Arithmetic properties of eigenvalues of generalized Harper operators on graphs

Let \Qbar denote the field of complex algebraic numbers. A discrete group $G$ is said to have the $\sigma$-multiplier algebraic eigenvalue property, if for every matrix $A$ with entries in the twisted group ring over the complex algebraic numbers M_d(\Qbar(G,\sigma)), regarded as an operator on $l^2(G)^d$, the eigenvalues of $A$ are algebraic numbers, where $\sigma$ is an algebraic multiplier. Such operators include the Harper operator and the discrete magnetic Laplacian that occur in solid state physics. We prove that any finitely generated amenable, free or surface group has this property for any algebraic multiplier $\sigma$. In the special case when $\sigma$ is rational ($\sigma^n$=1 for some positive integer $n$) this property holds for a larger class of groups, containing free groups and amenable groups, and closed under taking directed unions and extensions with amenable quotients. Included in the paper are proofs of other spectral properties of such operators.Comment: 28 pages, latex2e, paper revise

On the naturality of the Mathai-Quillen formula

We give an alternative proof for the Mathai-Quillen formula for a Thom form using its natural behaviour with respect to fiberwise integration. We also study this phenomenon in general context.Comment: 6 page

Distribution of mangroves in relation to topography and selection of ecotonal communities for reclaimed areas of Sunderbans

91-94Marked differences were recorded in structure and composition of mangroves from the islands in the eastern and western sectors of Sunderbans in relation to the topography. Avicennia sp. and Aegiceras sp. preferred low lying areas towards the western and eastern sides of Sunderbans respectively. Ceriops-Phoenix association was frequent in high land areas and Excoecaria and Ceriops decandra occurred over the entire forest with different salinity and topography. Association patterns of different mangroves were shown in profile diagrams and ideal ecotonal mangrove communities were suggested for reclaimed regions

Astrophysical thermonuclear functions

As theoretical knowledge and experimental verification of nuclear cross sections increases it becomes possible to refine analytic representations for nuclear reaction rates. In this paper mathematical/statistical techniques for deriving closed-form representations of thermonuclear functions are summarized and numerical results for them are given.The purpose of the paper is also to compare numerical results for approximate and closed-form representations of thermonuclear functions.Comment: 17 pages in LaTeX, 8 figures available on request from [email protected]

Solar Structure in terms of Gauss' Hypergeometric Function

Hydrostatic equilibrium and energy conservation determine the conditions in the gravitationally stabilized solar fusion reactor. We assume a matter density distribution varying non- linearly through the central region of the Sun. The analytic solutions of the differential equations of mass conservation, hydrostatic equilibrium, and energy conservation, together with the equation of state of the perfect gas and a nuclear energy generation rate $\epsilon=\epsilon_0\rho^nT^m$, are given in terms of Gauss' hypergeometric function. This model for the structure of the Sun gives the run of density, mass pressure, temperature, and nuclear energy generation through the central region of the Sun. Because of the assumption of a matter density distribution, the conditions of hydrostatic equilibrium and energy conservation are separated from the mode of energy transport in the Sun.Comment: Invited Paper (A.M.Mathai) at the Fourth UN/ESA Workshop on Basic Space Science, Cairo, Egypt, July 1994, 10 pages LaTeX,4 figures available on reques