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.

On an Extremal Problem concerning Bernstein Operators

* The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China.

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.

An unusual, dwarf new species of Neotropical freshwater stingray, Plesiotrygon nana sp. nov., from the upper and mid Amazon basin: the second species of Plesiotrygon (Chondrichthyes: Potamotrygonidae)

A new species of the relatively poorly known Neotropical freshwater stingray genus Plesiotrygon Rosa, Castello & Thorson, 1987 is described from the main channel and smaller tributaries (Ríos Itaya and Pachitea) of the upper Amazon basin in Peru. The first specimen to be collected, however, was from much farther east in Rio Solimões in 1996, just down-river from Rio Purus (specimen unavailable for this study). Plesiotrygon nana sp. nov., is a very distinctive and unusually small species of freshwater stingray (Potamotrygonidae), described here mostly from three specimens representing different size classes and stages of sexual maturity. Plesiotrygon nana sp. nov., is distinguished from its only congener, P. iwamae Rosa, Castello & Thorson, 1987, by numerous unique features, including: dorsal coloration composed of very fine rosettes or a combination of spots and irregular ocelli; very circular disc and snout; very small and less rhomboidal spiracles; short snout and anterior disc region; narrow mouth and nostrils; denticles on dorsal tail small, scattered, not forming row of enlarged spines; adult and preadult specimens with significantly fewer tooth rows; fewer caudal vertebrae; higher total pectoral radials; very small size, probably not surpassing 250 mm disc length or width, males maturing sexually at around 180 mm disc length and 175 mm disc width; distal coloration of tail posterior to caudal stings usually dark purplish-brown; and features of the ventral lateral-line canals (hyomandibular canal very narrow, infraorbital and supraorbital canals not undulated, supraorbital and infraorbital loops small and narrow, supraorbital loop very short, not extending posteriorly to level of mouth, jugular and posterior infraorbital canals short, not extending caudally to first gill slits, subpleural loop very narrow posteriorly; absence of anterior and posterior subpleural tubules). To provide a foundation for the description of P. nana sp. nov., morphological variation in P. iwamae was examined based on all type specimens as well as newly collected and previously unreported material. Two specimens topotypic with the male paratype of P. nana sp. nov., referred to here as Plesiotrygon cf. iwamae, are also reported. Relationships of the new species to P. iwamae are discussed; further characters indicative of Plesiotrygon monophyly are proposed, but the genus may still not be valid. Plesiotrygon nana sp. nov., is commercialized with some regularity in the international aquarium trade from Iquitos (Peru), an alarming circumstance because nothing is known of its biology or conservation requirements.

Second record of bioluminescence in larvae of Xantholinus Dejean (Staphylinidae, Xantholinini) from Brazil

Second record of bioluminescence in larvae of Xantholinus Dejean, (Staphylinidae, Xantholinini) from Brazil. Bioluminescent Xantholinus larvae (Xantholinini, Staphylinidae) were collected in the Cerrado biome of Mato Grosso state, Brazil. These larvae are morphologically similar to the first bioluminescent larvae of this genus collected in the Atlantic Forest in São Paulo state; however they differ by their bioluminescent emission.

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.

The appearance of a second genotype of Japanese encephalitis virus in the Australasian region

In mid-January 2000, the reappearance of Japanese encephalitis (JE) virus activity in the Australasian region was first demonstrated by the isolation of JE virus from 3 sentinel pigs on Badu Island in the Torres Strait. Further evidence of JE virus activity was revealed through the isolation of JE virus from Cidex gelidus mosquitoes collected on Badu Island and the detection of specific JE virus neutralizing antibodies in 3 pigs from Saint Pauls community on Moa Island. Nucleotide sequencing and phylogenetic analyses of the premembrane and envelope genes were performed which showed that both the pig and mosquito JE virus isolates (TSOO and TS4152, respectively) clustered in genotype I, along with northern Thai, Cambodian, and Korean isolates. All previous Australasian JE virus isolates belong to genotype II, along with Malaysian and Indonesian isolates. Therefore, for the first time, the appearance and transmission of a second genotype of JE virus in the Australasian region has been demonstrated.

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.

Soft tissue abscess and lymphadenitis due to Mycobacterium avium Complex as an expression of immune reconstitution inflammatory syndrome after a second scheme of highly active antiretroviral therapy

Immune reconstitution inflammatory syndrome (IRIS) is an atypical and unexpected reaction related to highly active antiretroviral therapy (HAART) in human immunodeficiency virus (HIV) infected patients. IRIS includes an atypical response to an opportunistic pathogen (generally Mycobacterium tuberculosis, Mycobacterium avium complex, cytomegalovirus and herpes varicella-zoster), in patients responding to HAART with a reduction of plasma viral load and evidence of immune restoration based on increase of CD4+ T-cell count. We reported a case of a patient with AIDS which, after a first failure of HAART, developed a subcutaneous abscess and supraclavicular lymphadenitis as an expression of IRIS due to Mycobacterium avium complex after starting a second scheme of HAART.