He II spectra of La, Ce and Yb: Novel features in the valence band region

He II photoelectron spectra of La, Ce and Yb show features which cannot be explained in terms of single electron excitations. It is proposed that these are due to formation of electron-hole paris.

Fibre diffraction of lithium DNA shows structural variability and deviation from a regular helical structure for the B-form

Recently, reports have appeared which show structural variations in B-DNA and indicate deviations from a uniform helical structure. We report for the first time that these indications are also present in the B-form fibre diffraction patterns for the lithium salt of natural DNA. We have used an improved method of controlling the salt concentration in the fibres. Our results are based on the appearance and disappearance of meridional reflections on different layer lines depending upon the salt.

Ce CORE level X-ray photo electron spectroscopy of CeX2Si2 (X = Fe, Co, Ni and Cu)

Ce(3d) and (4d) core level XPS spectra of CeX = Fe, Co, Ni and Cu) suggest that the mean valence of Ce was as well as 4f hybridization strength decrease systematically from Fe to Cu. This observation is in agreement with the results of Bremstrahlung Isochromat Spectroscopy (BIS), but in disagreement with LIII-edge data reported earlier.

Multipath Dissemination in Regular Mesh Topologies

Mesh topologies are important for large-scale peer-to-peer systems that use low-power transceivers. The Quality of Service (QoS) in such systems is known to decrease as the scale increases. We present a scalable approach for dissemination that exploits all the shortest paths between a pair of nodes and improves the QoS. Despite th presence of multiple shortest paths in a system, we show that these paths cannot be exploited by spreading the messages over the paths in a simple round-robin manner; nodes along one of these paths will always handle more messages than the nodes along the other paths. We characterize the set of shortest paths between a pair of nodes in regular mesh topologies and derive rules, using this characterization, to effectively spread the messages over all the available paths. These rules ensure that all the nodes that are at the same distance from the source handle roughly the same number of messages. By modeling the multihop propagation in the mesh topology as a multistage queuing network, we present simulation results from a variety of scenarios that include link failures and propagation irregularities to reflect real-world characteristics. Our method achieves improved QoS in all these scenarios.

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Multipliers of Sobolev spaces

Let Wm,p denote the Sobolev space of functions on Image n whose distributional derivatives of order up to m lie in Lp(Image n) for 1 less-than-or-equals, slant p less-than-or-equals, slant ∞. When 1 < p < ∞, it is known that the multipliers on Wm,p are the same as those on Lp. This result is true for p = 1 only if n = 1. For, we prove that the integrable distributions of order less-than-or-equals, slant1 whose first order derivatives are also integrable of order less-than-or-equals, slant1, belong to the class of multipliers on Wm,1 and there are such distributions which are not bounded measures. These distributions are also multipliers on Lp, for 1 < p < ∞. Moreover, they form exactly the multiplier space of a certain Segal algebra. We have also proved that the multipliers on Wm,l are necessarily integrable distributions of order less-than-or-equals, slant1 or less-than-or-equals, slant2 accordingly as m is odd or even. We have obtained the multipliers from L1(Image n) into Wm,p, 1 less-than-or-equals, slant p less-than-or-equals, slant ∞, and the multiplier space of Wm,1 is realised as a dual space of certain continuous functions on Image n which vanish at infinity.

A Team of Continuous-Action Learning Automata for Noise-Tolerant Learning of Half-Spaces

Learning automata are adaptive decision making devices that are found useful in a variety of machine learning and pattern recognition applications. Although most learning automata methods deal with the case of finitely many actions for the automaton, there are also models of continuous-action-set learning automata (CALA). A team of such CALA can be useful in stochastic optimization problems where one has access only to noise-corrupted values of the objective function. In this paper, we present a novel formulation for noise-tolerant learning of linear classifiers using a CALA team. We consider the general case of nonuniform noise, where the probability that the class label of an example is wrong may be a function of the feature vector of the example. The objective is to learn the underlying separating hyperplane given only such noisy examples. We present an algorithm employing a team of CALA and prove, under some conditions on the class conditional densities, that the algorithm achieves noise-tolerant learning as long as the probability of wrong label for any example is less than 0.5. We also present some empirical results to illustrate the effectiveness of the algorithm.

Harmonic Analysis On Heisenberg Nilmanifolds

In these lectures we plan to present a survey of certain aspects of harmonic analysis on a Heisenberg nilmanifold Gammakslash}H-n. Using Weil-Brezin-Zak transform we obtain an explicit decomposition of L-2 (Gammakslash}H-n) into irreducible subspaces invariant under the right regular representation of the Heisenberg group. We then study the Segal-Bargmann transform associated to the Laplacian on a nilmanifold and characterise the image of L-2 (GammakslashH-n) in terms of twisted Bergman and Hermite Bergman spaces.

Active nucleoprotein filaments of single-stranded binding protein and recA protein on single-stranded DNA have a regular repeating structure

When E. coli single-stranded DNA binding protein (SSB) coats single-stranded DNA (ssDNA) in the presence of 1 mM MgCl2 it inhibits the subsequent binding of recA protein, whereas SSB binding to ssDNA in 12 mM MgCl2 promotes the binding of recA protein. These two conditions correspond respectively to those which produce 'smooth' and 'beaded' forms of ssDNA-SSB filaments. By gel filtration and immunoprecipitation we observed active nucleoprotein filaments of recA protein and SSB on ssDNA that contained on average 1 monomer of recA protein per 4 nucleotides and 1 monomer of SSB per 20-22 nucleotides. Filaments in such a mixture, when digested with micrococcal nuclease produced a regular repeating pattern, approximately every 70-80 nucleotides, that differed from the pattern observed when only recA protein was bound to the ssDNA. We conclude that the beaded ssDNA-SSB nucleoprotein filament readily binds recA protein and forms an intermediate that is active in the formation of joint molecules and can retain substantially all of the SSB that was originally bound.

Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

d-Regular Graphs of Acyclic Chromatic Index at Least d+2

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). It was conjectured by Alon, Suclakov and Zaks (and earlier by Fiamcik) that a'(G) <= Delta+2, where Delta = Delta(G) denotes the maximum degree of the graph. Alon et al. also raised the question whether the complete graphs of even order are the only regular graphs which require Delta+2 colors to be acyclically edge colored. In this article, using a simple counting argument we observe not only that this is not true, but in fact all d-regular graphs with 2n vertices and d>n, requires at least d+2 colors. We also show that a'(K-n,K-n) >= n+2, when n is odd using a more non-trivial argument. (Here K-n,K-n denotes the complete bipartite graph with n vertices on each side.) This lower bound for Kn,n can be shown to be tight for some families of complete bipartite graphs and for small values of n. We also infer that for every d, n such that d >= 5, n >= 2d+3 and dn even, there exist d-regular graphs which require at least d+2-colors to be acyclically edge colored. (C) 2009 Wiley Periodicals, Inc. J Graph Theory 63: 226-230, 2010.

Proximinality in Banach spaces

In this paper, we study approximatively τ-compact and τ-strongly Chebyshev sets, where τ is the norm or the weak topology. We show that the metric projection onto τ-strongly Chebyshev sets are norm-τ continuous. We characterize approximatively τ-compact and τ-strongly Chebyshev hyperplanes and use them to characterize factor reflexive proximinal subspaces in τ-almost locally uniformly rotund spaces. We also prove some stability results on approximatively τ-compact and τ-strongly Chebyshev subspaces.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

Studies on the ionic transport and structural investigations of La0.5Li0.5TiO3 perovskite synthesized by wet chemical methods and the effect of Ce, Zr substitution at Ti site

La0.5Li0.5TiO3 perovskite was synthesized by various wet chemical methods. By adopting low temperature methods of preparation lithium loss from the material is prevented. La0.5Li0.5TiO3 (LLTO) was formed with cubic symmetry at 1473 K. LLTO was formed at relatively lower temperature by using hydrothermal preparation method. PVA gel-decomposition route yield tetragonal LLTO on annealing the dried gel at 1473 K. By using gel-carbonate route LiTi2O4 minor phase was found to remain even after heat-treatment at 1473 K. The hydroxylation of LLTO was done in deionized water as well as in dilute acetic acid medium. By hydroxylation process incorporation of hydroxyls and leaching out of Li+ was observed from the material. The Li+ concentration of these compositions was examined by AAS. The electrical conductivities of these compositions were measured by dc and ac impedance techniques at elevated temperatures. The activation energies of electrical conduction for these compositions were estimated from the experimental results. The measured activation energy of Li+ conduction is 0.34 eV. Unhydroxylated samples exhibit only Li+ conduction, whereas, the hydroxylated LLTO show proton conductivity at 298-550 K in addition to Li+ conductivity. The effect of Zr or Ce substitution in place of Ti were attempted. La0.5Li0.5ZrO3 Perovskite was not formed; instead pyrochlore phase (La2Zr2O7) along with monoclinic ZrO2 phases was observed above 1173 K; below 1173 K cubic ZrO2 is stable. (La0.5Li0.5)(2)CeO4 solid solution was formed in the case of Ce substitution at Ti sublattice on heat-treatment up to 1673 K. (c) 2005 Springer Science + Business Media, Inc.