Similarity of Operators in the Bergman Space Setting

We give a necessary and sufficient condition for an n-hypercontraction to be similar to the backward shift operator in a weighted Bergman space. This characterization serves as a generalization of the description given in the Hardy space setting, where the geometry of the eigenvector bundles of the operators is used

Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation

We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary condition. Equipped with this formulation, we go on to establish the well-posedness of entropy solutions to the initial-boundary value problem. The proof utilizes the kinetic formulation and the compensated compactness method. Finally, we make use of these results to demonstrate the well-posedness in a class of discontinuous solutions to the initial-boundary value problem for the Degasperis-Procesi shallow water equation, which is a third order nonlinear dispersive equation that can be rewritten in the form of a nonlinear conservation law with a nonlocal source term.Comment: 24 page

Influence of Dzyaloshinskii-Moriya interactions on magnetic structure of a spin-1/2 deformed kagome lattice antiferromagnet

Motivated by the recent neutron scattering experiment on Rb2Cu3SnF12 [Nat. Phys. 6, 865 (2010)], we investigate the effect of Dzyaloshinskii-Moriya interactions in a theoretical model for the magnetic structure of this material. Considering the valence bond solid ground state, which has a 12-site unit cell, we develop the bond operator mean-field theory. It is shown that the Dzyaloshinskii-Moriya interactions significantly modify the triplon dispersions around the Gamma point and cause a shift of the spin gap (the minimum triplon gap) position from the K to Gamma point in the first Brilloin zone. The spin gap is also evaluated in exact diagonalization studies on a 24-site cluster. We discuss a magnetic transition induced by the Dzyaloshinskii-Moriya interactions in the bond operator framework. Moreover, the magnetization process under external magnetic fields is studied within the exact diagonalization and strong coupling expansion approaches. We find that the results of all above approaches are consistent with the experimental findings.Comment: 14 pages, 10 figures; typos corrected, and acknowledgements and references adde

An Adaptive Algorithm to Optimize the Dynamics of IEEE 802.15.4 Networks

Presentado en ICST 2013IEEE 802.15.4 standard is becoming one of the most popular technologies for the deployment of low rate Wireless Personal Area Networks with strong power constraints. In order to reduce the energy consumption, beacon-enabled networks with long network inactive periods can be employed. However, the duration of these inactivity periods, as some other configuration parameters, are conventionally set to default values and remain fixed during the whole network operation. This implies that if they are misconfigured the network will not adapt to changes in the conditions of the environment, particularly to the most determining one, i.e. the traffic load. This paper proposes a simple procedure for the dynamic adaptation of several key parameters of IEEE 802.15.4 networks. Under this procedure, the 802.15.4 parameters are modified as a function of the existing traffic conditions.Spanish National Project No.TEC2009-13763-C02-01

Orientational Melting in Carbon Nanotube Ropes

Using Monte Carlo simulations, we investigate the possibility of an orientational melting transition within a "rope" of (10,10) carbon nanotubes. When twisting nanotubes bundle up during the synthesis, orientational dislocations or twistons arise from the competition between the anisotropic inter-tube interactions, which tend to align neighboring tubes, and the torsion rigidity that tends to keep individual tubes straight. We map the energetics of a rope containing twistons onto a lattice gas model and find that the onset of a free "diffusion" of twistons, corresponding to orientational melting, occurs at T_OM > 160 K.Comment: 4 page LaTeX file with 3 figures (10 PostScript files

Extending Romanovski polynomials in quantum mechanics

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally-extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties of second-order differential equations of Schr\"odinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.Comment: 25 pages, no figure, small changes, 3 additional references, published versio

Critical renormalized coupling constants in the symmetric phase of the Ising models

Using a novel finite size scaling Monte Carlo method, we calculate the four, six and eight point renormalized coupling constants defined at zero momentum in the symmetric phase of the three dimensional Ising system. The results of the 2D Ising system that were directly measured are also reported. Our values of the six and eight point coupling constants are significantly different from those obtained from other methods.Comment: 7 pages, 2 figure