Beurling algebra analogues of the classical theorems of Wiener and Levy on absolutely convergent Fourier series

Let $f$ be a continuous function on the unit circle $\Gamma$, whose Fourier series is $\omega$-absolutely convergent for some weight $\omega$ on the set of integers $\mathcal{Z}$. If $f$ is nowhere vanishing on $\Gamma$, then there exists a weight $\nu$ on $\mathcal{Z}$ such that $1/f$ had $\nu$-absolutely convergent Fourier series. This includes Wiener's classical theorem. As a corollary, it follows that if $\phi$ is holomorphic on a neighbourhood of the range of $f$, then there exists a weight $\chi$ on $\mathcal{Z}$ such that \hbox{$\phi\circ f$} has $\chi$-absolutely convergent Fourier series. This is a weighted analogue of L\'{e}vy's generalization of Wiener's theorem. In the theorems, $\nu$ and $\chi$ are non-constant if and only if $\omega$ is non-constant. In general, the results fail if $\nu$ or $\chi$ is required to be the same weight $\omega$.Comment: 4 page

Fatigue behavior of SiC reinforced titanium composites

The low cycle axial fatigue properties of 25 and 44 fiber volume percent SiC/Ti(6Al-4V) composites were measured at room temperature and at 650 deg C. The S-N curves for the composites showed no anticipated improvement over bulk matrix behavior at room temperature. Although axial and transverse tensile strength results suggest a degradation in SiC fiber strength during composite fabrication, it appears that the poor fatigue life of the composites was caused by a reduced fatigue resistance of the reinforced Ti(6Al-4V) matrix. The reduced matrix behavior was due, to the presence of flawed and fractured fibers created near the specimen surfaces by preparation techniques and to the large residual tensile stresses that can exist in fiber reinforced matrices. The effects of fatigue testing at high temperature are discussed

Search for Ferromagnetism in doped semiconductors in the absence of transition metal ions

In contrast to semiconductors doped with transition metal magnetic elements, which become ferromagnetic at temperatures below ~ 100K, semiconductors doped with non-magnetic ions (e.g. silicon doped with phosphorous) have not shown evidence of ferromagnetism down to millikelvin temperatures. This is despite the fact that for low densities the system is expected to be well modeled by the Hubbard model, which is predicted to have a ferromagnetic ground state at T=0 on 2- or 3-dimensional bipartite lattices in the limit of strong correlation near half-filling. We examine the impurity band formed by hydrogenic centers in semiconductors at low densities, and show that it is described by a generalized Hubbard model which has, in addition to strong electron-electron interaction and disorder, an intrinsic electron-hole asymmetry. With the help of mean field methods as well as exact diagonalization of clusters around half filling, we can establish the existence of a ferromagnetic ground state, at least on the nanoscale, which is more robust than that found in the standard Hubbard model. This ferromagnetism is most clearly seen in a regime inaccessible to bulk systems, but attainable in quantum dots and 2D heterostructures. We present extensive numerical results for small systems that demonstrate the occurrence of high-spin ground states in both periodic and positionally disordered 2D systems. We consider how properties of real doped semiconductors, such as positional disorder and electron-hole asymmetry, affect the ground state spin of small 2D systems. We also discuss the relationship between this work and diluted magnetic semiconductors, such as Ga_(1-x)Mn_(x)As, which though disordered, show ferromagnetism at relatively high temperatures.Comment: 47 page

Two-component approach for thermodynamic properties in diluted magnetic semiconductors

We examine the feasibility of a simple description of Mn ions in III-V diluted magnetic semiconductors (DMSs) in terms of two species (components), motivated by the expectation that the Mn-hole exchange couplings are widely distributed, expecially for low Mn concentrations. We find, using distributions indicated by recent numerical mean field studies, that the thermodynamic properties (magnetization, susceptibility, and specific heat) cannot be fit by a single coupling as in a homogeneous model, but can be fit well by a two-component model with a temperature dependent number of ``strongly'' and ``weakly'' coupled spins. This suggests that a two-component description may be a minimal model for the interpretation of experimental measurements of thermodynamic quantities in III-V DMS systems.Comment: 10 pages, 9 figures, 1 new figure, substantial revision

Narasimham Committee Report - Some Further Ramifications and Suggestions

This paper while agreeing with the general thrust of the Narasimham Committee Report. Calls attention to some logical corollaries of the Report and analyses some possible fallout from implementing the Report. We agree with the view that control of banking system should be under an autonomous body supervised by the RBI. However at the level of individual banks, closer scrutiny of lending procedures may be called for than is envisaged in the Report. In a freely functioning capital market the potential of government bonds is enormous, but this necessitates restructuring of the government bond market. The government bonds may then also be used as suitable hedging mechanisms by introducing options and futures trading. We recommend freeing up the operation of pension and provident fund to enable at least partial investment of such funds in risky securities. In the corporate sector, we believe that the current 2:1 debt equity norm is too high and not sustainable in the long term. We envisage that high debt levels and higher interest rates, combined with higher business risk may result in greater incidence of corporate sickness. This may call for various schemes for retrenched workers and amendment to land laws for easy exit of companies. On account of interdependencies across different policies, any sequencing of their implementation may be highly problematic. We therefore suggest a near simultaneity in the implementation of various reforms in order to build up a momentum which would be irreversible if people are to have confidence that the reforms will endure, and if we are to retain our credibility with international financial institutions.