A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Predictive formulas for food base excess and urine pH estimations of cats

Food base excess (BE, mEq/kg) can be calculated from the diet macroelements, together with either the sulfur amino acids methionine and cysteine (BEaa) or total sulfur (BEs) concentrations. The present study compared the use of sulfur or methionine and cysteine for calculating the food BE (experiment 1) and investigated the influence of food BE on blood gas analysis and the urine pH of cats, and proposes a prediction equation to estimate the urine pH of cats fed kibble diets based on the calculated food BE (experiments 2 and 3). In experiment 1, nine healthy, adult cats were used in a change-over design and fed with nine commercial dry cat foods. The cats were housed in metabolism cages over seven days for adaptation and three days for total urine collection. All of the urine produced over 24h was pooled by cat and diet. The cats' acid-base status was assessed through blood gas analysis after 10 days of diet consumption. A mean difference of -115mEq/kg between BEs and BEaa was observed, which could be explained by a greater concentration of sulfur in the whole diet than in methionine and cysteine. Urine pH presented a stronger correlation with food BEs (R2=0.95; P<0.001) than with food BEaa (R2=0.86; P<0.001). Experiment 2 included 30 kibble diets, and each diet was tested in six cats. The food BEs varied between -180 and +307mEq/kg, and the urine pH of the cats varied between 5.60 and 7.74. A significant correlation was found between the measured urine pH and the food BEs (urinary pH=6.269+[0.0036×BEs]+[0.000003×BEs2]; R2=0.91; P<0.001). In experiment 3, eight kibble diets were tested (food BEs between -187mEq/kg and +381mEq/kg) to validate the equation proposed in experiment 2 and to compare the obtained results with previously published formulae. The results of the proposed formula presented a high concordance correlation coefficient (0.942) and high accuracy (0.979) with the measured values, and the estimates of urine pH did not differ from the values obtained in cats (P>0.05). The cats' venous blood pH, bicarbonate, and blood BE were correlated with food BEs (P<0.001); the consumption of diets with low food BEs induced a reduction in these parameters. In conclusion, food macroelement composition has a strong influence on cats' acid-base equilibrium and food BEs calculation is a useful tool to formulate and balance kibble diets for felines. © 2013 Elsevier B.V.

Orthogonality relations and supercharacter formulas of U(m vertical bar n) representations

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m + n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented. © 1997 American Institute of Physics.

Avaliação da qualidade de calcários agrícolas através do PRNT

Foram comparados os valores do PRNT de calcários agrícolas, empregando fórmulas que se baseiam em diferentes valores de eficiência relativa das frações granulométricas que compõem esses materiais. Foram utilizadas 22 amostras de calcários, sendo 12 de Rio Claro, Piracicaba e Tietê, Estado de São Paulo e as demais especialmente escolhidas visando variação nas composições granulométrica e química. Os resultados sugerem que as fórmulas de PRNT que têm sido utilizadas no Brasil , devem estar substimando a eficiência desses produtos , além de carecerem de um respaldo experimental mais convincente. A nova fórmula proposta pode ser mais confiável, apesar de estar também sujeita a várias críticas.

Método não destrutivo de estimativa da área foliar de plantas daninhas de ambiente aquático: tanner-grass e capim-fino

The continuous inputs from agriculture areas and human or industrial sewer have been provided a widely demographic explosion of tropical tanner-grass and para grasss plants in the rivers and water reservoirs of Brazil. Considering the importance of these noxious weeds there is a vast necessity of basic studies on aspects related to reproduction, growing, development, nutritional requirements, responses to control systems and others. In most studies, leaf area knowledge is crucial and it is one of the most difficult characteristics to be measured because it usually requires expensive equipments or it uses a destructive technique. The objective of this work was to develop equations for leaf blade dimensional parameters to allow determination of the leaf area of African tanner-grass (Brachiaria subquadripara (Trin.) Hitchc) and para grass (Brachiaria mutica (Forsk.) Stapf.). Correlations between real leaf area and dimensional parameters of leaf blade such as length along the main vein (L) and maximum width (W) perpendicular to the main axis were studied. Only the linear equations allowed a good leaf area estimate. It is suggested to opt for a simple linear equation involving respective products of length times maximum width considering linear coefficient equal to zero. Thus, B. subquadripara (SS) and B. mutica (SM) non destructive leaf blade area estimates may be performed by the following formulas: SS = 0.7719 (L x W) and SM = 0.7479 (L x W), with coefficients of determination (R(2)) of 0.9594 and 0.9408, respectively.

6-Mercaptopurine complexes with silver and gold ions: Anti-tuberculosis and anti-cancer activities

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Cistatina C e taxa de filtração glomerular em cirurgia cardíaca com circulação extracorpórea

OBJETIVO: Avaliar a cistatina C como marcador de função renal em pacientes submetidos à cirurgia de cardíaca com circulação extracorpórea, comparando com a dosagem sérica de creatinina. MÉTODOS: Foram analisados 50 pacientes consecutivos submetidos à cirurgia de revascularização do miocárdio. A função renal foi avaliada com a dosagem sérica de cistatina C e de creatinina no pré-operatório, no primeiro e no quinto dia de pós-operatório. Foram utilizadas as fórmulas de Cockcroft-Gault (CG) e Modification of Diet in Renal Disease (MDRD) para calcular a taxa de filtração glomerular estimada (TFG) através da creatinina, e a fórmula de Larsson para a TFG estimada através da cistatina C (TFG-Cis). RESULTADOS: A creatinina e o TFG através das fórmulas de CG e MDRD não mostraram diferença significativa nos momentos estudados. Após a agressão renal pela cirurgia, houve um aumento da cistatina C no 1º e 5º pós-operatório, sendo que no 5º pós-operatório com diferença estatisticamente significativa (P < 0,01). Houve uma queda da TFG estimada pela cistatina C de 105,2 ± 41,0 ml/min, no pré-operatório, para 89,5 ± 31,5 ml/min no 5º dia pós-operatório (P < 0,012). CONCLUSÃO: A cistatina C e a TFG-Cis apresentaram mudanças significativas no pós-operatório de cirurgia de revascularização do miocárdio quando comparadas a creatinina e a respectiva TFG estimada pelas fórmulas de Cockcroft-Gault e MDRD

Mensurações do bulbo ocular e cálculo do poder dióptrico de lentes intraoculares em coelhos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Análise de Bolton: uma proposta alternativa para a simplificação de seu uso

INTRODUÇÃO: as discrepâncias entre o tamanho mesiodistal dos dentes superiores e inferiores e seus efeitos sobre a oclusão têm sido relatados há muito tempo. O método proposto por Bolton para o diagnóstico de discrepância de tamanho dentário é, inegavelmente, um dos mais difundidos no meio ortodôntico, devido à sua relativa simplicidade. Entretanto, a aplicação desse método requer cálculos matemáticos e o uso de tabelas que, muitas vezes, inviabilizam a sua utilização durante a avaliação clínica. OBJETIVO: avaliar o método proposto por Wolford, que não requer o uso de tabelas, como alternativa ao método tradicional de Bolton. MÉTODOS: a amostra foi composta por 90 pares de modelos dentários iniciais de pacientes adultos, com diferentes más oclusões. A proporção entre os dentes inferiores e superiores foi calculada para cada paciente, resultando na obtenção de dois índices (a razão total e a razão anterior). Os índices foram obtidos por meio do método originalmente proposto por Bolton e por um método alternativo, composto por duas fórmulas (uma simplificada e a variação da mesma), que foram analisadas separadamente. RESULTADOS: comparadas ao método de Bolton, as fórmulas simplificadas mostraram uma tendência de superestimar as discrepâncias dentárias inferiores (total e anterior), embora em pequena proporção. CONCLUSÕES: ambas as fórmulas do método alternativo podem ser utilizadas em substituição ao método tradicional, uma vez que mostraram diferenças médias menores que 0,58mm quando comparadas ao método de Bolton, não apresentando, portanto, significância clínica.

Respostas do lactato sanguíneo e da freqüência cardíaca em duas diferentes provas do automobilismo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

One-loop N-point superstring amplitudes with manifest d=4 supersymmetry

The hybrid formalism for the superstring is used to compute one-loop amplitudes with an arbitrary number of external d = 4 supergravity states. These one-loop N-point amplitudes are expressed as Koba-Nielsen-like formulas with manifest d = 4 supersymmetry. (C) 2002 Published by Elsevier B.V. B.V.

Critical temperature for first-order phase transitions in confined systems

We consider the Euclidean D-dimensional -lambda vertical bar phi vertical bar(4)+eta vertical bar rho vertical bar(6) (lambda,eta > 0) model with d (d <= D) compactified dimensions. Introducing temperature by means of the Ginzburg-Landau prescription in the mass term of the Hamiltonian, this model can be interpreted as describing a first-order phase transition for a system in a region of the D-dimensional space, limited by d pairs of parallel planes, orthogonal to the coordinates axis x(1), x(2),..., x(d). The planes in each pair are separated by distances L-1, L-2, ... , L-d. We obtain an expression for the transition temperature as a function of the size of the system, T-c({L-i}), i = 1, 2, ..., d. For D = 3 we particularize this formula, taking L-1 = L-2 = ... = L-d = L for the physically interesting cases d = 1 (a film), d = 2 (an infinitely long wire having a square cross-section), and for d = 3 (a cube). For completeness, the corresponding formulas for second-order transitions are also presented. Comparison with experimental data for superconducting films and wires shows qualitative agreement with our theoretical expressions.

Dynamics of Bose-Einstein condensates in cigar-shaped traps

The Gross-Pitaevskii equation for a Bose-Einstein condensate confined in an elongated cigar-shaped trap is reduced to an effective system of nonlinear equations depending on only one space coordinate along the trap axis. The radial distribution of the condensate density and its radial velocity are approximated by Gaussian functions with real and imaginary exponents, respectively, with parameters depending on the axial coordinate and time. The effective one-dimensional system is applied to a description of the ground state of the condensate, to dark and bright solitons, to the sound and radial compression waves propagating in a dense condensate, and to weakly nonlinear waves in repulsive condensate. In the low-density limit our results reproduce the known formulas. In the high-density case our description of solitons goes beyond the standard approach based on the nonlinear Schrodinger equation. The dispersion relations for the sound and radial compression waves are obtained in a wide region of values of the condensate density. The Korteweg-de Vries equation for weakly nonlinear waves is derived and the existence of bright solitons on a constant background is predicted for a dense enough condensate with a repulsive interaction between the atoms.