On the behaviour of zeros of Jacobi polynomials

Denote by x(n,k)(alpha, beta) and x(n,k) (lambda) = x(n,k) (lambda - 1/2, lambda - 1/2) the zeros, in decreasing order, of the Jacobi polynomial P-n((alpha, beta))(x) and of the ultraspherical (Gegenbauer) polynomial C-n(lambda)(x), respectively. The monotonicity of x(n,k)(alpha, beta) as functions of a and beta, alpha, beta > - 1, is investigated. Necessary conditions such that the zeros of P-n((a, b)) (x) are smaller (greater) than the zeros of P-n((alpha, beta))(x) are provided. A. Markov proved that x(n,k) (a, b) < x(n,k)(α, β) (x(n,k)(a, b) > x(n,k)(alpha, beta)) for every n is an element of N and each k, 1 less than or equal to k less than or equal to n if a > alpha and b < β (a < alpha and b > beta). We prove the converse statement of Markov's theorem. The question of how large the function could be such that the products f(n)(lambda) x(n,k)(lambda), k = 1,..., [n/2] are increasing functions of lambda, for lambda > - 1/2, is also discussed. Elbert and Siafarikas proved that f(n)(lambda) = (lambda + (2n(2) + 1)/ (4n + 2))(1/2) obeys this property. We establish the sharpness of their result. (C) 2002 Elsevier B.V. (USA).

Sharp bounds for the extreme zeros of classical orthogonal polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

L-orthogonal polynomials associated with related measures

A positive measure psi defined on [a, b] such that its moments mu(n) = integral(b)(a)t(n) d psi(t) exist for n = 0, +/-1, +/-2. can be called a strong positive measure on [a, b] When 0 <= a < b <= infinity the sequence of polynomials {Q(n)} defined by integral(b)(a) t(-n+s) Q(n)(t) d psi(t) = 0, s = 0, ., n - 1, exist and they are referred here as L-orthogonal polynomials We look at the connection between two sequences of L-orthogonal polynomials {Q(n)((1))} and {Q(n)((0))} associated with two closely related strong positive measures and th defined on [a, b]. To be precise, the measures are related to each other by (t - kappa) d psi(1)(t) = gamma d psi(0)(t). where (t - kappa)/gamma is positive when t is an element of (n, 6). As applications of our study. numerical generation of new L-orthogonal polynomials and monotonicity properties of the zeros of a certain class of L-orthogonal polynomials are looked at. (C) 2010 IMACS Published by Elsevier B V All rights reserved

A Characterization of L-orthogonal Polynomials from Three Term Recurrence Relations

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

Effect of adhesive system type and tooth region on the bond strength to dentin

Purpose: This study evaluated the bond strength of two etch-and-rinse adhesive systems (two- and three-step) and a self-etching system to Coronal and root canal dentin.Materials and Methods: The root canals of 30 human incisors and canines were instrumented and prepared with burs. The posts used for luting were duplicated with dual resin cement (Duo-link) inside Aestheti Plus #2 molds. Thus, three groups were formed (n = 10) according to the adhesive system employed: All-Bond 2 (TE3) + resin cement post (rcp) + Duo-link (DI); One-Step Plus (TE2) + rcp + DI; Tyrian/One-Step Plus (SE) + rcp + DI. Afterwards, 8 transverse sections (1.5 mm) were cut from 4 mm above the CEJ up to 4 mm short of the root canal apex, comprising coronal and root canal dentin. The sections were submitted to push-out testing in a universal testing machine EMIC (1 mm/min). Bond strength data were analyzed with two-way repeated measures ANOVA and Tukey's test (p < 0.05).Results: The relationship between the adhesives was not the same in the different regions (p < 0.05). Comparison of the means achieved with the adhesives in each region (Tukey; p < 0.05) revealed that TE3 (mean standard deviation: 5.22 +/- 1.70) was higher than TE2 (2.60 +/- 1.74) and SE (1.68 +/- 1.85).Conclusion: Under the experimental conditions, better bonding to dentin was achieved using the three-step etch-and-rinse system, especially in the coronal region. Therefore, the traditional etch-and-rinse three-step adhesive system seems to be the best choice for teeth needing adhesive endodontic restorations.

On the V-type asteroids outside the Vesta family - II. Is (21238) 1995 WV7 a fragment of the long-lost basaltic crust of (15) Eunomia?

Context. The V-type asteroids are associated with basaltic composition. Apart from ( 1459) Magnya, an asteroid that is clearly dynamically and mineralogically unconnected to the Vesta family, all currently known V-type asteroids are either members of the Vesta family, or are hypothesized to be former members of the dynamical family that migrated to their current orbital positions. The recent identification of ( 21238) 1995 WV7 as a V-type asteroid introduces the possibility that a second basaltic asteroid not connected with the Vesta family exists. This asteroid is on the opposite side of the 3: 1 mean motion resonance with respect to Vesta, and it would be very unlikely that a member of the Vesta family of its size (D > 5km) migrating via either the Yarkovsky effect or repeated close encounters with Vesta survived the passage through such a resonance.Aims. In this work we investigate the possibility that ( 21238) 1995 WV7 originated as a fragment of the parent body of the Eunomia family and then migrated via the interplay of the Yarkovsky effect and some powerful nonlinear secular resonances, such as the (s - s(6)) - ( g(5) - g(6)). If (15) Eunomia is, as claimed, a differentiated object whose originally pyroxene-enriched crust layer was lost in a collision that either created the Eunomia family or preceded its formation, can (21238) be a fragment of its long-lost basaltic crust that migrated to the current position?Methods. We mapped the phase space around (21238) and determined which of the nonlinear secular resonances that we identified are stronger and more capable of having caused the current difference in proper i between (21238) and members of the Eunomia family. We simulated the Yarkovsky effect by using the SWIFT-RMVSY integrator.Results. Our results suggest that it is possible to migrate from the Eunomia dynamical family to the current orbital location of ( 21238) via the interplay of the Yarkovsky effect and the (s - s6) - (g5 - g6) nonlinear secular resonance, on time-scales of at least 2.6 Gyr.Conclusions. (15) Eunomia might be the third currently known parent body for V-type asteroids.

Influence of ball-milled low purity boron powder on the superconductivity of MgB2

MgB2 samples were prepared using as-supplied commercial 96% boron with strong crystalline phase and the same 96% boron (B) after ball milling. The effects of the properties of the starting B powder on the superconductivity were evaluated. We observed that samples using ball-milled 96% B, in comparison with the one made from the as-supplied 96% B, were character- ized by small grain size, broadened full width at half maximum (FWHM), and enhanced magnetic critical current density (J(c)). J(c) reached 2 x 10(3) Acm(-2) at 5 K and 8 T. The improved pinning of these samples seems to be caused by enhanced grain boundary pinning at high field.

Effect of the type of environmental stress on the emergence of sunflower (Helianthus annus L.), soybean (Glycine max (L.) Merril) and maize (Zea mays L.) seeds with different levels of vigor

Sowing is a critical time in the cycle of a crop and the seeds are frequently exposed to adverse conditions that may compromise the establishment of seedlings in the field. on this basis, the objective of the present study was to determine the effect of types of environmental stress on the emergence of sunflower, maize and soybean seeds with different levels of vigor. High vigor seeds were artificially aged in order to obtain medium and low vigor seeds and then they were sown in clay soil in plastic boxes and submitted to the following types of environmental stress during the germination process : 1) high temperature (35degreesC), 2) low temperature (15 or 18degreesC), 3) water excess (Psi > -0.0001 MPa), 4) water deficiency (Psi approximately equal to -1.1; -1.2 and -0.6 MPa for sunflower, maize and soybean, respectively), 5) sowing at a depth of 7 cm and 6) pathogenic infection of sunflower seeds with Alternaria helianthi, of maize seeds with Fusarium moniliforme and of soybean seeds with Colletotrichum dematium, var. truncata. The results were compared to those obtained with controls sown under optimal condition. It was concluded that: 1) the effect of seed vigor on emergence depends on the type of enviromental stress to which the seeds are exposed, 2) the stress to which the the seeds demonstrated highest sensitivity varied with species and 3) high temperature stress was the one that most impaired the emergence of the three species.

Companion orthogonal polynomials: some applications

In this paper the recurrence relations of symmetric orthogonal polynomials whose measures are related to each other in a certain way are considered. Many of the relations satisfied by the coefficients of the recurrence relations are exposed. The results are applied to obtain, for example, information regarding certain Sobolev orthogonal polynomials and regarding the measures of certain orthogonal polynomial sequences with twin periodic recurrence coefficients. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

Crystallographic studies on the binding of isonicotinyl-NAD adduct to wild-type and isoniazid resistant 2-trans-enoyl-ACP (CoA) reductase from Mycobacterium tuberculosis

The resumption of tuberculosis led to an increased need to understand the molecular mechanisms of drug action and drug resistance, which should provide significant insight into the development of newer compounds. Isoniazid (INH), the most prescribed drug to treat TB, inhibits an NADH-dependent enoyl-acyl carrier protein reductase (InhA) that provides precursors of mycolic acids, which are components of the mycobacterial cell wall. InhA is the major target of the mode of action of isoniazid. INH is a pro-drug that needs activation to form the inhibitory INH-NAD adduct. Missense mutations in the inhA structural gene have been identified in clinical isolates of Mycobacterium tuberculosis resistant to INH. To understand the mechanism of resistance to INH, we have solved the structure of two InhA mutants (121V and S94A), identified in INH-resistant clinical isolates, and compare them to INH-sensitive WT InhA structure in complex with the INH-NAD adduct. We also solved the structure of unliganded INH-resistant S94A protein, which is the first report on apo form of InhA. The salient features of these structures are discussed and should provide structural information to improve our understanding of the mechanism of action of, and resistance to, INH in M. tuberculosis. The unliganded structure of InhA allows identification of conformational changes upon ligand binding and should help structure-based drug design of more potent antimycobacterial agents. (c) 2007 Elsevier B.V. All rights reserved.

Blumenthal's theorem for Laurent orthogonal polynomials

We investigate polynomials satisfying a three-term recurrence relation of the form B-n(x) = (x - beta(n))beta(n-1)(x) - alpha(n)xB(n-2)(x), with positive recurrence coefficients alpha(n+1),beta(n) (n = 1, 2,...). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. We analyse in more detail the case where alpha(n) --> alpha and beta(n) --> beta and show that the zeros of beta(n) are dense on an interval and that the support of the Laurent orthogonality measure is equal to this interval and a set which is at most denumerable with accumulation points (if any) at the endpoints of the interval. This result is the Laurent version of Blumenthal's theorem for orthogonal polynomials. (C) 2002 Elsevier B.V. (USA).

Chain sequences and symmetric generalized orthogonal polynomials

in this paper, we derive an explicit expression for the parameter sequences of a chain sequence in terms of the corresponding orthogonal polynomials and their associated polynomials. We use this to study the orthogonal polynomials K-n((lambda.,M,k)) associated with the probability measure dphi(lambda,M,k;x), which is the Gegenbauer measure of parameter lambda + 1 with two additional mass points at +/-k. When k = 1 we obtain information on the polynomials K-n((lambda.,M)) which are the symmetric Koornwinder polynomials. Monotonicity properties of the zeros of K-n((lambda,M,k)) in relation to M and k are also given. (C) 2002 Elsevier B.V. B.V. All rights reserved.

The influence of cervical finish line, internal relief, and cement type on the cervical adaptation of metal crowns

Objective: the aim of this investigation was to evaluate the cervical adaptation of metal crowns under several conditions, namely (1) variations in the cervical finish line of the preparation, (2) application of internal relief inside the crowns, and (3) cementation using different luting materials. Method and Materials: One hundred eighty stainless-steel master dies were prepared simulating full crown preparations: 60 in chamfer (CH), 60 in 135-degree shoulder (OB), and 60 in rounded shoulder (OR). The finish lines were machined at approximate dimensions of a molar tooth preparation (height: 5.5 mm; cervical diameter: 8 mm; occlusal diameter: 6.4 mm; taper degree: 6; and cervical finish line width: 0.8 mm). One hundred eighty corresponding copings with the same finish lines were fabricated. A 30-mu m internal relief was machined 0.5 mm above the cervical finish line in 90 of these copings. The fit of the die and the coping was measured from all specimens (L0) prior to cementation using an optical microscope. After manipulation of the 3 types of cements (zinc phosphate, glass-ionomer, and resin cement), the coping was luted on the corresponding standard master die under 5-kgf loading for 4 minutes. Vertical discrepancy was again measured (L1), and the difference between L1 and L0 indicated the cervical adaptation. Results: Significant influence of the finish line, cement type, and internal relief was observed on the cervical adaptation (P < .001). The CH type of cervical finish line resulted in the best cervical adaptation of the metal crowns regardless of the cement type either with or without internal relief (36.6 +/- 3 to 100.8 +/- 4 mu m) (3-way analysis of variance and Tukey's test, alpha = .05). The use of glass-ionomer cement resulted in the least cervical discrepancy (36.6 +/- 3 to 115 +/- 4 mu m) than those of other cements (45.2 +/- 4 to 130.3 +/- 2 mu m) in all conditions. Conclusion: the best cervical adaptation was achieved with the chamfer type of finish line. The internal relief improved the marginal adaptation significantly, and the glass-ionomer cement led to the best cervical adaptation, followed by zinc phosphate and resin cement.

The Yang-Lee zeros of the 1D Blume-Capel model on connected and non-connected rings

We carry out a numerical and analytic analysis of the Yang-Lee zeros of the ID Blume-Capel model with periodic boundary conditions and its generalization on Feynman diagrams for which we include sums over all connected and nonconnected rings for a given number of spins. In both cases, for a specific range of the parameters, the zeros originally on the unit circle are shown to depart from it as we increase the temperature beyond some limit. The curve of zeros can bifurcate- and become two disjoint arcs as in the 2D case. We also show that in the thermodynamic limit the zeros of both Blume-Capel models on the static (connected ring) and on the dynamical (Feynman diagrams) lattice tend to overlap. In the special case of the 1D Ising model on Feynman diagrams we can prove for arbitrary number of spins that the Yang-Lee zeros must be on the unit circle. The proof is based on a property of the zeros of Legendre polynomials.