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101.
Varghese Mathai Thomas Schick Stuart Yates 《Proceedings of the American Mathematical Society》2003,131(6):1917-1923
We study Harper operators and the closely related discrete magnetic Laplacians (DML) on a graph with a free action of a discrete group, as defined by Sunada. The spectral density function of the DML is defined using the von Neumann trace associated with the free action of a discrete group on a graph. The main result in this paper states that when the group is amenable, the spectral density function is equal to the integrated density of states of the DML that is defined using either Dirichlet or Neumann boundary conditions. This establishes the main conjecture in a paper by Mathai and Yates. The result is generalized to other self adjoint operators with finite propagation speed.
102.
In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell–Boltzmann and Rayleigh densities in the real and complex domains, multivariate Student-t, Cauchy, matrix-variate type-1 beta, type-2 beta, and gamma densities and their generalizations. 相似文献
103.
104.
This paper is an attempt to construct simple analytic models to study the internal structure of main sequence stars. Explicit closed form expressions, which are computable, are given for a number of quantities such as nuclear reaction rate, luminosity, and the number of two particle reactions when the radial matter density of the stellar model is a nonlinear function decreasing from the center to the surface. All analytic results are obtained by taking advantage of the integration theory of generalized hypergeometric functions. 相似文献
105.
106.
A general Laplace transform and its inverse and their generalizations are considered in this article. This inverse contains the density functions of quadratic expressions in nonsingular as well as singular normal variables and a non-central version of linear functions of gamma variables, among others. Various representations of the inverse in power series, in gamma series, in Laguerre polynomials, in hypergeometric functions and in zonal polynomials are also discussed. 相似文献
107.
Kinetic data are reported for the decarboxylation of malonic acid in esters at different temperatures. The activation parameters are calculated and shown to favour the polar mechanism for the decarboxylation. Inductive and steric effects of the various solvents on the rate are discussed. 相似文献
108.
Jacek Brodzki Varghese Mathai Jonathan Rosenberg Richard J. Szabo 《Communications in Mathematical Physics》2008,277(3):643-706
We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation
of T-duality as well as establishing a very general formula for D-brane charges. This formula is closely related to a noncommutative
Grothendieck-Riemann-Roch theorem that is proved here. Our approach relies on a very general form of Poincaré duality, which
is studied here in detail. Among the technical tools employed are calculations with iterated products in bivariant -theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams. 相似文献
109.
Michael Tan Paul Rosenberg Jong Souk Yeo Moray McLaren Sagi Mathai Terry Morris Huei Pei Kuo Joseph Straznicky Norman P. Jouppi Shih-Yuan Wang 《Applied Physics A: Materials Science & Processing》2009,95(4):945-953
Buses have historically provided a flexible communications structure in computer systems. However, signal integrity constraints
of high-speed electronics have made multi-drop electrical buses infeasible. Instead, we propose an optical data bus for computer
interconnections. It has two sets of optical waveguides, one as a fan-out and the other as a fan-in, that are used to interconnect
different modules attached to the bus. A master module transmits optical signals which are received by all the slave modules
attached to the bus. Each slave module in turn sends data back on the bus to the master module. Arrays of lasers, photodetectors,
waveguides, microlenses, beamsplitters, and Tx/Rx integrated circuits are used to realize the optical data bus. With 1 mW
of laser power, we are able to interconnect eight different modules at 10 Gb/s per channel. An aggregate bandwidth of over
25 GB/s is achievable with 10-bit wide signaling paths. 相似文献
110.
J. S. Yeo R. N. Bicknell S. Mathai P. E. Kornilovitch H.-P. Kuo P. Rosenberg M. Tan L. King 《Applied Physics A: Materials Science & Processing》2009,95(4):1073-1077
Hollow metal waveguides feature well collimated beams and small losses across air gaps. This enables introduction of multiple
optical beam splitters, or taps, along the waveguide to multicast signals from a source to multiple receivers. The splitters
need to be of sufficient thickness to provide mechanical integrity and ease of handling. As a result, passing through the
thickness leads to a beam walk-off. Walk-off dependence on the splitter thickness and its effect on the system optical efficiency are investigated. Two methods
to compensate the walk-off are described: by offsetting the outgoing waveguide, and by introducing an additional symmetric
optical element to shift the beam back to the original optical path. Both methods have been shown to effectively mitigate
the walk-off effects. 相似文献