Composition and invertibility for a class of generalized functions in the Colombeau's theory

In this work we define the composite function for a special class of generalized mappings and we study the invertibility for a certain class of generalized functions with real values.

Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a simpler version of the algebra G,(Ω). Although this subalgebra does not contain, in canonical way, the space D′(Ω) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

Degree of conversion and mechanical properties of a BisGMA : TEGDMA composite as a function of the applied radiant exposure

Objective: Verify the influence of radiant exposure (H) on composite degree of conversion (DC) and mechanical properties. Methods: Composite was photoactivated with 3, 6, 12, 24, or 48 J/cm(2). Properties were measured after 48-h dry storage at room temperature. DC was determined on the flat surfaces of 6 mm x 2 mm disk-shaped specimens using FTIR. Flexural strength (FS) and modulus (FM) were accessed by three-point bending. Knoop microhardness number (KHN) was measured on fragments of FS specimens. Data were analyzed by one-way ANOVA/Tukey test, Student`s t-test, and regression analysis. Results: DC/top between 6 and 12 J/cm(2) and between 24 and 48 J/cm(2) were not statistically different. No differences between DC/top and bottom were detected. DC/bottom, FM, and KHN/top showed significant differences among all H levels. FS did not vary between 12 and 24 J/cm(2) and between 24 and 48 J/cm(2). KHN/bottom at 3 and 6 J/cm(2) was similar. KHN between top and bottom was different up to 12 J/cm(2). Regression analyses having H as independent variable showed a plateau region above 24 J/cm(2). KHN increased exponentially (top) or linearly (bottom) with DC. FS and FM increased almost linearly with DC/bottom up to 55% conversion. Conclusions: DC and mechanical properties increased with radiant exposure. Variables leveled off at high H levels. (C) 2007 Wiley Periodicals, Inc.

Analysis of camphorquinone in composite resins as a function of shade

Objective. To identify and quantify the camphorquinone (CQ) used in different brands of composite resins as a function of the shade analyzed.Materials and methods. Filtek Z250 A3 (FZA3), Filtek Z-250 Incisal (FZI), Pyramid Enamel A1 (PEA1), Pyramid Enamel Translucent (PET), Filtek Supreme A3E (FSA3) and Filtek Supreme GT (FSGT) were used. Five hundred milligrams of each resin were weighed and then dissolved in 1.0 ml of methanol. The samples were centrifuged to accelerate the sedimentation of the inorganic particles. 0.8 ml of the supernatant solution was collected with a pipette and assessed under gas chromatography coupled to the mass spectrometer (GC-MS). The results were compared to pure CQ solutions, used as a standard. Student's t-test, (p = 0.05) significant at the level of 5%, compared the results of each brand shade.Results. A smaller amount of camphorquinone was found in Filtek Z-250 (FZI) resin incisal shade when compared to (FZA3) A3 shade. on the other hand, Filtek Supreme resin featured a statistically larger camphorquinone amount in the incisal shade. in Pyramid Enamel resin camphorquinone was found only in shade Al, while the photoinitiator used in the Translucent shade was not identified.Significance. Based on the data obtained, it is possible to conclude that a single composite resin brand may feature differences in amount and type of photoinitiator used. (C) 2006 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Resin composite characterizations following a simplified protocol of accelerated aging as a function of the expiration date

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Esthetic and function improvement by direct composite resins and biomimetic concept

Aim: This case report describe a resin layering restorative technique based on biomimetic concept to improve esthetics in a patient with dental defects that affected both enamel and dentin in anterior teeth. Background: Severe structural defect in anterior teeth compromises esthetics and it is a high challenge to become the defect imperceptible after the restoration. Case description: A clinical sequence of applying different composite resin layers allowed the reproduction of the interaction between hard dental tissues and the restorative material. Conclusion: This technique achieved a satisfactory final esthetic outcome, preserving sound teeth structure and at same time, improved the quality of life of the young patient. Clinical significance: The utilization of the biomimetic concept to increase a disharmonic smile with dental defects is based in a conservative approach, which reached a satisfactory and esthetic outcome.

The changes on microstructure and electrical properties of Bi:2223/Ag composite as a function of the granulation and the content of the added silver powder

The Bi-Sr-Ca-Cu-O system has been one of the most studied superconducting ceramic materials for industry applications. The most of the studies with this aim are on silver/ceramic composites, due to the benefits and great compatibility of this metal with the oxide. In this paper we describe a systematic and comparative study on Ag/BSCCO composite, made by the citrate route, in which the ceramic pellets are sintered in the presence of silver powder using several proportions and having several granulations. It was observed that the introduction of fine (0.5 and 2 μm) silver powder in the proportions of 5 wt. % always implies in a better critical current density compared to the no silver pellet. According to the results, the silver powder in excess of 5 wt.% may not promote best electrical properties, depending on the size of the silver particles.

Kinetic of water diffusion and color stability of a resin composite as a function of the curing tip distance

The influence of curing tip distance and storage time in the kinetics of water diffusion (water sorption-W SP, solubility-W SB, and net water uptake) and color stability of a composite were evaluated. Composite samples were polymerized at different distances (5, 10, and 15 mm) and compared to a control group (0 mm). After desiccation, the specimens were stored in distilled water to evaluate the water diffusion over a 120-day period. Net water uptake was calculated (sum of WSP and WSB). The color stability after immersion in a grape juice was compared to distilled water. Data were submitted to three-way ANOVA/Tukey's test (α = 5%). The higher distances caused higher net water uptake (p < 0.05). The immersion in the juice caused significantly higher color change as a function of curing tip distance and the time (p < 0.05). The distance of photoactivation and storage time provide the color alteration and increased net water uptake of the resin composite tested.

Polymerization stress of resin composites as a function of system compliance

Objectives. Evaluate the effect of testing system compliance on polymerization stress and stress distribution of composites. Methods. Composites tested were Filtek Z250 (FZ), Herculite (HL), Tetric Ceram (TC), Helio Fill-AP (HF) and Heliomolar (HM). Stress was determined in 1-mm thick specimens, inserted between two rods of either poly(methyl methacrylate), PMMA, or glass. Experimental nominal stress (sigma(exp)) was calculated by dividing the maximum force recorded 5 min after photoactivation by the cross-sectional area of the rod. Composites` elastic modulus (E) was obtained by three-point bending. Data were submitted to one-way ANOVA/Tukey`s test (alpha = 0.05). Stress distribution on longitudinal (sigma(y)) and transverse (sigma(x)) axes of models representing the composites with the highest and lowest E (FZ and HM, respectively) were evaluated by finite element analysis (FEA). Results. sigma(exp) ranged from 5.5 to 8.8 MPa in glass and from 2.6 to 3.4 MPa in PMMA. Composite ranking was not identical in both substrates, since FZ showed or sigma(exp) statistically higher than HM in glass, while in PMMA FZ showed values similar to the other composites. A strong correlation was found between stress reduction (%) from glass to PMMA and composite`s E (r(2) = 0.946). FEA revealed that system compliance was influenced by the composite (FZ led to higher compliance than HM). sigma(x) distribution was similar in both substrates, while cry distribution showed larger areas of compressive stresses in specimens built on PMMA. Significance. sigma(exp) determined in PMMA was 53-68% lower than in glass. Composite ranking varied slightly due to differences in substrates` longitudinal and transverse deformation. (c) 2007 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Network structures of Bis-GMA/TEGDMA resins differ in DC, shrinkage-strain, hardness and optical properties as a function of reducing agent

Objectives. To evaluate the influence of different tertiary amines on degree of conversion (DC), shrinkage-strain, shrinkage-strain rate, Knoop microhardness, and color and transmittance stabilities of experimental resins containing BisGMA/TEGDMA (3: 1 wt), 0.25wt% camphorquinone, 1wt% amine (DMAEMA, CEMA, DMPT, DEPT or DABE). Different light-curing protocols were also evaluated. Methods. DC was evaluated with FTIR-ATR and shrinkage-strain with the bonded-disk method. Shrinkage-strain-rate data were obtained from numerical differentiation of shrinkage-strain data with respect to time. Color stability and transmittance were evaluated after different periods of artificial aging, according to ISO 7491: 2000. Results were evaluated with ANOVA, Tukey, and Dunnett`s T3 tests (alpha = 0.05). Results. Studied properties were influenced by amines. DC and shrinkage-strain were maximum at the sequence: CQ < DEPT < DMPT <= CEMA approximate to DABE < DMAEMA. Both DC and shrinkage were also influenced by the curing protocol, with positive correlations between DC and shrinkage-strain and DC and shrinkage-strain rate. Materials generally decreased in L* and increased in b*. The strong exception was the resin containing DMAEMA that did not show dark and yellow shifts. Color varied in the sequence: DMAEMA < DEPT < DMPT < CEMA < DABE. Transmittance varied in the sequence: DEPT approximate to DABE < DABE approximate to DMPT approximate to CEMA < DMPT approximate to CEMA approximate to DMAEMA, being more evident at the wavelength of 400 nm. No correlations between DC and optical properties were observed. Significance. The resin containing DMAEMA showed higher DC, shrinkage-strain, shrinkage-strain rate, and microhardness, in addition to better optical properties. (C) 2011 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Mechanical Testing of Indirect Composite Materials Directly Applied on Implant Abutments

Purpose: To test the strength to failure and fracture mode of three indirect composite materials directly applied onto Ti-6Al-4V implant abutments vs cemented standard porcelain-fused-to-metal (PFM) crowns. Materials and Methods: Sixty-four locking taper abutments were randomly allocated to four groups and were cleaned in ethanol in an ultrasonic bath for 5 min. After drying under ambient conditions, the abutments were grit blasted and a custom 4-cusp molar crown mold was utilized to produce identical crowns (n = 16 per group) of Tescera (Bisco), Ceramage (Shofu), and Diamond Crown (DRM) according to the manufacturer`s instructions. The porcelain-fused-to-metal crowns were fabricated by conventional means involving the construction and a wax pattern and casting of a metallic coping followed by sintering of increasing layers of porcelain. All crowns were loaded to failure by an indenter placed at one of the cusp tips at a 1 mm/min rate. Subsequently, fracture analysis was performed by means of stereomicroscopy and scanning electron microscopy. One-way ANOVA at 95% level of significance was utilized for statistical analysis. Results: The single load to failure (+/- SD) results were: Tescera (1130 +/- 239 N), Ceramage (1099 +/- 257 N), Diamond Crown (1155 +/- 284 N), and PFM (1081 +/- 243 N). Stereomicroscopy analysis showed two distinct failure modes, where the loaded cusp failed either with or without abutment/metallic coping exposure. SEM analysis of the fractures showed multiple crack propagation towards the cervical region of the crown below a region of plastic deformation at the indenter contact region. Conclusion: The three indirect composites and PFM systems fractured at loads higher than those typically associated with normal occlusal function. Although each material had a different composition and handling technique, no significant differences were found concerning their single load to fracture resistance among composite systems and PFM.

Modelling of Lamb waves in composite laminated plates excited by interdigital transducers

The technique of permanently attaching interdigital transducers (IDT) to either flat or curved structural surfaces to excite single Lamb wave mode has demonstrated great potential for quantitative non-destructive evaluation and smart materials design, In this paper, the acoustic wave field in a composite laminated plate excited by an IDT is investigated. On the basis of discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the surface velocity response of the plate due to the IDTs excitation. In this approach, the frequency spectrum and wave number spectrum of the output of IDT are obtained directly. The corresponding time domain results are calculated by applying a standard inverse fast Fourier transformation technique. Numerical examples are presented to validate the developed method and show the ability of mode selection and isolation. A new effective way of transfer function estimation and interpretation is presented by considering the input wave number spectrum in addition to the commonly used input frequency spectrum. The new approach enables the simple physical evaluation of the influences of IDT geometrical features such as electrode finger widths and overall dimension and excitation signal properties on the input-output characteristics of IDT. Finally, considering the convenience of Mindlin plate wave theory in numerical computations as well as theoretical analysis, the validity is examined of using this approximate theory to design IDT for the excitation of the first and second anti-symmetric Lamb modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

From local to global importance measures of uncertainty propagation in composite structures

The influence of uncertainties of input parameters on output response of composite structures is investigated in this paper. In particular, the effects of deviations in mechanical properties, ply angles, ply thickness and on applied loads are studied. The uncertainty propagation and the importance measure of input parameters are analysed using three different approaches: a first-order local method, a Global Sensitivity Analysis (GSA) supported by a variance-based method and an extension of local variance to estimate the global variance over the domain of inputs. Sample results are shown for a shell composite laminated structure built with different composite systems including multi-materials. The importance measures of input parameters on structural response based on numerical results are established and discussed as a function of the anisotropy of composite materials. Needs for global variance methods are discussed by comparing the results obtained from different proposed methodologies. The objective of this paper is to contribute for the use of GSA techniques together with low expensive local importance measures.

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.