Combinatorics of lattice paths with and without spikes

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are useful when performing strong coupling (hopping parameter) expansions of lattice models. Some applications are described.Comment: Latex. 25 page

Confinement of electrons in layered metals

We analyze the out of plane hopping in models of layered systems where the in--plane properties deviate from Landau's theory of a Fermi liquid. We show that the hopping term acquires a non trivial energy dependence, due to the coupling to in plane excitations, and can be either relevant or irrelevant at low energies or temperatures. The latter is always the case if the Fermi level lies close to a saddle point in the dispersion relation.Comment: 4 pages, 1 eps figur

Comparative aspects of phytase and xylanase effects on performance, mineral digestibility, and ileal phytate degradation in broilers and turkeys

Two experiments were performed, using broilers or turkeys, each utilizing a 3 × 2 factorial arrangement, to compare their response to phytase and xylanase supplementation with growth performance, nutrient digestibility, and ileal phytate degradation as response criteria. For both experiments, 960 Ross 308 or 960 BUT 10 (0-day-old) birds were allocated to 6 treatments: (1) control diet, containing phytase at 500 FTU/kg; (2) the control diet with xylanase (16,000 BXU/kg); (3) the control diet supplemented on top with phytase (1,500 FTU/kg); (4) diet supplemented with 1,500 FTU/kg phytase and xylanase (16,000 BXU/kg); (5) the control diet supplemented with phytase (3,000 FTU/kg); and (6) diet supplemented with 3,000 FTU/kg phytase and xylanase (16,000 BXU/kg). Each treatment had 8 replicates of 20 birds each. Water and diets based on wheat, soybean meal, oilseed rape meal, and barley were available ad libitum. Body weight gain and feed intake were measured from 0 to 28 D, and feed conversion ratio (FCR) corrected for mortality was calculated. Ileal digestibility for dry matter and minerals on day 7 and 28 were analyzed in addition to levels of inositol phosphate esters (InsP6-3) and myo-inositol. Statistical comparisons were performed using ANOVA. Xylanase supplementation improved 28D FCR in broilers and turkeys. Increasing doses of phytase reduced FI and improved FCR only in broilers. In broilers, the age × phytase interaction for phosphorous digestibility showed that increasing phytase dose was more visible on day 7, than on day 28. Mineral digestibility was lower in 28-day-old turkey compared with 7-day-old turkey. InsP6 disappearance increased with increasing phytase levels in both species, with lower levels analyzed in turkeys. InsP6 disappearance was greater in younger turkeys (day 7 compared with day 28). In conclusion, although broilers and turkeys shared several similarities in their growth and nutrient utilization responses, the outcomes of the 2 trials also differed in many aspects. Whether this is because of difference in diets (InsP or Ca level) or differences between species needs further investigation

Anisotropic Fermi surfaces and Kohn-Luttinger superconductivity in two dimensions

The instabilities induced on a two-dimensional system of correlated electrons by the anisotropies of its Fermi line are analyzed on general grounds. Simple scaling arguments allow to predict the opening of a superconducting gap with a well-defined symmetry prescribed by the geometry of the Fermi line. The same arguments predict a critical dimension of 3/2 for the transition of the two-dimensional system to non-Fermi liquid behavior. The methods are applied to the t-t' Hubbard model in a wide range of dopings.Comment: 25 pages, 13 postscript figure

On the families of orthogonal polynomials associated to the Razavy potential

We show that there are two different families of (weakly) orthogonal polynomials associated to the quasi-exactly solvable Razavy potential V(x)=(\z \cosh 2x-M)^2 (\z>0, $M\in\mathbf N$). One of these families encompasses the four sets of orthogonal polynomials recently found by Khare and Mandal, while the other one is new. These results are extended to the related periodic potential U(x)=-(\z \cos 2x -M)^2, for which we also construct two different families of weakly orthogonal polynomials. We prove that either of these two families yields the ground state (when $M$ is odd) and the lowest lying gaps in the energy spectrum of the latter periodic potential up to and including the $(M-1)^{\rm th}$ gap and having the same parity as $M-1$. Moreover, we show that the algebraic eigenfunctions obtained in this way are the well-known finite solutions of the Whittaker--Hill (or Hill's three-term) periodic differential equation. Thus, the foregoing results provide a Lie-algebraic justification of the fact that the Whittaker--Hill equation (unlike, for instance, Mathieu's equation) admits finite solutions.Comment: Typeset in LaTeX2e using amsmath, amssymb, epic, epsfig, float (24 pages, 1 figure

Soliton tunneling with sub-barrier kinetic energies

We investigate (theoretically and numerically) the dynamics of a soliton moving in an asymmetrical potential well with a finite barrier. For large values of the width of the well, the width of the barrier and/or the height of the barrier, the soliton behaves classically. On the other hand, we obtain the conditions for the existence of soliton tunneling with sub-barrier kinetic energies. We apply these results to the study of soliton propagation in disordered systems.Comment: 6 eps figures. To appear in Physical Review E (Rapid Communications

OTELO survey: optimal emission-line flux determination with OSIRIS/GTC

Emission-line galaxies are important targets for understanding the chemical evolution of galaxies in the universe. Deep, narrow-band imaging surveys allow to detect and study the flux and the equivalent widths (EW) of the emission line studied. The present work has been developed within the context of the OTELO project, an emission line survey using the Tunable Filters (TF) of OSIRIS, the first generation instrument on the GTC 10.4m telescope located in La Palma, Spain, that will observe through selected atmospheric windows relatively free of sky emission lines. With a total survey area of 0.1 square degrees distributed in different fields, reaching a 5 \sigma depth of 10^-18 erg/cm^2/s and detecting objects of EW < 0.3 A, OTELO will be the deepest emission line survey to date. As part of the OTELO preparatory activities, the objective of this study is to determine the best combination of sampling and full width at half maximum (FWHM) for the OSIRIS tunable filters for deblending H\alpha from [NII] lines by analyzing the flux errors obtained. We simulated the OTELO data by convolving a complete set of synthetic HII galaxies in EW with different widths of the OSIRIS TFs. We estimated relative flux errors of the recovered H\alpha and [NII]6583 lines. We found that, for the red TF, a FWHM of 12 A and a sampling of 5 A is an optimal combination that allow deblending H\alpha from the [NII]6583 line with a flux error lower than 20%. This combination will allow estimating SFRs and metallicities using the H\alpha flux and the N2 method, respectively.Comment: 16 pages, 9 figures. Some authors added. Accepted for publication in PAS

Present and future of the OTELO project

OTELO is an emission-line object survey carried out with the red tunable filter of the instrument OSIRIS at the GTC, whose aim is to become the deepest emission-line object survey to date. With 100% of the data of the first pointing finally obtained in June 2014, we present here some aspects of the processing of the data and the very first results of the OTELO survey. We also explain the next steps to be followed in the near future.Comment: Oral contribution presented in the XI Scientific Meeting of the Spanish Astronomical Society held on September 8-12, in Teruel, Spain (7 pages, 2 figures, 1 table). To appear in Highlights of Spanish Astrophysics VIII, Proceedings of the XI Scientific Meeting of the Spanish Astronomical Society. Eds. A. J. Cenarro, F. Figueras, C. Hern\'andez-Monteagudo, J. Trujillo, L. Valdiviels

On Existence of a Biorthonormal Basis Composed of Eigenvectors of Non-Hermitian Operators

We present a set of necessary conditions for the existence of a biorthonormal basis composed of eigenvectors of non-Hermitian operators. As an illustration, we examine these conditions in the case of normal operators. We also provide a generalization of the conditions which is applicable to non-diagonalizable operators by considering not only eigenvectors but also all root vectors.Comment: 6 pages, no figures; (v2) minor revisions based on the comment quant-ph/0603096; (v3) presentation improved, final version to appear in Journal of Physics