LU factorizations, q=0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q=0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relations which admit a dual system of orthogonal polynomials. For the q=0 orthogonal limit functions we discuss interpretations on p-adic spaces. In the little 0-Jacobi case we also discuss product formulas.Comment: changed title, references updated, minor changes matching the version to appear in Ramanujan J.; 22 p

Central extension of the reflection equations and an analog of Miki's formula

Two different types of centrally extended quantum reflection algebras are introduced. Realizations in terms of the elements of the central extension of the Yang-Baxter algebra are exhibited. A coaction map is identified. For the special case of $U_q(\hat{sl_2})$, a realization in terms of elements satisfying the Zamolodchikov-Faddeev algebra - a `boundary' analog of Miki's formula - is also proposed, providing a free field realization of $O_q(\hat{sl_2})$ (q-Onsager) currents.Comment: 11 pages; two references added; to appear in J. Phys.

Manual pages for SAGA software tools, appendix H

Several pages from the SAGA UNIX programmer's manual are presented. These pages are for SAGA software tools

SAGA: A project to automate the management of software production systems

The project to automate the management of software production systems is described. The SAGA system is a software environment that is designed to support most of the software development activities that occur in a software lifecycle. The system can be configured to support specific software development applications using given programming languages, tools, and methodologies. Meta-tools are provided to ease configuration. Several major components of the SAGA system are completed to prototype form. The construction methods are described

SAGA: A project to automate the management of software production systems

The SAGA system is a software environment that is designed to support most of the software development activities that occur in a software lifecycle. The system can be configured to support specific software development applications using given programming languages, tools, and methodologies. Meta-tools are provided to ease configuration. The SAGA system consists of a small number of software components that are adapted by the meta-tools into specific tools for use in the software development application. The modules are design so that the meta-tools can construct an environment which is both integrated and flexible. The SAGA project is documented in several papers which are presented

Structure of HrcQ(B)-C, a conserved component of the bacterial type III secretion systems

Type III secretion systems enable plant and animal bacterial pathogens to deliver virulence proteins into the cytosol of eukaryotic host cells, causing a broad spectrum of diseases including bacteremia, septicemia, typhoid fever, and bubonic plague in mammals, and localized lesions, systemic wilting, and blights in plants. In addition, type III secretion systems are also required for biogenesis of the bacterial flagellum. The HrcQ(B) protein, a component of the secretion apparatus of Pseudomonas syringae with homologues in all type III systems, has a variable N-terminal and a conserved C-terminal domain (HrcQ(B)-C). Here, we report the crystal structure of HrcQ(B)-C and show that this domain retains the ability of the full-length protein to interact with other type III components. A 3D analysis of sequence conservation patterns reveals two clusters of residues potentially involved in protein–protein interactions. Based on the analogies between HrcQ(B) and its flagellum homologues, we propose that HrcQ(B)-C participates in the formation of a C-ring-like assembly

Implementation of a combined association-linkage model for quantitative traits in linear mixed model procedures of statistical packages

Atransmission disequilibrium test for quantitative traits which combines association and linkage analyses is currently available in several dedicated software packages. We describe how to implement such models in linear mixed model procedures that are available in widely used statistical packages such as SPSS. We also briefly mention a few extensions of the model that become naturally available once the model is implemented in such procedures. Genotyping of many microsatellite markers or single nucleotide polymorphisms (SNPs) over the entire genome is becoming increasingly common in human genetics. In those high-resolution maps the average distance between microsatellite markers may be as small as 5 cM and between SNPs one half cM or less. At those small distances it becomes fairly likely that some markers in the set are in linkage disequilibrium (LD) with a gene affecting the trait (a so-called quantitative trait locus or QTL if the trait or the vulnerability distribution is quantitative). Different alleles or combinations of alleles of the markers or SNPs can then be associated with different trait means. Association studies are conducted to discover such allelic effects. Abecasis et al. (2000) generalized the model proposed by Fulker et al. (1999) for combined linkage and association tests, within and between families. The Fulker-Abecasis or F-A model is implemented in the program QTD

Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm

In papers\cite{js,jsa}, the amplitudes of continuous-time quantum walk on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated to their adjacency matrix. Here in this paper, it is shown that the continuous-time quantum walk on any arbitrary graph can be investigated by spectral distribution method, simply by using Krylov subspace-Lanczos algorithm to generate orthonormal bases of Hilbert space of quantum walk isomorphic to orthogonal polynomials. Also new type of graphs possessing generalized quantum decomposition have been introduced, where this is achieved simply by relaxing some of the constrains imposed on QD graphs and it is shown that both in QD and GQD graphs, the unit vectors of strata are identical with the orthonormal basis produced by Lanczos algorithm. Moreover, it is shown that probability amplitude of observing walk at a given vertex is proportional to its coefficient in the corresponding unit vector of its stratum, and it can be written in terms of the amplitude of its stratum. Finally the capability of Lanczos-based algorithm for evaluation of walk on arbitrary graphs (GQD or non-QD types), has been tested by calculating the probability amplitudes of quantum walk on some interesting finite (infinite) graph of GQD type and finite (infinite) path graph of non-GQD type, where the asymptotic behavior of the probability amplitudes at infinite limit of number of vertices, are in agreement with those of central limit theorem of Ref.\cite{nko}.Comment: 29 pages, 4 figure

A deformed analogue of Onsager's symmetry in the XXZ open spin chain

The XXZ open spin chain with general integrable boundary conditions is shown to possess a q-deformed analogue of the Onsager's algebra as fundamental non-abelian symmetry which ensures the integrability of the model. This symmetry implies the existence of a finite set of independent mutually commuting nonlocal operators which form an abelian subalgebra. The transfer matrix and local conserved quantities, for instance the Hamiltonian, are expressed in terms of these nonlocal operators. It follows that Onsager's original approach of the planar Ising model can be extended to the XXZ open spin chain.Comment: 12 pages; LaTeX file with amssymb; v2: typos corrected, clarifications in the text; v3: minor changes in references, version to appear in JSTA