Noncommutative Jordan superalgebras of degree n > 2

We prove a coordinatization theorem for noncommutative Jordan superalgebras of degree n > 2, describing such algebras. It is shown that the symmetrized Jordan superalgebra for a simple finite-dimensional noncommutative Jordan superalgebra of characteristic 0 and degree n > 1 is simple. Modulo a ""nodal"" case, we classify central simple finite-dimensional noncommutative Jordan superalgebras of characteristic 0.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

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.

Acetylation of cellulose in LiCl-N,N-dimethylacetamide: first report on the correlation between the reaction efficiency and the aggregation number of dissolved cellulose

The acylation of three cellulose samples by acetic anhydride, Ac(2)O, in the solvent system LiCl/N,N-dimethylacetamide, DMAc (4 h, 110 A degrees C), has been revisited in order to investigate the dependence of the reaction efficiency on the structural characteristics of cellulose, and its aggregation in solution. The cellulose samples employed included microcrystalline, MCC; mercerized cotton linters, M-cotton, and mercerized sisal, M-sisal. The reaction efficiency expresses the relationship between the degree of substitution, DS, of the ester obtained, and the molar ratio Ac(2)O/AGU (anhydroglucose unit of the biopolymer); 100% efficiency means obtaining DS = 3 at Ac(2)O/AGU = 3. For all celluloses, the dependence of DS on Ac(2)O/AGU is described by an exponential decay equation: DS = DS(o) - Ae(-[(Ac2O/AGU)/B]); (A) and (B) are regression coefficients, and DS(o) is the calculated maximum degree of substitution, achieved under the conditions of each experiment. Values of (B) are clearly dependent on the cellulose employed: B((M-cotton)) > B((M-sisal)) > B((MCC)); they correlate qualitatively with the degree of polymerization of cellulose, and linearly with the aggregation number, N(agg), of the dissolved biopolymer, as calculated from static light scattering measurements: (B) = 1.709 + 0.034 N(agg). To our knowledge, this is the first report on the latter correlation; it shows the importance of the physical state of dissolved cellulose, and serves to explain, in part, the need to use distinct reaction conditions for MCC and fibrous celluloses, in particular Ac(2)O/AGU, time, temperature.

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.

Micellar properties of surface active ionic liquids: A comparison of 1-hexadecyl-3-methylimidazolium chloride with structurally related cationic surfactants

Ionic liquids, ILs, carrying long-chain alkyl groups are surface active, SAIIs. We investigated the micellar properties of the SAIL 1-hexadecyl-3-methylimidazolium chloride, C(16)MeImCl, and compared the data with 1-hexadecylpyridinium chloride, C(16)PYCl, and benzyl (3-hexadecanoylaminoethyl)dimethylammonium chloride, C(15)AEtBzMe(2)Cl. The properties compared include critical micelle concentration, cmc; thermodynamic parameters of micellization; empirical polarity and water concentrations in the interfacial regions. In the temperature range from 15 to 75 degrees C, the order of cmc in H(2)O and in D(2)O is C(16)PYCl > C(16)MeImCl > C(15)AEtBzMe(2)Cl. The enthalpies of micellization, Delta H(mic)(degrees), were calculated indirectly from by use of the van`t Hoff treatment; directly by isothermal titration calorimetry, ITC. Calculation of the degree of counter-ion dissociation, alpha(mic), from conductivity measurements, by use of Evans equation requires knowledge of the aggregation numbers, N(agg), at different temperatures. We have introduced a reliable method for carrying out this calculation, based on the volume and length of the monomer, and the dependence of N(agg) on temperature. The N(agg) calculated for C(16)PyCl and C(16)MeImCl were corroborated by light scattering measurements. Conductivity- and ITC-based Delta H(mic)(degrees) do not agree; reasons for this discrepancy are discussed. Micelle formation is entropy driven: at all studied temperatures for C(16)MeImCl; only up to 65 degrees C for C(16)PyCl; and up to 55 degrees C for C(15)AEtBzMe(2)Cl. All these data can be rationalized by considering hydrogen-bonding between the head-ions of the monomers in the micellar aggregate. The empirical polarities and concentrations of interfacial water were found to be independent of the nature of the head-group. (C) 2010 Elsevier Inc. All rights reserved.

Evaluation of the light polymerization efficiency of copolymers used in dental formulations by differential scanning calorimetry

Different compositions of visible-light-curable triethylene glycol dimethacrylate/bisglycidyl methacrylate copolymers used in dental resin formulations were prepared through copolymerization photoinitiated by a camphorquinone/ethyl 4-dimethylaminobenzoate system irradiated with an Ultrablue IS light-emitting diode. The obtained copolymers were evaluated with differential scanning calorimetry. From the data for the heat of polymerization, before and after light exposure, obtained from exothermic differential scanning calorimetry curves, the light polymerization efficiency or degree of conversion of double bonds was calculated. The glass-transition temperature also was determined before and after photopolymerization. After the photopolymerization, the glass-transi-tion temperature was not well defined because of the breadth of the transition region associated with the properties of the photocured dimethacrylate. The glass-transition temperature after photopolymerization was determined experimentally and compared with the values determined with the Fox equation. In all mixtures, the experimental value was lower than the calculated value. Scanning electron microscopy was used to analyze the morphological differences in the prepared copolymer structures. (C) 2007 Wiley Periodicals, Inc.