C*-Algebras of Singular Integral Operators with Shifts Having the Same Nonempty Set of Fixed Points

The C*-subalgebra of generated by all multiplication operators by slowly oscillating and piecewise continuous functions, by the Cauchy singular integral operator and by the range of a unitary representation of an amenable group of diffeomorphisms with any nonempty set of common fixed points is studied. A symbol calculus for the C*-algebra and a Fredholm criterion for its elements are obtained. For the C*-algebra composed by all functional operators in , an invertibility criterion for its elements is also established. Both the C*-algebras and are investigated by using a generalization of the local-trajectory method for C*-algebras associated with C*-dynamical systems which is based on the notion of spectral measure. Submitted: April 30, 2007. Accepted: November 5, 2007.     

On-off scheduling schemes for power-constrained electric vehicle charging

In this paper, we study the problem of establishing a dynamic charging schedule of electric vehicles (EVs) at a charging station, assuming that limited power implies that only a limited number of EVs can charge simultaneously. The only control we assume to be available to the charging station is the ability to (at any given time) turn on or off the power supply to any EV, with this tool we want to develop a charging schedule that will satisfy the energy demands of the EVs in their intended deadlines. We propose two distinct approaches to this problem: a discretized time version, based on a greedy-like algorithm, and a continuous time version, based on linear programming. We compare these two approaches and numerically study the improvement they yield in the efficiency of the charging procedure, when applied to simulated data based on real parking data. Finally, we illustrate the flexibility of the models by sketching several possible extensions.     

Uniqueness of complete spacelike hypersurfaces via their higher order mean curvatures in a conformally stationary spacetime

We study complete noncompact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds endowed with a timelike conformal vector field V. In this setting, by using as main analytical tool a suitable maximum principle for complete noncompact Riemannian manifolds, we establish new characterizations of totally umbilical hypersurfaces in terms of their higher order mean curvatures. For instance, supposing an appropriated restriction on the norm of the tangential component of the vector field V, we are able to show that such hypersurfaces must be totally umbilical provided that either some of their higher order mean curvatures are linearly related or one of them is constant. Applications to the so‐called generalized Robertson‐Walker spacetimes are given. In particular, we extend to the Lorentzian context a classical result due to Jellett  29 .     

On the computation of all eigenvalues for the eigenvalue complementarity problem

In this paper, a parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature. The algorithm searches a finite number of nested intervals \([\bar{l}, \bar{u}]\) in such a way that, in each iteration, either an eigenvalue is computed in \([\bar{l}, \bar{u}]\) or a certificate of nonexistence of an eigenvalue in \([\bar{l}, \bar{u}]\) is provided. A hybrid method that combines an enumerative method [1] and a semi-smooth algorithm [2] is discussed for dealing with the Eigenvalue Complementarity Problem over an interval \([\bar{l}, \bar{u}]\) . Computational experience is presented to illustrate the efficacy and efficiency of the proposed techniques.     

On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle

We consider the general problem of determining the maximum possible multiplicity of an eigenvalue in a Hermitian matrix whose graph contains exactly one cycle. For some cases we express that maximum multiplicity in terms of certain parameters associated with the graph.     

Integrated optical temporal Fourier transformer based on a chirped Bragg grating waveguide

We experimentally demonstrate the first integrated temporal Fourier transformer based on a linearly chirped Bragg grating waveguide written in silica glass with a femtosecond laser. The operation is based on mapping the energy spectrum of the input optical signal to the output temporal waveform by making use of first-order chromatic dispersion. The device operates in reflection, has a bandwidth of 10 nm, and can be used for incident temporal waveforms as long as 20 ps. Experimental results, obtained through both temporal oscilloscope traces and Fourier transform spectral interferometry, display a successful Fourier transformation of in-phase and out-of-phase pairs of input optical pulses, and demonstrate the correct functionality of the device for both amplitude and phase of the temporal output.     

(Im-)possible ISOL beams

Refractory elements, i.e. elements with very high melting point and low vapor pressure, cannot be released in atomic form from an ISOL target. Therefore most of these elements are presently not available as ISOL beams. However, when reactive gases are introduced into the target, they may form volatile compounds with the refractory elements, allowing for an easier transport to the ion source. Particularly useful are high-temperature stable fluorides and oxides. By these chemical evaporation methods so far ISOL beams of the refractory elements C, Zr, Hf and Ta have been produced. We discuss how ISOL beams of B, Ti, Nb, Mo, Tc, Ru, W, Re, Os and Ir could be produced in a similar way.     

Instrumentation for beam-foil spectroscopic studies in the UV-visible region

A facility for carrying out beam-foil spectroscopic studies in the UV and visible region using the 400 kV electrostatic ion accelerator at Tata Institute of Fundamental Research, Bombay is described.     

Influence of surface composition on hydrogen peroxide decomposition catalyzed by Co(II) aminopyridine-supported compounds on amorphous silica gel

Cobalt compounds supported on 2-, 3-, and 4-aminopyridine-modified silica surfaces, named Sil2Co, Sil3Co, and Sil4Co, respectively, were used to catalyze the decomposition of hydrogen peroxide on ethanolic solutions at 293, 298, and 303 K. The calculated k values (x10(-4) s(-1)) for Sil2Co, Sil3Co, and Sil4Co are 0.65, 1.24, and 4.78 (293 K); 1.23, 1.87, and 6.33 (298 K); and 1.80, 2.80, and 10.30 (303 K), respectively. All obtained results evidence that such decomposition is a first-order reaction. Zinc-, nickel-, and copper-supported compounds were also tested, but exhibited a very low catalytic activity. By using the k values at 298 and 303 K, and employing the equation ln (k1/k2) = E(a)/R(1/T2-1/T1), the activation energy values for the considered reaction were Sil2Co = 57.20, Sil3Co = 60.60, and Sil4Co = 73.10 kJ mol(-1), respectively. The low values calculated for E(a) are in agreement with a free-radical mechanism.