A Classification of Homogeneous Operators in the Cowen-Douglas Class

A complete list of homogeneous operators in the Cowen-Douglas class B-n(D) is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi-holomorphic automorphism group of the unit disc.

Local structure of Sr2FeMoxW1-xO6 double perovskites across the composition-driven metal to insulator transition

Sr2FeMoO6 oxides exhibit a half-metallic ferromagnetic (HM-FM) ground state and peculiar magnetic and magnetotransport properties, which are interesting for applications in the emerging field of spintronics and attractive for fundamental research in the field of heavily correlated electron systems. Sr2FeWO6 is an insulator with an antiferromagnetic (I-AFM) ground state. The solid solutions Sr2FeMoxW1-xO6 also have peculiar properties-W doping enhances chemical order which allows stabilization of the HM-FM state; as the W content exceeds a certain value a metal to insulator transition (MIT) occurs. The role of W in determining the physical properties of Sr2FeMoxW1-xO6 systems has been a matter of intense investigation. This work deals with the problem of the structural and electronic changes related to the MIT from a local perspective by means of x-ray absorption spectroscopy (XAS). This technique allows one to probe in detail the local structure and electronic modifications around selected absorber ions (W, Mo, Fe and Sr in our case). The results of XAS analysis in the whole composition range (0 <= x <= 1), in the near edge (XANES) and extended (EXAFS) regions, demonstrate an abrupt change of the local structure around the Fe and Mo sites at the critical composition, x(c). This change represents the microstructural counterpart associated with the MIT. Conversely, the local structure and electronic configuration of W ions remain unaltered in the whole composition range, suggesting indirect participation of W in the MIT.

Composition-controlled metal-insulator transitions and minimum metallic conductivity in the oxide systems LaNi1-xMxO3 (M = Cr, Mn, Fe, or Co)

The composition-controlled metal-insulator transition in the perovskite systems LaNi1-xMxO3 (M = Cr, Mn, Fe, and Co) has been investigated by transport measurements over the temperature range 12-300 K. These systems, which have critical electron densities (nc) in the range (1-2) -1020 electrons cm-3, exhibit sharp metal-insulator transitions at the base temperature. The corresponding minimum metallic conductivity (Ï-min), separating the localized and itinerant electronic regimes, is of the order of 102 ohm-1 cm-1. Particular attention is paid to the idea of Ï-min scaling with nc, and our present results are compared with earlier studies of the metal-insulator transition in low (e.g., Ge:Sb) and high (e.g., metal-ammonia, supercritical Hg) electron-density systems. A link is established between the transport and magnetic properties of the title systems at the metal-insulator transition.

On the eigenvalues and eigenfunctions of some integral operators

Some properties of the eigenvalues of the integral operator Kgt defined as Kτf(x) = ∫0τK(x − y) f (y) dy were studied by [1.], 554–566), with some assumptions on the kernel K(x). In this paper the eigenfunctions of the operator Kτ are shown to be continuous functions of τ under certain circumstances. Also, the results of Vittal Rao and the continuity of eigenfunctions are shown to hold for a larger class of kernels.

The effect of composition, electron irradiation and quenching on ionic conductivity in a new solid polymer electrolyte: (PEG) (x) NH4I

We have prepared, characterized and investigated a new PEG-2000 based solid polymer electrolyte (PEG) x NH4I. Ionic conductivity measurements have been made as a function of salt concentration as well as temperature in the range 265–330 K. Selected compositions of the electrolyte were exposed to a beam of 8 MeV electrons to an accumulated dose of 10 kGy to study the effect on ionic conductivity. The electrolyte samples were also quenched at liquid nitrogen temperature and conductivity measurements were made. The ionic conductivity at room temperature exhibits a characteristic double peak for the composition x = 20 and 70. Both electron beam irradiation and quenching at low temperature have resulted in an increase in conductivity by 1–2 orders of magnitude. The enhancement of conductivity upon irradiation and quenching is interpreted as due to an increase in amorphous region and decrease in crystallinity of the electrolyte. DSC and proton NMR measurements also support this conclusion.

Depth profile composition studies of thin film CdS: Cu,S solar cells using XPS and AES

Surface composition and depth profile studies of hemiplated thin film CdS:CuzS solar cells have been carried out using x-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) techniques. These studies indicate that the junction is fairly diffused in the as-prepared cell. However, heat treatment of the cell at 210°C in air relatively sharpens the junction and improves the cell performance. Using the Cu(2p3p)/S(2p) ratio as well as the Cu(LVV)/(LMM) Auger intensity ratio, it can be inferred that the nominal valency of copper in the layers above the junction is Cut and it is essentially in the CUSS form. Copper signals are observed from layers deep down in the cell. These seem to appear mostly from the grain boundary region. From the observed concentration of Cd, Cu and S in these deeper layers and the Cu(LVV)/(LMM) ratio it appears that the signals from copper essentially originate partly from copper in CuS and partly from Cu2t trapped in the lattice. It is significant to note that the nominal valence state of copper changes rather abruptly from Cut to Cuz+ across the junction.

Quaternary unary operators

Unary operators are functions of a single variable. Realization of quaternary unary operators (QUOs) using quaternary multiplexer (QMUX) is presented in this paper. QUOs are divided into eight groups on the basis of the number of change overs in the output for an input sequence of 0, 1, 2, 3. This grouping reduces the hardware required to realize them. QMUX with two, three, and four input lines are proposed for the realization of QUOs belonging to the eight groups. A systematic procedure for the selection of QMUX and the implementation of the QUOs are given. The QMUXs are designed using CMOS ICs. The hardware required for their implementation is also discussed.

Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation [script D]alpha of the para-Bose system is obtained as the direct sum Dbeta[direct-sum]Dbeta+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation [script D]alpha, using the matrix mechanical method. The orthogonality, completeness, and the overlap of these eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Parallel processor scheduling for minimizing total weighted tardiness using ant colony optimization

In the modern business environment, meeting due dates and avoiding delay penalties are very important goals that can be accomplished by minimizing total weighted tardiness. We consider a scheduling problem in a system of parallel processors with the objective of minimizing total weighted tardiness. Our aim in the present work is to develop an efficient algorithm for solving the parallel processor problem as compared to the available heuristics in the literature and we propose the ant colony optimization approach for this problem. An extensive experimentation is conducted to evaluate the performance of the ACO approach on different problem sizes with the varied tardiness factors. Our experimentation shows that the proposed ant colony optimization algorithm is giving promising results compared to the best of the available heuristics.

Vapour composition and activities in Mg-Zn liquid alloy at 923 K

Vapour species effusing from a magnesia Knudsen cell containing Mg-Zn alloy at 923 K were condensed on a water cooled copper plate. The equilibrium composition of the vapour phase over the alloy was determined from chemical analysis of the condensate. The activity coefficients of both components in the alloy have been derived from the data using a modified Gibbs-Duhem relation. The ratio of saturation vapour pressures of pure Zn and Mg obtained from the analysis of alloy data agree well with values from the literature, providing an internal check on the accuracy of data obtained in this study. Both components of the alloy exhibit negative deviations from Raoult's law. The concentration-concentration structure factor of Bhatia and Thomton at zero wave vector, evaluated from the measurements, indicate the presence of MgZn2 type complex in the liquid state. The associated regular solution model has been used for the thermodynamic description of liquid Mg-Zn alloys.

Lipids of nervous tissue: composition and metabolism

As indicated in the Introduction, the many significant developments in the recent past in our knowledge of the lipids of the nervous system have been collated in this article. That there is a sustained interest in this field is evident from the rather long bibliography which is itself selective. Obviously, it is not possible to summarize a review in which the chemistry, distribution and metabolism of a great variety of lipids have been discussed. However, from the progress of research, some general conclusions may be drawn. The period of discovery of new lipids in the nervous system appears to be over. All the major lipid components have been discovered and a great deal is now known about their structure and metabolism. Analytical data on the lipid composition of the CNS are available for a number of species and such data on the major areas of the brain are also at hand but information on the various subregions is meagre. Such investigations may yet provide clues to the role of lipids in brain function. Compared to CNS, information on PNS is less adequate. Further research on PNS would be worthwhile as it is amenable for experimental manipulation and complex mechanisms such as myelination can be investigated in this tissue. There are reports correlating lipid constituents with the increased complexity in the organization of the nervous system during evolution. This line of investigation may prove useful. The basic aim of research on the lipids of the nervous tissue is to unravel their functional significance.

Spectral analysis of finite section normal integral operators

Some continuity and differentiability properties of the eigenvalues and eigenfunctions of finite section normal integral operators are proved. These are the extension of corresponding results for symmetric operators ([4.], 554–566; K. B. Athreya and R. Vittal Rao, to appear; [10.], 463–471.

Kac-Akhiezer formula for normal integral operators

The Kac-Akhiezer formula for finite section normal Wiener-Hopf integral operators is proved. This is an extension of the corresponding result for symmetric operator [2, 3, 4, 5, 6, 7].

Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.