On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

MSC 2010: 42A32; 42A20

On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

Study of the surface hardness and modulus of elasticity of conventional and microwave-cured acrylic resins

The aim of this study was to evaluate the following acrylic resins: Clássico®, QC-20® and Lucitone®, recommended specifically for thermal polymerization, and Acron MC® and VIPI-WAVE®, made for polymerization by microwave energy. The resins were evaluated regarding their surface nanohardness and modulus of elasticity, while varying the polymerization time recommended by the manufacturer. They were also compared as to the presence of water absorbed by the samples. The technique used was nanoindentation, using the Nano Indenter XP®, MTS. According to an intra-group analysis, when using the polymerization time recommended by the manufacturer, a variation of 0.14 to 0.23 GPa for nanohardness and 2.61 to 3.73 GPa for modulus of elasticity was observed for the thermally polymerized resins. The variation for the resins made for polymerization by microwave energy was 0.15 to 0.22 GPa for nanohardness and 2.94 to 3.73 GPa for modulus of elasticity. The conclusion was that the Classico® resin presented higher nanohardness and higher modulus of elasticity values when compared to those of the same group, while Acron MC® presented the highest values for the same characteristics when compared to those of the same group. The water absorption evaluation showed that all the thermal polymerization resins, except for Lucitone®, presented significant nanohardness differences when submitted to dehydration or rehydration, while only Acron MC® presented no significant differences when submitted to a double polymerization time. Regarding the modulus of elasticity, it was observed that all the tested materials and products, except for Lucitone®, showed a significant increase in modulus of elasticity when submitted to a lack of hydration.

Using the ultrasound and instrumented indentation techniques to measure the elastic modulus of engineering materials

Currently, the acoustic and nanoindentation techniques are two of the most used techniques for material elastic modulus measurement. In this article fundamental principles and limitations of both techniques are shown and discussed. Last advances in nanoindentation technique are also reviewed. An experimental study in ceramic, metallic, composite and single crystals was also done. Results shown that ultrasonic technique is capable to provide results in agreement with those reported in literature. However, ultrasonic technique does not allow measuring the elastic modulus of some small samples and single crystals. On the other hand, the nanoindentation technique estimates the elastic modulus values in reasonable agreement with those measured by acoustic methods, particularly in amorphous materials, while in some policristaline materials some deviation from expected values was obtained.

Polymerization stress, shrinkage and elastic modulus of current low-shrinkage restorative composites

Objective. To compare currently available low-shrinkage composites with others regarding polymerization stress, volumetric shrinkage (total and post-gel), shrinkage rate and elastic modulus. Methods. Seven BisGMA-based composites (Durafill/DU, Filtek Z250/FZ, Heliomolar/HM, Aelite LS Posterior/AP, Point 4/P4, Filtek Supreme/SU, ELS/EL), a silorane-based (Filtek LS, LS), a urethane-based (Venus Diamond, VD) and one based on a dimethacrylate-derivative of dimer acid (N`Durance, ND) were tested. Polymerization stress was determined in 1-mm high specimens inserted between two PMMA rods attached to a universal testing machine. Total volumetric shrinkage was measured using a mercury dilatometer. Maximum shrinkage rate was used as a parameter of the reaction speed. Post-gel shrinkage was measured using strain-gages. Elastic modulus was obtained by three-point bending. Data were submitted to one-way ANOVA/Tukey test (p = 0.05), except for elastic modulus (Kruskal-Wallis). Results. Composites ranked differently for total and post-gel shrinkage. Among the materials considered as ""low-shrinkage"" by the respective manufacturers, LS, EL and VD presented low post-gel shrinkage, while AP and ND presented relatively high values. Polymerization stress showed a strong correlation with post-gel shrinkage except for LS, which presented high stress. Elastic modulus and shrinkage rate showed weak relationships with polymerization stress. Significance. Not all low-shrinkage composites demonstrated reduced polymerization shrinkage. Also, in order to effectively reduce polymerization stress, a low post-gel shrinkage must be associated to a relatively low elastic modulus. (C) 2010 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Elastic modulus of posts and the risk of root fracture

The definition of an optimal elastic modulus for a post is controversial. This work hypothesized that the influence of the posts` elastic modulus on dentin stress concentration is dependent on the load direction. The objective was to evaluate, using finite element analysis, the maximum principal stress (sigma(max)) on the root, using posts with different elastic modulus submitted to different loading directions. Nine 3D models were built, representing the dentin root, gutta-percha, a conical post and the cortical bone. The softwares used were: MSC.PATRAN2005r2 (preprocessing) and MSC.Marc2005r2 (processing). Load of 100 N was applied, varying the directions (0 degrees, 45 degrees and 90 degrees) in relation to the post`s long axis. The magnitude and direction of the sigma(max) were recorded. At the 45 degrees and 90 degrees loading, the highest values of sigma(max) were recorded for the lowest modulus posts, on the cervical region, with a direction that suggests debonding of the post. For the 0 degrees loading, the highest values of sigma(max) were recorded for higher modulus posts, on the apical region, and the circumferential direction suggests vertical root fracture. The hypothesis was accepted: the effect of the elastic modulus on the magnitude and direction of the sigma(max) generated on the root was dependent on the loading direction.

Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

Explosion of smoothness from a point to everywhere for conjugacies between Markov families

For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Canter sets. We also present similar statements for (uaa:) and C-r Markov families. These results generalize the similar ones of Sullivan and de Faria for C-r expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.

Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfaces

For diffeomorphisms on surfaces with basic sets, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point in the basic set then the conjugacy has a smooth extension to the surface. These results generalize the similar ones of D. Sullivan, E. de Faria and ours for one-dimensional expanding dynamics.

Application of Continuous Wavelet Transform to the Analysis of the Modulus of the Fractional Fourier Transform Bands for Resolving Two Component Mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

Moduli of smoothness and rate of a.e. convergence for some convolution operators

Vegeu el resum a l'inici del document del fitxer adjunt.

Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

We prove two-sided inequalities between the integral moduli of smoothness of a function on R d[superscript] / T d[superscript] and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is given by the equivalence results for functions satisfying certain regular conditions. Applications include a quantitative form of the Riemann-Lebesgue lemma as well as several other questions in approximation theory and the theory of function spaces.

Analysis of the tensile modulus of polypropylene composites reinforced with stone groundwood fibers

One of the most relevant properties of composite materials to be considered is stiffness. Fiberglass has been used traditionally as a fibrous reinforcing element when stiff materials are required. However, natural fibers are been exploited as replacements for synthetic fibers to satisfy environmental concerns. Among the different natural fibers, wood fibers show the combination of relatively high aspect ratio, good specific stiffness and strength, low density, low cost, and less variability than other natural fibers of such those from annual crops. In this work, composites from polypropylene and stone groundwood fibers from softwood were prepared and mechanically characterized under tensile loads. The Young’s moduli of the ensuing composites were analyzed and their micromechanics aspects evaluated. The reinforcing effect of stone groundwood fibers was compared to that of conventional reinforcement such fiberglass. The Halpin-Tsai model with the modification proposed by Tsai-Pagano accounted fairly for the behavior of PP composites reinforced with stone groundwood fibers. It was also demonstrated that the aspect ratio of the reinforcement plays a role in the Young’s modulus of injection molded specimens

Numerical evaluation of the modulus of longitudinal elasticity in structural round timber elements of the Eucalyptus genus

Currently, the standards that deal with the determination of the properties of rigidity and strength for structural round timber elements do not take in consideration in their calculations and mathematical models the influence of the existing irregularities in the geometry of these elements. This study has as objective to determine the effective value of the modulus of longitudinal elasticity for structural round timber pieces of the Eucalyptus citriodora genus by a technique of optimization allied to the Inverse Analysis Method, to the Finite Element Method and the Least Square Method.

The position effect of structural Eucalyptus round timber on the flexural modulus of elasticity

Round timber has great use in civil construction, performing the function of beams, columns, foundations, poles for power distribution among others, with the advantage of not being processed, such as lumber. The structural design of round timber requires determining the elastic properties, mainly the modulus of elasticity. The Brazilian standards responsible for the stiffness and strength determination of round timber are in effect for over twenty years with no technical review. Round timber, for generally present an axis with non-zero curvature according to the position of the element in the bending test, may exhibit different values of modulus of elasticity. This study aims to analyze the position effect of Eucalyptus grandis round timber on the flexural modulus of elasticity. The three-point bending test was evaluated in two different positions based on the longitudinal rotation of the round timber element. The results revealed that at least two different positions of the round timber element are desired to obtain significant modulus of elasticity.