Continuous and gradual photo-activation methods: influence on degree of conversion and crosslink density of composite resins

Thermal properties and degree of conversion (DC%) of two composite resins (microhybrid and nanocomposite) and two photo-activation methods (continuous and gradual) displayed by the light-emitting diode (LED) light-curing units (LCUs) were investigated in this study. Differential scanning calorimetry (DSC) thermal analysis technique was used to investigate the glass transition temperature (T(g)) and degradation temperature. The DC% was determined by Fourier transform infrared spectroscopy (FT-IR). The results showed that the microhybrid composite resin presented the highest T(g) and degradation temperature values, i.e., the best thermal stability. Gradual photo-activation methods showed higher or similar T(g) and degradation temperature values when compared to continuous method. The Elipar Freelight 2 (TM) LCU showed the lowest T(g) values. With respect to the DC%, the photo-activation method did not influence the final conversion of composite resins. However, Elipar Freelight 2 (TM) LCU and microhybrid resin showed the lowest DC% values. Thus, the presented results suggest that gradual method photo-activation with LED LCUs provides adequate degree of conversion without promoting changes in the polymer chain of composite resins. However, the thermal properties and final conversion of composite resins can be influenced by the kind of composite resin and LCU.

Influence of light guide tip used in the photo-activation on degree of conversion and hardness of one nanofilled dental composite

The aim of this study was to evaluate the degree of conversion and hardness of a dental composite resin Filtek (TM) Z-350 (3M ESPE, Dental Products St. Paul, MN) photo-activated for 20 s of irradiation time with two different light guide tips, metal and polymer, coupled on blue LED Ultraled LCU (Dabi Atlante, SP, Brazil). With the metal light tip, power density was of 352 and with the polymer was of 456 mW/cm(2), respectively. Five samples (4 mm in diameter and 2mm in thickness-ISO 4049), were made for each Group evaluated. The measurements for DC (%) were made in a Nexus-470 FT-IR, Thermo Nicolet, E.U.A. Spectroscopy (FTIR). Spectra for both uncured and cured samples were analyzed using an accessory of reflectance diffuse. The measurements were recorded in absorbance operating under the following conditions: 32 scans, 4 cm(-1) resolution, 300-4000 cm(-1) wavelength. The percentage of unreacted carbon double bonds (% C=C) was determined from the ratio of absorbance intensities of aliphatic C=C (peak at 1637 cm(-1)) against internal standard before and after curing of the sample: aromatic C-C (peak at 1610 cm(-1)). The Vickers hardness measurements (top and bottom surfaces) were performed in a universal testing machine (Buehler MMT-3 digital microhardness tester Lake Bluff, Illinois USA). A 50 gf load was used and the indenter with a dwell time of 30 s. The data were submitted to the test t Student at significance level of 5%. The mean values of degree of conversion for the polymer and metal light guide tip no were statistically different (p = 0.8389). The hardness mean values were no statistically significant different among the light guide tips (p = 0.6244), however, there was difference between top and bottom surfaces (p < 0.001). The results show that so much the polymer light tip as the metal light tip can be used for the photo-activation, probably for the low quality of the light guide tip metal.

Approximation algorithms and hardness results for the clique packing problem

For a fixed family F of graphs, an F-packing in a graph G is a set of pairwise vertex-disjoint subgraphs of G, each isomorphic to an element of F. Finding an F-packing that maximizes the number of covered edges is a natural generalization of the maximum matching problem, which is just F = {K(2)}. In this paper we provide new approximation algorithms and hardness results for the K(r)-packing problem where K(r) = {K(2), K(3,) . . . , K(r)}. We show that already for r = 3 the K(r)-packing problem is APX-complete, and, in fact, we show that it remains so even for graphs with maximum degree 4. On the positive side, we give an approximation algorithm with approximation ratio at most 2 for every fixed r. For r = 3, 4, 5 we obtain better approximations. For r = 3 we obtain a simple 3/2-approximation, achieving a known ratio that follows from a more involved algorithm of Halldorsson. For r = 4, we obtain a (3/2 + epsilon)-approximation, and for r = 5 we obtain a (25/14 + epsilon)-approximation. (C) 2008 Elsevier B.V. All rights reserved.

Approximations of modal logics: K and beyond

Inspired by the recent work on approximations of classical logic, we present a method that approximates several modal logics in a modular way. Our starting point is the limitation of the n-degree of introspection that is allowed, thus generating modal n-logics. The semantics for n-logics is presented, in which formulas are evaluated with respect to paths, and not possible worlds. A tableau-based proof system is presented, n-SST, and soundness and completeness is shown for the approximation of modal logics K, T, D, S4 and S5. (c) 2008 Published by Elsevier B.V.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

Polynomial identities for the ternary cyclic sum

We simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.

d-Koszul algebras, 2-d-determined algebras and 2-d-Koszul algebras

The relationship between an algebra and its associated monomial algebra is investigated when at least one of the algebras is d-Koszul It is shown that an algebra which has a reduced Grobnerbasis that is composed of homogeneous elements of degree d is d-Koszul if and only if its associated monomial algebra is d-Koszul The class of 2-d-determined algebras and the class 2-d-Koszul algebras are introduced In particular it is shown that 2-d-determined monomial algebras are 2-d-Koszul algebras and the structure of the ideal of relations of such an algebra is completely determined (C) 2010 Elsevier B V All rights reserved

UNIQUENESS OF THE EXTENSION OF 2-HOMOGENEOUS POLYNOMIALS

Homogeneous polynomials of degree 2 on the complex Banach space c(0)(l(n)(2)) are shown to have unique norm-preserving extension to the bidual space. This is done by using M-projections and extends the analogous result for c(0) proved by P.-K. Lin.

Decomposability problem on branched coverings

Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected closed surface N with chi(N) <= 0. This shows that decomposable and indecomposable realizations may coexist. Moreover, we characterize the branch data of a decomposable primitive branched covering. Bibliography: 20 titles.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

Flexural properties, microleakage, and degree of conversion of a resin polymerized with conventional light and argon laser

Objective: To evaluate the flexural strength, microleakage, and degree of conversion of a microhybrid resin polymerized with argon laser and halogen lamp. Method and Materials: For both flexural test and degree of conversion analysis, 5 bar samples of composite resin were prepared and polymerized according to ISO 4049. The halogen light-curing unit was used with 500 MW/cm(2) for 20 seconds and the argon laser with 250 mW for 10 and 20 seconds. Samples were stored in distilled water in a dark environment at 37 degrees C for 24 hours. The flexural property was quantified by a 3-point loading test. For the microleakage evaluation, 60 bovine incisors were used to prepare standardized Class 5 cavities, which were restored and polished. Specimens were stored in distilled water for 24 hours at 37 degrees C and thermocycled 500 times (6 degrees C to 60 degrees C). Specimens were then immersed in art aqueous solution of basic fuchsin for 24 hours. Longitudinal sections of each restoration were obtained and examined with a stereomicroscope for qualitative evaluation of microleakage. Fourier transform (FT)-Raman RFS 100/S spectrometer (Bruker) was used to analyze the degree of conversion. Results: ANOVA showed no statistically significant differences of flexural strength between the photoactivation types evaluated in the flexural study. Microleakage data were statistically analyzed by Mann-Whitney and Kruskal-Wallis tests. Enamel margins resulted in a statistically lower degree of leakage than dentin margins. No statistically significant difference was found among the 3 types of photocuring studied. ANOVA also showed no statistically significant difference in the degree of conversion among the studied groups. Conclusion: According to the methodology used in this research, the argon laser is a possible alternative for photocuring, providing the same quality of polymerization as the halogen lamp. None of the photocured units tested in this study completely eliminated microleakage.

Expedient, accurate methods for the determination of the degree of substitution of cellulose carboxylic esters: Application of UV-vis spectroscopy (dye solvatochromism) and FTIR

Two techniques, namely UV-vis- and FTIR spectroscopy, have been employed in order to calculate the degree of substitution (DS) of cellulose carboxylic esters, including acetates, CAs, butyrates, CBs, and hexanoates, CHs. Regarding UV-vis spectroscopy, we have employed a novel approach, based on measuring the dependence of lambda(max) of the intra-molecular charge-transfer bands of polarity probes adsorbed on DS of the ester films (solvatochromism). Additionally, we have revisited the use of FTIR for DS determination. Several methods have been used in order to plot Beer`s law graph, namely: Absorption of KBr pellets, pre-coated with CA: reflectance (DRIFTS) of CAs-KBr solid-solid mixtures with, or without the use of 1.4-dicyanobenzene as an internal reference; reflectance of KBr powder pre-coated with CA. The methods indicated are simple, fast, and accurate, requiring much less ester than the titration method. The probe method is independent of the experimental variables examined. (c) 2010 Published by Elsevier Ltd.

Probing the dependence of the properties of cellulose acetates and their films on the degree of biopolymer substitution: use of solvatochromic indicators and thermal analysis

Although cellulose acetates, CAs, are extensively employed there is scant information about the systematic dependence of their properties on their degree of substitution, DS; this is the subject of the present work. Nine CAs samples, DS from 0.83 to 3.0 were synthesized; their films were prepared. The following solvatochromic probes have been employed in order to determine the empirical polarity, E (T)(33); ""acidity, alpha""; ""basicity, beta"", and ""dipolarity/polarizability, pi*"" of the casted films: 2,6-dichloro-4-(2,4,6-triphenyl-pyridinium-1-yl) phenolate, WB; 4-nitroaniline; 4-nitroanisole; 4-nitro-N,N-dimethylaniline; 2,6-diphenyl-4-(2,4,6-triphenyl-pyridinium-1-yl)phenolate, RB. Additionally, two systems, ethanol plus ethyl acetate (EtOH-EtAc), and cellulose plus cellulose triacetate, CTA, were employed as models for CAs of different DS. Regarding the model systems, the following was observed: (i) For EtOH-EtAc, the dependence of all solvatochromic parameters on the ""equivalent-DS"" of the binary mixture was non-linear because of preferential solvation; (ii) The dependence of E (T)(33) on equivalent DS of the cellulose-CTA films is linear, but the slope is smaller than that of the corresponding plot for CAs. This is attributed to the more efficient hydrogen bonding in the model system, a conclusion corroborated by IR measurements. The dependence of solvatochromic parameters of CAs on their DS is described by the simple equations; a consequence of the substitution of the OH by the ester group. The thermal properties of bulk CAs samples were investigated by DSC and TGA; their dependence on DS is described by simple equations. The relevance of these data to the processing and applications of CAs is briefly discussed.

Recreational Mathematics - Only For Fun?

In this paper, I explore recreational mathematics from two perspectives. I first study how the concept appears in educational policy documents such as standards, syllabi, and curricula from a selection of countries to see if and in what way recreational mathematics can play a part in school mathematics. I find that recreational mathematics can be a central part, as in the case of India, but also completely invisible, as in the standards from USA. In the second part of the report, I take an educational historical approach. I observe that throughout history, recreational mathematics has been an important tool for learning mathematics. Recreational mathematics is then both a way of bringing pleasure and a tool for learning mathematics. Can it also be a tool for social empowerment?