Modules with Pure Resolutions

We show that the property of a standard graded algebra R being Cohen-Macaulay is characterized by the existence of a pure Cohen-Macaulay R-module corresponding to any degree sequence of length at most depth(R). We also give a relation in terms of graded Betti numbers, called the Herzog-Kuhl equations, for a pure R-module M to satisfy the condition dim(R) - depth(R) = dim(M) - depth(M). When R is Cohen-Macaulay, we prove an analogous result characterizing all graded Cohen-Macaulay R-modules.Comment: 9 page

Analytical results connecting stellar structure parameters and extended reaction rates

Possible modification in the velocity distribution in the non-resonant reaction rates leads to an extended reaction rate probability integral. The closed form representation for these thermonuclear functions are used to obtain the stellar luminosity and neutrino emission rates. The composite parameter {C} that determines the standard nuclear reaction rate through the Maxwell-Boltzmann energy distribution is extended to {C}^* by the extended reaction rates through a more general distribution than the Maxwell-Boltzmann distribution. The new distribution is obtained by the pathway model introduced by Mathai in 2005 [Linear Algebra and Its Applications, 396, 317-328]. Simple analytic models considered by various authors are utilized for evaluating stellar luminosity and neutrino emission rates and are obtained in generalized special functions such as Meijer's G-function and Fox's H-function. The standard and extended non-resonant thermonuclear functions are compared by plotting them. Behavior of the new energy distribution, more general than Maxwell-Boltzmann is also studied.Comment: 20 pages, LaTe

Growth of shocked gaseous interfaces in a conical geometry

The results of experiments on Richtmyer-Meshkov instability growth of multimode initial perturbations on an air-sulfur hexafluoride (SF6) interface in a conical geometry are presented. The experiments are done in a relatively larger shock tube. A nominally planar interface is formed by sandwiching a polymeric membrane between wire-mesh frames. A single incident shock wave ruptures the membrane resulting in multimode perturbations. The instability develops from the action of baroclinically deposited vorticity at the interface. The visual thickness delta of the interface is measured from schlieren photographs obtained in each run. Data are presented for delta at times when the interface has become turbulent. The data are compared with the experiments of Vetter [Shock Waves 4, 247 (1995)] which were done in a straight test section geometry, to illustrate the effects of area convergence. It is found from schlieren images that the interface thickness grows about 40% to 50% more rapidly than in Vetter's experiments. Laser induced scattering is used to capture the air-helium interface at late times. Image processing of pictures is also used to determine the interface thickness in cases where it was not clear from the pictures and to obtain the dominant eddy-blob sizes in the mixing zone. Some computational studies are also presented to show the global geometry changes of the interface when it implodes into a conical geometry in both light-heavy and heavy-light cases

DSDV, DYMO, OLSR: Link Duration and Path Stability

In this paper, we evaluate and compare the impact of link duration and path stability of routing protocols; Destination Sequence Distance vector (DSDV), Dynamic MANET On- Demand (DYMO) and Optimized Link State Routing (OLSR) at different number of connections and node density. In order to improve the efficiency of selected protocols; we enhance DYMO and OLSR. Simulation and comparison of both default and enhanced routing protocols is carried out under the performance parameters; Packet Delivery Ratio (PDR), Average End-to End Delay (AE2ED) and Normalized Routing Overhead (NRO). From the results, we observe that DYMO performs better than DSDV, MOD-OLSR and OLSR in terms of PDR, AE2ED, link duration and path stability at the cost of high value of NRO

Study of effective interaction from single particle transfer reactions on f-p shell nuclei

The present study concentrates on the average effective two-body interaction matrix elements being extracted, using sum-rule techniques, from transfer reactions on target states having single orbital as well as two orbitaloccupancy. This investigation deals with transfer reactions on f-p shell nuclei involving (i) $1f_{7/2}$ and $2p_{3/2}$ transfer on target states using $^{40}$Ca as inert core, and (ii) $2p_{3/2}$ and$1f_{5/2}$ transfer on states using $^{56}$Ni as core.Comment: 12 pages, ptptex Subj-Classes: Nuclear Shell Structure e-mail:[email protected]

Polymer precursors for ceramic matrix composites

The synthesis and characterization of a polycyclohexasilane is reported. Because of its cyclic structure, it is anticipated that this polymer might serve as a precursor to SIC having a high char yield with little rearrangement to form small, volatile cyclic silanes, and, as such, would be of interest as a precursor to SiC composite matrices and fibers, or as a binder in ceramic processing. Several approaches to the synthesis of a bifunctional cyclic monomer were attempted; the most successful of these was metal coupling of PhMeSiCl2 and Me2SiCl2. The procedure gives six-membered ring compounds with all degrees of phenyl substitution, from none to hexaphenyl. The compounds with from 0-2 groups were isolated and characterized. The fraction with degree of phenyl substitution equal to 2, a mixture of cis and trans 1,2-; 1,3-; and 1,4 isomers, was isolated in 32 percent yield. Pure 1,4 diphenyldecamethylcyclohexasilane was isolated from the mixed diphenyl compounds and characterized. Diphenyldecamethylcyclohexasilanes were dephenylated to dichlorodecamethylcyclohexasilanes by treating with H2SO4.NH4Cl in benzene. The latter were purified and polymerized by reacting with sodium in toluene. The polymers were characterized by HPGPC, elemental analysis, proton NMR, and IR. Thermogravimetric analyses were carried out on the polymers. As the yield of residual SiC was low, polymers were heat treated to increase the residual char yield. As high as 51.52 percent residual char yield was obtained in one case

Predictions of Dynamic Behavior Under Pressure for Two Scenarios to Explain Water Anomalies

Using Monte Carlo simulations and mean field calculations for a cell model of water we find a dynamic crossover in the orientational correlation time $\tau$ from non-Arrhenius behavior at high temperatures to Arrhenius behavior at low temperatures. This dynamic crossover is independent of whether water at very low temperature is charaterized by a ``liquid-liquid critical point'' or by the ``singularity free'' scenario. We relate $\tau$ to fluctuations of hydrogen bond network and show that the crossover found for $\tau$ for both scenarios is a consequence of the sharp change in the average number of hydrogen bonds at the temperature of the specific heat maximum. We find that the effect of pressure on the dynamics is strikingly different in the two scenarios, offering a means to distinguish between them.Comment: 10 Pages, 4 figure