Embedding complete binary trees in product graphs

This paper shows how to embed complete binary trees in products of complete binary trees, products of shuffle-exchange graphs, and products of de Bruijn graphs with small dilation and congestion. In the embedding results presented here the size of the host graph can be fixed to an arbitrary size, while we define no bound on the size of the guest graph. This is motivated by the fact that the host architecture has a fixed number of processors due to its physical design, while the guest graph can grow arbitrarily large depending on the application. The results of this paper widen the class of computations that can be performed on these product graphs which are often cited as being low-cost alternatives for hypercubes. © J.C. Baltzer AG, Science Publishers

The Fractionary Schr\"{o}dinger Equation, Green Functions and Ultradistributions

In this work, we generalize previous results about the Fractionary Schr\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate the Green's function for a free particle in the general case, for an arbitrary order of the derivative index.Comment: 32 pages. No figure

On unbounded p-summable Fredholm modules

We prove that odd unbounded p-summable Fredholm modules are also bounded p-summable Fredholm modules (this is the odd counterpart of a result of A. Connes for the case of even Fredholm modules)

Correlations equalities and some upper bounds for the critical temperature for spin one systems

Starting from correlation identities for the Blume-Capel spin 1 systems and using correlation inequalities, we obtain rigorous upper bounds for the critical temperature.The obtained results improve over effective field type results.Comment: 13 page

Clonidina en el tratamiento de la deshabituación tabáquica. Comparación con chicles de nicotina

The objective of our work was to carry out a prospective study on the effectiveness of clonidine and nicotine gum in the treatment of tobacco withdrawal. Sixty smokers were randomly distributed in two groups and were included in a tobacco withdrawal program. One group received oral clonidine treatment while the other group was given nicotine gum. Adjuvant therapy such as group therapy or psychotherapy was not performed. At the end of one year there were no significant differences between the two groups with regards to the number of subjects who have continued to stop smoking. There were also no significant differences between the two groups with regards to the symptoms of tobacco abstinence. When we studied the relation between treatment fulfillment and tobacco withdrawal we observed that the clonidine treated group had a significantly greater number of success compared to the nicotine group (p < 0.01)

Star formation histories in mergers: the spatially resolved properties of the early-stage merger luminous infrared galaxies IC 1623 and NGC 6090

The role of major mergers in galaxy evolution is investigated through a detailed characterization of the stellar populations, ionized gas properties and star formation rates (SFR) in the early-stage merger luminous infrared galaxies (LIRGs) IC 1623 W and NGC 6090, by analysing optical integral field spectroscopy and high-resolution Hubble Space Telescope imaging. The spectra were processed with the starlight full spectral fitting code, and the emission lines measured in the residual spectra. The results are compared with non-interacting control spiral galaxies from the Calar Alto Legacy Integral Field Area survey. Merger-induced star formation is extended and recent, as revealed by the young ages (50–80 Myr) and high contributions to light of young stellar populations (50–90 per cent), in agreement with merger simulations in the literature. These early-stage mergers have positive central gradients of the stellar metallicity, with an average ∼0.6 Z⊙. Compared to non-interacting spirals, they have lower central nebular metallicity, and flatter profiles, in agreement with the gas inflow scenario. We find that they are dominated by star formation, although shock excitation cannot be discarded in some regions, where high velocity dispersion is found (170–200 km s−1). The average SFR in these early-stage mergers (∼23–32 M⊙ yr−1) is enhanced with respect to main-sequence Sbc galaxies by factors of 6–9, slightly above the predictions from classical merger simulations, but still possible in about 15 per cent of major galaxy mergers, where U/LIRGs belong

Reconfigurable surfaces using fringing electric fields from nanostructured electrodes in nematic liquid crystals

Liquid crystals with a varying phase profile enable reconfigurable and intelligent devices to be designed, which are capable of manipulating incident electromagnetic fields in display, telecommunications as well as wearable applications. The active control of defects in these devices is becoming more important, especially since the electrodes used to manipulate them are shrinking to nanometer length scales. In this paper, a simple subwavelength, 1D, interdigitated metal electrode structure that can be reconfigured using nematic liquid crystals aligned in the homeotropic, planar, and hybrid methods are demonstrated. Accurate electro‐optic modeling of the directors and the defects are shown, which are induced by the fringing electric fields. Applied voltages result in liquid crystal reorientation near the bottom surface, such that defects are induced between the electrodes. The height of the electrodes does not affect the lateral position of these defects. Rather, this can be achieved by increasing the biasing voltage on the top electrode, which also leads to greater splay‐bend in the bulk of the material. These results therefore aim to generalize the control of defects in complex anisotropic nematic liquid crystals using simple interdigitated structures for a range of reconfigurable intelligent surface applications

Introducing Small-World Network Effect to Critical Dynamics

We analytically investigate the kinetic Gaussian model and the one-dimensional kinetic Ising model on two typical small-world networks (SWN), the adding-type and the rewiring-type. The general approaches and some basic equations are systematically formulated. The rigorous investigation of the Glauber-type kinetic Gaussian model shows the mean-field-like global influence on the dynamic evolution of the individual spins. Accordingly a simplified method is presented and tested, and believed to be a good choice for the mean-field transition widely (in fact, without exception so far) observed on SWN. It yields the evolving equation of the Kawasaki-type Gaussian model. In the one-dimensional Ising model, the p-dependence of the critical point is analytically obtained and the inexistence of such a threshold p_c, for a finite temperature transition, is confirmed. The static critical exponents, gamma and beta are in accordance with the results of the recent Monte Carlo simulations, and also with the mean-field critical behavior of the system. We also prove that the SWN effect does not change the dynamic critical exponent, z=2, for this model. The observed influence of the long-range randomness on the critical point indicates two obviously different hidden mechanisms.Comment: 30 pages, 1 ps figures, REVTEX, accepted for publication in Phys. Rev.