A family of tridiagonal pairs and related symmetric functions

A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure of their matrix realizations with respect the dual eigenbasis are described. The overlap functions between the two dual basis are shown to satisfy a coupled system of recurrence relations and a set of discrete second-order $q-$difference equations which generalize the ones associated with the Askey-Wilson orthogonal polynomials with a discrete argument. Normalizing the fundamental solution to unity, the hierarchy of solutions are rational functions of one discrete argument, explicitly derived in some simplest examples. The weight function which ensures the orthogonality of the system of rational functions defined on a discrete real support is given.Comment: 17 pages; LaTeX file with amssymb. v2: few minor changes, to appear in J.Phys.A; v3: Minor misprints, eq. (48) and orthogonality condition corrected compared to published versio

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.

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

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

Examining UAS Employment Expectations and Requirements

Unmanned aircraft system (UAS) technology is radically changing how organizations, such as government agencies, non-profit corporations, and companies, apply aviation resources. Unmanned aviation is supporting improved efficiency, expanded capability, and heightened reliability through an increasing number of uses relating to: a) research and development and training-education, b) event filming, c) industrial, utility, and environmental projects, d) real estate, e) construction activities, f) agricultural, g) press and media, and h) state/local emergency services. The increasing application, and subsequent operational growth, is occurring in response to maturing technology, refined operational management and permissibility, innovative concept development, demonstrated capability, enhanced supportability, and the availability of specialized education and training opportunities. Technological advancement, regulatory changes, economic development, and widespread adoption of this technology is also leading to an observable growth of related employment opportunities. The Federal Aviation Administration has indicated that there are currently 116,027 remote pilots certified to operate small UAS in the National Airspace System, with growth to almost 350,000 by 2023. The examination of current career opportunities, in connection with commonly advertised job types and the associated roles and responsibilities, could better inform future UAS curricula design and enhancement efforts. This paper and associated presentation will feature an in-depth examination of such positions to categorize type and summarize prevalent attributes, while also highlighting notable features such as popular hiring locations, salary estimation, and experience-levels. The intent is to provide a detailed summary of hiring expectations and identify potential opportunities for improving academic alignment and career development efforts

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

Structure of the Mg-Chelatase Cofactor GUN4 Reveals a Novel Hand-Shaped Fold for Porphyrin Binding

In plants, the accumulation of the chlorophyll precursor Mg-protoporphyrin IX (Mg-Proto) in the plastid regulates the expression of a number of nuclear genes with functions related to photosynthesis. Analysis of the plastid-to-nucleus signaling activity of Mg-Proto in Arabidopsis thaliana led to the discovery of GUN4, a novel porphyrin-binding protein that also dramatically enhances the activity of Mg-chelatase, the enzyme that synthesizes Mg-Proto. GUN4 may also play a role in both photoprotection and the cellular shuttling of tetrapyrroles. Here we report a 1.78-Å resolution crystal structure of Synechocystis GUN4, in which the porphyrin-binding domain adopts a unique three dimensional fold with a “cupped hand” shape. Biophysical and biochemical analyses revealed the specific site of interaction between GUN4 and Mg-Proto and the energetic determinants for the GUN4 • Mg-Proto interaction. Our data support a novel protective function for GUN4 in tetrapyrrole trafficking. The combined structural and energetic analyses presented herein form the physical-chemical basis for understanding GUN4 biological activity, including its role in the stimulation of Mg-chelatase activity, as well as in Mg-Proto retrograde signaling