Monotonicity of zeros of Jacobi polynomials

Denote by x(nk)(alpha, beta), k = 1...., n, the zeros of the Jacobi polynornial P-n((alpha,beta)) (x). It is well known that x(nk)(alpha, beta) are increasing functions of beta and decreasing functions of alpha. In this paper we investigate the question of how fast the functions 1 - x(nk)(alpha, beta) decrease as beta increases. We prove that the products t(nk)(alpha, beta) := f(n)(alpha, beta) (1 - x(nk)(alpha, beta), where f(n)(alpha, beta) = 2n(2) + 2n(alpha + beta + 1) + (alpha + 1)(beta + 1) are already increasing functions of beta and that, for any fixed alpha > - 1, f(n)(alpha, beta) is the asymptotically extremal, with respect to n, function of beta that forces the products t(nk)(alpha, beta) to increase. (c) 2007 Elsevier B.V. All rights reserved.

Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials

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Monotonicity of zeros of Jacobi-Sobolev type orthogonal polynomials

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Asymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures

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Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The X-ray crystallographic structure of Escherichia coli branching enzyme

Branching enzyme catalyzes the formation of alpha-1,6 branch points in either glycogen or starch. We report the 2.3-Angstrom crystal structure of glycogen branching enzyme from Escherichia coli. The enzyme consists of three major domains, an NH2-terminal seven-stranded beta-sandwich domain, a COOH-terminal domain, and a central alpha/beta-barrel domain containing the enzyme active site. While the central domain is similar to that of all the other amylase family enzymes, branching enzyme shares the structure of all three domains only with isoamylase. Oligosaccharide binding was modeled or branching enzyme using the enzyme-oligosaccharide complex structures of various alpha-amylases and cyclodextrin glucanotransferase and residues were implicated in oligosaccharide binding. While most of the oligosaccharides modeled well in the branching enzyme structure, an approximate 50degrees rotation between two of the glucose units was required to avoid steric clashes with Trp(298) of branching enzyme. A similar rotation was observed in the mammalian alpha-amylase structure caused by an equivalent tryptophan residue in this structure. It appears that there are two binding modes for oligosaccharides in these structures depending on the identity and location of this aromatic residue.

Structural basis for branching-enzyme activity of glycoside hydrolase family 57: Structure and stability studies of a novel branching enzyme from the hyperthermophilic archaeon Thermococcus Kodakaraensis KOD1

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

Implicit differential equations with impasse singularities and singular perturbation problems

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

Production of cyclodextrins by CGTase from Bacillus clausii using different starches as substrates

Cyclodextrins ( CDs) are cyclic oligasaccharides composed by D- glucose monomers joined by alpha- 1,4-D glicosidic linkages. The main types of CDs are alpha-,beta-and gamma-CDs consisting of cycles of six, seven, and eight glucose monomers, respectively. Their ability to form inclusion complexes is the most important characteristic, allowing their wide industrial application. The physical property of the CD-complexed compound can be altered to improve stability, volatility, solubility, or bio-availability. The cyclomaltodextrin glucanotransferase ( CGTase, EC 2.4.1.19) is an enzyme capable of converting starch into CD molecules. In this work, the CGTase produced by Bacillus clausii strain E16 was used to produce CD from maltodextrin and different starches ( commercial soluble starch, corn, cassava, sweet potato, and waxy corn starches) as substrates. It was observed that the substrate sources influence the kind of CD obtained and that this CGTase displays a beta- CGTase action, presenting a better conversion of soluble starch at 1.0%, of which 80% was converted in CDs. The ratio of total CD produced was 0: 0.89: 0.11 for alpha/beta/gamma. It was also observed that root and tuber starches were more accessible to CGTase action than seed starch under the studied conditions.

Entropy of bosonic open string and boundary conditions

The entropy of the states associated to the solutions of the equations of motion of the bosonic open string with combinations of Neumann and Dirichlet boundary conditions is given. Also, the entropy of the string in the states \A(i)] = alpha(-1)(i)\0] and \phi(a)]= alpha(-1)(a)\0] that describe the massless fields on the world-volume of the Dp-brane is computed. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Discretizing the deformation parameter in the su(q)(2) quantum algebra

Inspired in recent works of Biedenham [1, 2] on the realization of the q-algebra su(q)(2), We show in this note that the condition [2j + 1](q) = N-q(j) = integer, implies the discretization of the deformation parameter alpha, where q = e(alpha). This discretization replaces the continuum associated to ct by an infinite sequence alpha(1), alpha(2), alpha(3),..., obtained for the values of j, which label the irreps of su(q)(2). The algebraic properties of N-q(j) are discussed in some detail, including its role as a trace, which conducts to the Clebsch-Gordan series for the direct product of irreps. The consequences of this process of discretization are discussed and its possible applications are pointed out. Although not a necessary one, the present prescription is valuable due to its algebraic simplicity especially in the regime of appreciable values of alpha.

Structure and Growth Kinetics of 3-Glycidoxypropyltrimethoxysilane-Derived Organic/Silica Hybrids at Different Temperatures

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

Dynamic Scaling and Growth Kinetics of 3-Glycidoxypropyltrimethoxysilane-Derived Organic/Silica Hybrids

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

Kinetic parameters for thermal decomposition of microcrystalline, vegetal, and bacterial cellulose

Cellulose can be obtained from innumerable sources such as cotton, trees, sugar cane bagasse, wood, bacteria, and others. The bacterial cellulose (BC) produced by the Gram-negative acetic-acid bacterium Acetobacter xylinum has several unique properties. This BC is produced as highly hydrated membranes free of lignin and hemicelluloses and has a higher molecular weight and higher crystallinity. Here, the thermal behavior of BC, was compared with those of microcrystalline (MMC) and vegetal cellulose (VC). The kinetic parameters for the thermal decomposition step of the celluloses were determined by the Capela-Ribeiro non-linear isoconversional method. From data for the TG curves in nitrogen atmosphere and at heating rates of 5, 10, and 20 A degrees C/min, the E(alpha) and B(alpha) terms could be determined and consequently the pre-exponential factor A(alpha) as well as the kinetic model g(alpha). The pyrolysis of celluloses followed kinetic model g(alpha) = [-ln(1 - alpha)](1.63) on average, characteristic for Avrami-Erofeev with only small differences in activation energy. The fractional value of n may be related to diffusion-controlled growth, or may arise from the distributions of sizes or shapes of the reactant particles.

Interaction between vitamin K nutriture and bacterial overgrowth in hypochlorhydria induced by omeprazole

Subjects taking a hydrogen pump blocking agent (omeprazole) develop bacterial overgrowth of the small intestine. We tested the hypothesis that this bacterial overgrowth produces menaquinones, which would meet the Vitamin requirement in situations of vitamin K deficiency. In a crossover-type design, 13 healthy Volunteers eating a phylloquinone-restricted diet for 35 d were randomly assigned to take omeprazole during the first period of study or starting on day 15 until the end of the study. Coagulation times, serum osteocalcin [total osteocalcin and undercarboxylated osteocalcin (ucOC)], plasma phylloquinone, urinary gamma-carboxyglutamic acid, and plasma undercarboxylated prothrombin (PIVKA-II) were measured. Plasma phylloquinone concentrations declined 82% with dietary phylloquinone restriction (P < 0.05) and were not significantly different in the period when the diet was combined with omeprazole treatment (P > 0.05), the mean value for PIVKA-II during the phylloquinone-restricted diet significantly increased 5.7-fold from baseline (P < 0.05); however, the combination of omeprazole treatment and the phylloquinone-restricted diet significantly reduced PIVKA-II values by 21% (P < 0.05) compared with the diet period alone. There were no alterations in total or percentage ucOC concentrations during the phylloquinone-restricted diet or during the period of diet plus omeprazole treatment. Our data support the hypothesis that bacterial overgrowth results in the synthesis and absorption of menaquinones. These menaquinones contribute to vitamin K nutriture during dietary phylloquinone restriction, but not enough to restore normal vitamin K status.