107,910 research outputs found
Multiplication Semigroups on Banach Function Spaces
In this paper we characterize multiplication operators induced by operator
valued maps on Banach function spaces. We also study multiplication semigroups
and stability of these operators.Comment: We want to withdraw the paper due to the paper needs a careful
revision and some proper citations are to be provided. Also there are certain
gaps in the results which need to be taken car
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
Alternative conformal quantum mechanics
We investigate a one dimensional quantum mechanical model, which is invariant
under translations and dilations but does not respect the conventional
conformal invariance. We describe the possibility of modifying the conventional
conformal transformation such that a scale invariant theory is also invariant
under this new conformal transformation
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
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
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