Discrete Darboux transformation for discrete polynomials of hypergeometric type

Darboux Transformation, well known in second order differential operator theory, is applied here to the difference equation satisfied by the discrete hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn)

Field evaluation of the CATT/Trypanosoma brucei gambiense on blood-impregnated filter papers for diagnosis of human African trypanosomiasis in southern Sudan.

Most Human African Trypanosomiasis (HAT) control programmes in areas endemic for Trypanosoma brucei gambiense rely on a strategy of active mass screening with the Card Agglutination Test for Trypanosomiasis (CATT)/T. b. gambiense. We evaluated the performance, stability and reproducibility of the CATT/T. b. gambiense on blood-impregnated filter papers (CATT-FP) in Kajo-Keji County, South-Sudan, where some areas are inaccessible to mobile teams. The CATT-FP was performed with a group of 100 people with a positive CATT on whole blood including 17 confirmed HAT patients and the results were compared with the CATT on plasma (CATT-P). The CATT-FP was repeated on impregnated filter papers stored at ambient and refrigerated temperature for 1, 3, 7 and 14 days. Another 82 patients with HAT, including 78 with a positive parasitology, were tested with the CATT-FP and duplicate filter paper samples were sent to a reference laboratory to assess reproducibility. The CATT-FP was positive in 90 of 99 patients with HAT (sensitivity: 91%). It was less sensitive than the CATT-P (mean dilution difference: -2.5). There was no significant loss of sensitivity after storage for up to 14 days both at ambient and cool temperature. Reproducibility of the CATT-FP was found to be excellent (kappa: 0.84). The CATT-FP can therefore be recommended as a screening test for HAT in areas where the use of CATT-P is not possible. Further studies on larger population samples in different endemic foci are still needed before the CATT-FP can be recommended for universal use

Specular sets

We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract generalization of the natural codings of linear involutions. We prove several results concerning the subgroups generated by return words and by maximal bifix codes in these sets.Comment: arXiv admin note: substantial text overlap with arXiv:1405.352

Superembeddings, Non-Linear Supersymmetry and 5-branes

We examine general properties of superembeddings, i.e., embeddings of supermanifolds into supermanifolds. The connection between an embedding procedure and the method of non-linearly realised supersymmetry is clarified, and we demonstrate how the latter arises as a special case of the former. As an illustration, the super-5-brane in 7 dimensions, containing a self-dual 3-form world-volume field strength, is formulated in both languages, and provides an example of a model where the embedding condition does not suffice to put the theory on-shell.Comment: plain tex, 28 p

Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity

We address the issue of mobility of localized modes in two-dimensional nonlinear Schr\"odinger lattices with saturable nonlinearity. This describes e.g. discrete spatial solitons in a tight-binding approximation of two-dimensional optical waveguide arrays made from photorefractive crystals. We discuss numerically obtained exact stationary solutions and their stability, focussing on three different solution families with peaks at one, two, and four neighboring sites, respectively. When varying the power, there is a repeated exchange of stability between these three solutions, with symmetry-broken families of connecting intermediate stationary solutions appearing at the bifurcation points. When the nonlinearity parameter is not too large, we observe good mobility, and a well defined Peierls-Nabarro barrier measuring the minimum energy necessary for rendering a stable stationary solution mobile.Comment: 19 pages, 4 figure

Reheating induced by competing decay modes

We address the problem of studying the decay of the inflaton field $\phi$ to another scalar field $\chi$ through parametric resonance in the case of a coupling that involves several decay modes. This amounts to the presence of extra harmonic terms in the perturbation of the $\chi$ field dynamics. For the case of two frequencies we compute the geometry of the resonance regions, which is significantly altered due to the presence of non-cuspidal resonance regions associated to higher harmonics and to the emergence of instability `pockets'. We discuss the effect of this change in the efficiency of the energy transfer process for the simplest case of a coupling given by a combination of the two interaction terms of homogeneous degree usually considered in the literature. We find that the presence of higher harmonics has limited cosmological implications.Comment: 14 pages, 4 figures Added references. Corrected typo

Actions of the braid group, and new algebraic proofs of results of Dehornoy and Larue

This article surveys many standard results about the braid group with emphasis on simplifying the usual algebraic proofs. We use van der Waerden's trick to illuminate the Artin-Magnus proof of the classic presentation of the algebraic mapping-class group of a punctured disc. We give a simple, new proof of the Dehornoy-Larue braid-group trichotomy, and, hence, recover the Dehornoy right-ordering of the braid group. We then turn to the Birman-Hilden theorem concerning braid-group actions on free products of cyclic groups, and the consequences derived by Perron-Vannier, and the connections with the Wada representations. We recall the very simple Crisp-Paris proof of the Birman-Hilden theorem that uses the Larue-Shpilrain technique. Studying ends of free groups permits a deeper understanding of the braid group; this gives us a generalization of the Birman-Hilden theorem. Studying Jordan curves in the punctured disc permits a still deeper understanding of the braid group; this gave Larue, in his PhD thesis, correspondingly deeper results, and, in an appendix, we recall the essence of Larue's thesis, giving simpler combinatorial proofs.Comment: 51`pages, 13 figure

Constraining ^(26)Al+p resonances using ^(26)Al(^3He,d)^(27)Si

The ^(26)Al(^3He,d)^(27)Si reaction was measured from 0°≤θ_(c.m.)≤35° at E(^3He)=20 MeV using a quadrupole-dipole-dipole-dipole magnetic spectrometer. States in ^(27)Si were observed above the background at 7652 and 7741 keV and upper limits were set for the state at 7592 keV. Implications for the ^(26)Al(p,γ)^(27)Si stellar reaction rate are discussed

Two-Hole Bound States from a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet

Identifying the correct low-energy effective theory for magnons and holes in an antiferromagnet has remained an open problem for a long time. In analogy to the effective theory for pions and nucleons in QCD, based on a symmetry analysis of Hubbard and t-J-type models, we construct a systematic low-energy effective field theory for magnons and holes located inside pockets centered at lattice momenta (\pm pi/2a,\pm pi/2a). The effective theory is based on a nonlinear realization of the spontaneously broken spin symmetry and makes model-independent universal predictions for the entire class of lightly doped antiferromagnetic precursors of high-temperature superconductors. The predictions of the effective theory are exact, order by order in a systematic low-energy expansion. We derive the one-magnon exchange potentials between two holes in an otherwise undoped system. Remarkably, in some cases the corresponding two-hole Schr\"odinger equations can even be solved analytically. The resulting bound states have d-wave characteristics. The ground state wave function of two holes residing in different hole pockets has a d_{x^2-y^2}-like symmetry, while for two holes in the same pocket the symmetry resembles d_{xy}.Comment: 35 pages, 11 figure