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

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

The Software Automation, Generation and Administration (SAGA) project is investigating the design and construction of practical software engineering environments for developing and maintaining aerospace systems and applications software. The research includes the practical organization of the software lifecycle, configuration management, software requirements specifications, executable specifications, design methodologies, programming, verification, validation and testing, version control, maintenance, the reuse of software, software libraries, documentation, and automated management

Age, Growth, Longevity, And Mortality Of Blackcheek Tonguefish, Symphurus Plagiusa (Cynoglossidae : Pleuronectiformes), In Chesapeake Bay, Virginia

Age structure, longevity, and mortality were determined for a population of blackcheek tonguefish, Symphurus plagiusa, in Chesapeake Bay. Blackcheek tonguefish (36-202 mm TL) were randomly collected by means of otter trawl in lower Chesapeake Bay and major Virginia tributaries (James, York, and Rappahannock rivers) from April 1994 through August 1995. Ages were determined by interpreting growth increments on thin transverse sections of sagittal otoliths. Marginal increment analysis showed that a single annulus was formed in June of each year. Blackcheek tonguefish caught during this study reached a maximum age of 5+ years. Growth was rapid during the first year, then slowed rapidly at a time coincident with maturation. We used the following von Bertalanffy growth equations: for males-L-t = 196.5(1- e(-0.285(t + 0.92))); and for females-L-t = 190.6(1 - e(-0.320(t + 0.78))). Von Bertalanffy parameters were not significantly different between sexes. Extrapolated instantaneous mortality rates for a possible seventh year class were 0.73 (Hoenig\u27s equation) and 0.77 (Royce\u27s equation). High estimates of instantaneous total mortality may reflect either loss due to emigration of adults from Chesapeake Bay onto the continental shelf or high natural mortality occurring in this northernmost population. Compared with sympatric pleuronectiforms, blackcheek tonguefish have a relatively high mortality rate, small asymptotic length, and high growth parameter K. Species, such as blackcheek tonguefish, that feature this combination of growth parameters are hypothesized to be better adapted at exploiting seasonally dynamic and highly unpredictable environments, such as those estuarine habitats within Chesapeake Bay