Cascaded multilevel inverters synthesize a medium-voltage output based on a series connection of power cells which use standard low-voltage component configurations. This characteristic allows one to achieve high-quality output voltages and input currents and also outstanding availability due to their intrinsic component redundancy. Due to these features, the cascaded multilevel inverter has been recognized as an important alternative in the medium-voltage inverter market. This paper presents a survey of different topologies, control strategies and modulation techniques used by these inverters. Regenerative and advanced topologies are also discussed. Applications where the mentioned features play a key role are shown. Finally, future developments are addressed.

Recent Advances and Industrial Applications of Multilevel Converters

Multilevel converters have been under research and development for more than three decades and have found successful industrial application. However, this is still a technology under development, and many new contributions and new commercial topologies have been reported in the last few years. The aim of this paper is to group and review these recent contributions, in order to establish the current state of the art and trends of the technology, to provide readers with a comprehensive and insightful review of where multilevel converter technology stands and is heading. This paper first presents a brief overview of well-established multilevel converters strongly oriented to their current state in industrial applications to then center the discussion on the new converters that have made their way into the industry. In addition, new promising topologies are discussed. Recent advances made in modulation and control of multilevel converters are also addressed. A great part of this paper is devoted to show nontraditional applications powered by multilevel converters and how multilevel converters are becoming an enabling technology in many industrial sectors. Finally, some future trends and challenges in the further development of this technology are discussed to motivate future contributions that address open problems and explore new possibilities.

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.

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.

Statistical properties of entropy-consuming fluctuations in jammed states of laponite suspensions: Fluctuation relations and generalized Gumbel distribution

We report a universal large deviation behavior of spatially averaged global injected power just before the rejuvenation of the jammed state formed by an aging suspension of laponite clay under an applied stress. The probability distribution function (PDF) of these entropy consuming strongly non-Gaussian fluctuations follow an universal large deviation functional form described by the generalized Gumbel (GG) distribution like many other equilibrium and nonequilibrium systems with high degree of correlations but do not obey the Gallavotti-Cohen steady-state fluctuation relation (SSFR). However, far from the unjamming transition (for smaller applied stresses) SSFR is satisfied for both Gaussian as well as non-Gaussian PDF. The observed slow variation of the mean shear rate with system size supports a recent theoretical prediction for observing GG distribution.

Loop transformations: convexity, pruning, and optimization

High-level loop transformations are a key instrument in mapping computational kernels to effectively exploit the resources in modern processor architectures. Nevertheless, selecting required compositions of loop transformations to achieve this remains a significantly challenging task; current compilers may be off by orders of magnitude in performance compared to hand-optimized programs. To address this fundamental challenge, we first present a convex characterization of all distinct, semantics-preserving, multidimensional affine transformations. We then bring together algebraic, algorithmic, and performance analysis results to design a tractable optimization algorithm over this highly expressive space. Our framework has been implemented and validated experimentally on a representative set of benchmarks running on state-of-the-art multi-core platforms.