Multilateral inversion of A_r, C_r and D_r basic hypergeometric series

In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix inversion result was directly extracted from an instance of Bailey's very-well-poised 6-psi-6 summation theorem, and involves two infinite matrices which are not lower-triangular. The present paper features three different multivariable generalizations of the above result. These are extracted from Gustafson's A_r and C_r extensions and of the author's recent A_r extension of Bailey's 6-psi-6 summation formula. By combining these new multidimensional matrix inverses with A_r and D_r extensions of Jackson's 8-phi-7 summation theorem three balanced very-well-poised 8-psi-8 summation theorems associated with the root systems A_r and C_r are derived.Comment: 24 page

The development and application of aerodynamic uncertainties: And flight test verification for the space shuttle orbiter

The approach used in establishing the predicted aerodynamic uncertainties and the process used in applying these uncertainties during the design of the Orbiter flight control system and the entry trajectories are presented. The flight test program that was designed to verify the stability and control derivatives with a minimum of test flights is presented and a comparison of preflight predictions with preliminary flight test results is made. It is concluded that the approach used for the Orbiter is applicable to future programs where testing is limited due to time constraints or funding

On an identity of Chaundy and Bullard. III. Basic and elliptic extensions

The identity by Chaundy and Bullard expresses $1$ as a sum of two truncated binomial series in one variable where the truncations depend on two different non-negative integers. We present basic and elliptic extensions of the Chaundy--Bullard identity. The most general result, the elliptic extension, involves, in addition to the nome $p$ and the base $q$, four independent complex variables. Our proof uses a suitable weighted lattice path model. We also show how three of the basic extensions can be viewed as B\'ezout identities. Inspired by the lattice path model, we give a new elliptic extension of the binomial theorem, taking the form of an identity for elliptic commuting variables. We further present variants of the homogeneous form of the identity for $q$-commuting and for elliptic commuting variables.Comment: 22 pages, dedicated to the memory of Richard Allen Askey; minor change

Relationship Between Body Satisfaction and Exercise Behavior: A Cross Cultural Comparison

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Alteração do campo visual em função do uso de cabinas em tratares agrícolas.

Com o objetivo de avaliar a alteração do campo visual de um trator, ocasionada pela instalação de uma cabina, foram determinadas as áreas de visibilidade nula em função da presença ou não da mesma, para cada campo visual. Os procedimentos adotados basearam-se na norma ISO 5721-1981 - Agricultural tractors - Operator's field of vision. A cabina aumentou em 34,42% a área de visibilidade nula. A relação área de projeção do trator/área total sombreada foi de 0,075 para o trator sem cabina, e 0,057 para o trator com cabina, indicando as melhores condições de visibilidade do primeiro em relação ao segundo. No que se refere aos campos visuais, a maior redução ocorreu no campo visual dos olhos e no obtido com o movimento da cabeça, em função dos suportes da cabina e da estrutura de proteção contra o capotamento. A cabina diminui o campo de visão do operador, e adequações no projeto da estrutura avaliada são necessárias para melhorar as condições de visibilidade. ALTERATION OF THE VISUAL FIELD IN FUNCTION OF THE USE OF CABINS IN AGRICULTURAL TRACTORS. Aiming to evaluate the alteration of the visual field of a tractor occasioned by the installation of a cabin were determined the null visibility areas due to the presence or not of this structure, for each visual field. The procedures adopted were based on ISO 5721-1981 - Agricultural tractors - Operator's field of vision. The cabin increased in 34,42% the area of null visibility. The relationship projection area of tractor/total shadowed area was 0,075 to the tractor without a cabin, and 0,057 for the tractor with cabin, indicating the best conditions of visibility of the first in relation to the second. With respect to the visual area, the largest reduction happened in the eyes visual field and in the obtained with the head movement in function of the cabin supports and the rollover protection structure. The cabin decreases the operator?s area of vision, and adjustments in the project of the structure evaluated are necessary to improve the visibility conditions

On an identity by Chaundy and Bullard. I

An identity by Chaundy and Bullard writes 1/(1-x)^n (n=1,2,...) as a sum of two truncated binomial series. This identity was rediscovered many times. Notably, a special case was rediscovered by I. Daubechies, while she was setting up the theory of wavelets of compact support. We discuss or survey many different proofs of the identity, and also its relationship with Gauss hypergeometric series. We also consider the extension to complex values of the two parameters which occur as summation bounds. The paper concludes with a discussion of a multivariable analogue of the identity, which was first given by Damjanovic, Klamkin and Ruehr. We give the relationship with Lauricella hypergeometric functions and corresponding PDE's. The paper ends with a new proof of the multivariable case by splitting up Dirichlet's multivariable beta integral.Comment: 20 pages; added in v3: more references to earlier occurrences of the identity and its multivariable analogue, combinatorial proof of the identity and extension to noninteger m,n, proof of multivariable identity by splitting up Dirichlet's multivariable beta integra

Anti-phospholipid-antibodies in patients with relapsing polychondritis

Relapsing polychondritis (RP) is an extremly rare multisystemic disease thought to be of autoimmune origin. In order to assess if RP is associated with anti-phospholipid antibodies (aPL), clinical data and sera of 21 patients with RP were collected in a multicentre study. Concentration of anti-cardiolipin antibodies (aCL) (IgG-, IgM-and IgA-isotypes), anti-phosphatidylserine-antibodies (aPS) (IgG-and IgM-isotypes) and anti-β-2-glycoprotein I-antibodies (aβ2 GPI) were measured by ELISA. In eight patients aCL were found to be elevated. One patient had elevated aPS. No patient had elevated aβ2 GPI. No patient had clinical signs and symptoms of a aPL syndrome. Interestingly, the two RP patients with the highest aPL had concomitant systemic lupus erythematosus (SLE). Therefore the presence of elevated aPL in RP is probably more closely related to an associated SLE than to RP itself. There is no convincing evidence that aPL are associated with RP