Long-term planning versus short-term planning in the asymptotical location problem

Given the probability measure $\nu$ over the given region $\Omega\subset \R^n$, we consider the optimal location of a set $\Sigma$ composed by $n$ points \Om in order to minimize the average distance \Sigma\mapsto \int_\Om \dist(x,\Sigma) d\nu (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all $n$ points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving the configuration built at previous steps. We show that the respective optimization problems exhibit qualitatively different asymptotic behavior as $n\to\infty$, although the optimization costs in both cases have the same asymptotic orders of vanishing.Comment: for more pictures and some movies as well, see http://www.sissa.it/~brancoli

ab-plane resistivity and possible charge stripe ordering in strongly underdoped La2−x_{2-x}Srx_{x}CuO4_{4} single crystals

We have measured the ab-plane resistivity of La$_{2-x}$Sr$_x$CuO$_4$ single crystals with small Sr content (x=0.052 $\div$ 0.075) between 4.2 and 300 K by using the AC Van der Pauw technique. As recently suggested by Ichikawa et al., the deviation from the linearity of the $\rho_{\mathrm{ab}}(T)$ curve starting at a temperature T$_{\mathrm{ch}}$ can be interpreted as due to a progressive slowing down of the fluctuations of pre-formed charge stripes. An electronic transition of the stripes to a more ordered phase could instead be responsible for some very sharp anomalies present in the $\rho_{\mathrm{ab}}(T)$ of superconducting samples just above $T_{\mathrm{c}}$.Comment: M2S-HTSC-VI Conference paper (2 pages, 2 figures), using Elsevier style espcrc2.st

Semiclassical treatment of logarithmic perturbation theory

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and exited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the harmonic oscillator perturbed by $\lambda x^{6}$ are considered.Comment: 6 pages, LATEX 2.09 using IOP style

Measuring the Dispersion Forces Near the van der Waals-Casimir Transition

Forces induced by quantum fluctuations of the electromagnetic field control adhesion phenomena between rough solids when the bodies are separated by distances of approximately 10 nm. However, this distance range remains largely unexplored experimentally in contrast with the shorter (van der Waals forces) or the longer (Casimir forces) separations. The reason for this is the pull-in instability of the systems with the elastic suspension that poses a formidable limitation. In this paper we propose a genuine experimental configuration that does not suffer from the short distance instability. The method is based on the adhered cantilever, whose shape is sensitive to the forces acting near the adhered end. The general principle of the method, its possible realization, and feasibility are extensively discussed. The dimensions of the cantilever are determined by the maximum sensitivity to the forces. If the adhesion is defined by strong capillary or chemical interactions, the method loses its sensitivity. Special discussion is presented for the determination of the minimum distance between the rough solids upon contact, and for the compensation of the residual electrostatic contribution. The proposed method can be applied to any kind of solids (metals, semiconductors, or dielectrics) and to any intervening medium (gas or liquid).</p

Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields

Let $F/E$ be a finite Galois extension of fields with abelian Galois group $\Gamma$. A self-dual normal basis for $F/E$ is a normal basis with the additional property that $Tr_{F/E}(g(x),h(x))=\delta_{g,h}$ for $g,h\in\Gamma$. Bayer-Fluckiger and Lenstra have shown that when $char(E)\neq 2$, then $F$ admits a self-dual normal basis if and only if $[F:E]$ is odd. If $F/E$ is an extension of finite fields and $char(E)=2$, then $F$ admits a self-dual normal basis if and only if the exponent of $\Gamma$ is not divisible by $4$. In this paper we construct self-dual normal basis generators for finite extensions of finite fields whenever they exist. Now let $K$ be a finite extension of \Q_p, let $L/K$ be a finite abelian Galois extension of odd degree and let \bo_L be the valuation ring of $L$. We define $A_{L/K}$ to be the unique fractional \bo_L-ideal with square equal to the inverse different of $L/K$. It is known that a self-dual integral normal basis exists for $A_{L/K}$ if and only if $L/K$ is weakly ramified. Assuming $p\neq 2$, we construct such bases whenever they exist

Deciphering solar turbulence from sunspots records

It is generally believed that sunspots are the emergent part of magnetic flux tubes in the solar interior. These tubes are created at the base of the convection zone and rise to the surface due to their magnetic buoyancy. The motion of plasma in the convection zone being highly turbulent, the surface manifestation of sunspots may retain the signature of this turbulence, including its intermittency. From direct observations of sunspots, and indirect observations of the concentration of cosmogenic isotopes $^{14}$C in tree rings or $^{10}$Be in polar ice, power spectral densities in frequency are plotted. Two different frequency scalings emerge, depending on whether the Sun is quiescent or active. %magnetic activity is maximum or minimum. From direct observations we can also calculate scaling exponents. These testify to a strong intermittency, comparable with that observed in the solar wind.Comment: 5 pages, 6 figures, accepted for publication in MNRAS Letter

Optical absorption and photoluminescence spectroscopy of the growth of silver nanoparticles

Results obtained from the optical absorption and photoluminescence (PL) spectroscopy experiments have shown the formation of excitons in the silver-exchanged glass samples. These findings are reported here for the first time. Further, we investigate the dramatic changes in the photoemission properties of the silver-exchanged glass samples as a function of postannealing temperature. Observed changes are thought to be due to the structural rearrangements of silver and oxygen bonding during the heat treatments of the glass matrix. In fact, photoelectron spectroscopy does reveal these chemical transformations of silver-exchanged soda glass samples caused by the thermal effects of annealing in a high vacuum atmosphere. An important correlation between temperature-induced changes of the PL intensity and thermal growth of the silver nanoparticles has been established in this Letter through precise spectroscopic studies.Comment: 15 pages,4 figures,PDF fil

The effect of magnetic impurities in a two-band superconductor: A point-contact study of Mn-substituted MgB2 single crystals

We present the first results of directional point-contact measurements in Mg_{1-x}Mn_{x}B_2 single crystals, with x up to 0.015 and bulk T_c down to 13.3 K. The order parameters Delta_{sigma} and Delta_{pi} were obtained by fitting the conductance curves with the two-band Blonder-Tinkham-Klapwijk (BTK) model. Both Delta_{pi} and Delta_{sigma} decrease with the critical temperature of the junctions T_c^A, but remain clearly distinct up to the highest Mn content. Once analyzed within the Eliashberg theory, the results indicate that spin-flip scattering is dominant in the sigma band, as also confirmed by first-principle band structure calculations.Comment: 4 pages, 5 eps figures. New theoretical results added, text and some figures changed. References adde