Influence of the Light-Curing Unit, Storage Time and Shade of a Dental Composite Resin on the Fluorescence

The aim of this study was to determine the influence of three light-curing units, storage times and colors of the dental composite resin on the fluorescence. The specimens (diameter 10.0 +/- 0.1 mm, thickness 1.0 +/- 0.1 mm) were made using a stainless steel mold. The mold was filled with the microhybrid composite resin and a polyethylene film covered each side of the mold. After this, a glass slide was placed on the top of the mold. To standardize the top surface of the specimens a circular weight (1 kg) with an orifice to pass the light tip of the LCU was placed on the top surface and photo-activated during 40 s. Five specimens were made for each group. The groups were divided into 9 groups following the LCUs (one QTH and two LEDs), storage times (immediately after curing, 24 hours, 7 and 30 days) and colors (shades: A(2)E, A(2)D, and TC) of the composite resin. After photo-activation, the specimens were storage in artificial saliva during the storage times proposed to each group at 37 C and 100% humidity. The analysis of variance (ANOVA) and Tukey's post-hoc tests showed no significant difference between storage times (immediately, 24 hours and 30 days) (P > 0.05). The means of fluorescence had difference significant to color and light-curing unit used to all period of storage (P < 0.05). The colors had difference significant between them (shades: A2D < A2E < TC) (P < 0.05). The Ultraled (LED) and Ultralux (QTH) when used the TC shade showed higher than Radii (LED), however to A2E shade and A2D shade any difference were found (P > 0.05).

Real orthogonal polynomials in frequency analysis

We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel numbers of polynomials orthogonal on the real line. This leads to a simple and fast algorithm for the estimation of frequencies. We also provide a new method, faster than the Levinson algorithm, for the determination of the reflection coefficients of the corresponding real Szego polynomials from the given moments.

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

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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

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

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.

Szego type polynomials and para-orthogonal polynomials

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

Effect of thickness of indirect restoration and distance from the light-curing unit tip on the hardness of a dual-cured resin cement

This study evaluated the Knoop hardness and polymerization depth of a dual-cured resin cement, light-activated at different distances through different thicknesses of composite resin. One bovine incisor was embedded in resin and its buccal surface was flattened. Dentin was covered with PVC film where a mold (0.8-mm-thick and 5 mm diameter) was filled with cement and covered with another PVC film. Light curing (40 s) was carried out through resin discs (2, 3, 4 or 5 mm) with a halogen light positioned 0, 1, 2 or 3 mm from the resin surface. After storage, specimens were sectioned for hardness measurements (top, center, and bottom). Data were subjected to split-plot ANOVA and Tukey's test (α=0.05). The increase in resin disc thickness decreased cement hardness. The increase in the distance of the light curing tip decreased hardness at the top region. Specimens showed the lowest hardness values at the bottom, and the highest at the center. Resin cement hardness was influenced by the thickness of the indirect restoration and by the distance between the light-curing unit tip and the resin cement surface.

Kernel polynomials from L-orthogonal polynomials

A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤athen the sequence of (monic) polynomials {Qn}, defined by ∫a bt-n+sQn(t)dψ(t)=0, s=0,1,⋯,n-1, is known to exist. We refer to these polynomials as the L-orthogonal polynomials with respect to the strong positive measure ψ. The purpose of this manuscript is to consider some properties of the kernel polynomials associated with these L-orthogonal polynomials. As applications, we consider the quadrature rules associated with these kernel polynomials. Associated eigenvalue problems and numerical evaluation of the nodes and weights of such quadrature rules are also considered. © 2010 IMACS. Published by Elsevier B.V. All rights reserved.

Monotonicity and asymptotics of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher order derivatives

In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product where α >-1, N ≥ 0, and j ∈ N. In particular, we focus our attention on their interlacing properties with respect to the zeros of Laguerre polynomials as well as on the monotonicity of each individual zero in terms of the mass N. Finally, we give necessary and sufficient conditions in terms of N in order for the least zero of any Laguerre-Sobolev-type orthogonal polynomial to be negative. © 2011 American Mathematical Society.

Effects of cement-curing mode and light-curing unit on the bond durability of ceramic cemented to dentin

The aim of this study was to evaluate the effects of different light-curing units and resin cement curing types on the bond durability of a feldspathic ceramic bonded to dentin. The crowns of 40 human molars were sectioned, exposing the dentin. Forty ceramic blocks of VITA VM7 were produced according to the manufacturer's recommendations. The ceramic surface was etched with 10% hydrofluoric acid/60s and silanized. The dentin was treated with37% phosphoric acid/15s, and the adhesive was applied. The ceramic blocks were divided and cemented to dentin according to resin cement/RC curing type(dual-and photocured), light-curing unit (halogen light/QTH and LED), and storage conditions (dry and storage/150 days + 12,000 cycles/thermocycling). All blocks were stored in distilled water (37°C/24h) and sectioned (n = 10): G1-QTH + RC Photo, G2-QTH + RC Dual, G3-LED + RC Photo, G4-LED + RC Dual. Groups G5, G6, G7, and G8 were obtained exactly as G1 through G4, respectively, and then stored and thermocycled. Microtensile bond strength tests were performed (EMIC), and data were statistically analyzed by ANOVA and Tukey's test (5%). The bond strength values (MPa) were: G1-12.95 (6.40)ab; G2-12.02 (4.59)ab; G3-13.09 (5.62)ab; G4-15.96 (6.32)a; G5-6.22 (5.90)c; G6-9.48 (5.99)bc; G7-12.78 (11.30)ab; and G8-8.34 (5.98)bc. The same superscript letters indicate no significant differences. Different light-curing units affected the bond strength betweenceramic cemented to dentin when the photocured cement was used, and only after aging (LED>QTH). There was no difference between the effects of dual-and photo-cured resin-luting agents on the microtensile bond strength of the cement used in this study.