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.

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.

Dynamics of transformation and fragmentation of composite liquid nano-particles

Recent research on particle size distributions and particle concentrations near a busy road cannot be explained by the conventional mechanisms for particle evolution of combustion aerosols. Specifically they appear to be inadequate to explain the experimental observations of particle transformation and the evolution of the total number concentration. This resulted in the development of a new mechanism based on their thermal fragmentation, for the evolution of combustion aerosol nano-particles. A complex and comprehensive pattern of evolution of combustion aerosols, involving particle fragmentation, was then proposed and justified. In that model it was suggested that thermal fragmentation occurs in aggregates of primary particles each of which contains a solid graphite/carbon core surrounded by volatile molecules bonded to the core by strong covalent bonds. Due to the presence of strong covalent bonds between the core and the volatile (frill) molecules, such primary composite particles can be regarded as solid, despite the presence of significant (possibly, dominant) volatile component. Fragmentation occurs when weak van der Waals forces between such primary particles are overcome by their thermal (Brownian) motion. In this work, the accepted concept of thermal fragmentation is advanced to determine whether fragmentation is likely in liquid composite nano-particles. It has been demonstrated that at least at some stages of evolution, combustion aerosols contain a large number of composite liquid particles containing presumably several components such as water, oil, volatile compounds, and minerals. It is possible that such composite liquid particles may also experience thermal fragmentation and thus contribute to, for example, the evolution of the total number concentration as a function of distance from the source. Therefore, the aim of this project is to examine theoretically the possibility of thermal fragmentation of composite liquid nano-particles consisting of immiscible liquid v components. The specific focus is on ternary systems which include two immiscible liquid droplets surrounded by another medium (e.g., air). The analysis shows that three different structures are possible, the complete encapsulation of one liquid by the other, partial encapsulation of the two liquids in a composite particle, and the two droplets separated from each other. The probability of thermal fragmentation of two coagulated liquid droplets is discussed and examined for different volumes of the immiscible fluids in a composite liquid particle and their surface and interfacial tensions through the determination of the Gibbs free energy difference between the coagulated and fragmented states, and comparison of this energy difference with the typical thermal energy kT. The analysis reveals that fragmentation was found to be much more likely for a partially encapsulated particle than a completely encapsulated particle. In particular, it was found that thermal fragmentation was much more likely when the volume ratio of the two liquid droplets that constitute the composite particle are very different. Conversely, when the two liquid droplets are of similar volumes, the probability of thermal fragmentation is small. It is also demonstrated that the Gibbs free energy difference between the coagulated and fragmented states is not the only important factor determining the probability of thermal fragmentation of composite liquid particles. The second essential factor is the actual structure of the composite particle. It is shown that the probability of thermal fragmentation is also strongly dependent on the distance that each of the liquid droplets should travel to reach the fragmented state. In particular, if this distance is larger than the mean free path for the considered droplets in the air, the probability of thermal fragmentation should be negligible. In particular, it follows form here that fragmentation of the composite particle in the state with complete encapsulation is highly unlikely because of the larger distance that the two droplets must travel in order to separate. The analysis of composite liquid particles with the interfacial parameters that are expected in combustion aerosols demonstrates that thermal fragmentation of these vi particles may occur, and this mechanism may play a role in the evolution of combustion aerosols. Conditions for thermal fragmentation to play a significant role (for aerosol particles other than those from motor vehicle exhaust) are determined and examined theoretically. Conditions for spontaneous transformation between the states of composite particles with complete and partial encapsulation are also examined, demonstrating the possibility of such transformation in combustion aerosols. Indeed it was shown that for some typical components found in aerosols that transformation could take place on time scales less than 20 s. The analysis showed that factors that influenced surface and interfacial tension played an important role in this transformation process. It is suggested that such transformation may, for example, result in a delayed evaporation of composite particles with significant water component, leading to observable effects in evolution of combustion aerosols (including possible local humidity maximums near a source, such as a busy road). The obtained results will be important for further development and understanding of aerosol physics and technologies, including combustion aerosols and their evolution near a source.

Lateral movements in composite high-rise buildings under seismic action

Daring human nature has already led to the construction of high-rise buildings in naturally challenging geological regions and in worse environments of the world. However; literature review divulges that there is a lag in research of certain generic principles and rules for the prediction of lateral movement in multistorey construction. The present competitive trend orders the best possible used of available construction material and resources. Hence; the mixed used of reinforced concrete with structural steel is gaining prevalence day by day. This paper investigates the effects of Seismic load on composite multistorey building provided with core wall and trusses through FEM modelling. The results showed that increased rigidity corresponds to lower period of vibration and hence higher seismic forces. Since Seismic action is a function of mass and response acceleration, therefore; mass increment generate higher earthquake load and thus cause higher impact base shear and overturning movement. Whereas; wind force depends on building exposed, larger the plan dimension greater is the wind impact. Nonetheless; outriggers trusses noticeably contribute, in improving the serviceability of structure subjected to wind and earthquake forces.

Composite SaaS resource management in cloud computing using evolutionary computation

Cloud computing is an emerging computing paradigm in which IT resources are provided over the Internet as a service to users. One such service offered through the Cloud is Software as a Service or SaaS. SaaS can be delivered in a composite form, consisting of a set of application and data components that work together to deliver higher-level functional software. SaaS is receiving substantial attention today from both software providers and users. It is also predicted to has positive future markets by analyst firms. This raises new challenges for SaaS providers managing SaaS, especially in large-scale data centres like Cloud. One of the challenges is providing management of Cloud resources for SaaS which guarantees maintaining SaaS performance while optimising resources use. Extensive research on the resource optimisation of Cloud service has not yet addressed the challenges of managing resources for composite SaaS. This research addresses this gap by focusing on three new problems of composite SaaS: placement, clustering and scalability. The overall aim is to develop efficient and scalable mechanisms that facilitate the delivery of high performance composite SaaS for users while optimising the resources used. All three problems are characterised as highly constrained, large-scaled and complex combinatorial optimisation problems. Therefore, evolutionary algorithms are adopted as the main technique in solving these problems. The first research problem refers to how a composite SaaS is placed onto Cloud servers to optimise its performance while satisfying the SaaS resource and response time constraints. Existing research on this problem often ignores the dependencies between components and considers placement of a homogenous type of component only. A precise problem formulation of composite SaaS placement problem is presented. A classical genetic algorithm and two versions of cooperative co-evolutionary algorithms are designed to now manage the placement of heterogeneous types of SaaS components together with their dependencies, requirements and constraints. Experimental results demonstrate the efficiency and scalability of these new algorithms. In the second problem, SaaS components are assumed to be already running on Cloud virtual machines (VMs). However, due to the environment of a Cloud, the current placement may need to be modified. Existing techniques focused mostly at the infrastructure level instead of the application level. This research addressed the problem at the application level by clustering suitable components to VMs to optimise the resource used and to maintain the SaaS performance. Two versions of grouping genetic algorithms (GGAs) are designed to cater for the structural group of a composite SaaS. The first GGA used a repair-based method while the second used a penalty-based method to handle the problem constraints. The experimental results confirmed that the GGAs always produced a better reconfiguration placement plan compared with a common heuristic for clustering problems. The third research problem deals with the replication or deletion of SaaS instances in coping with the SaaS workload. To determine a scaling plan that can minimise the resource used and maintain the SaaS performance is a critical task. Additionally, the problem consists of constraints and interdependency between components, making solutions even more difficult to find. A hybrid genetic algorithm (HGA) was developed to solve this problem by exploring the problem search space through its genetic operators and fitness function to determine the SaaS scaling plan. The HGA also uses the problem's domain knowledge to ensure that the solutions meet the problem's constraints and achieve its objectives. The experimental results demonstrated that the HGA constantly outperform a heuristic algorithm by achieving a low-cost scaling and placement plan. This research has identified three significant new problems for composite SaaS in Cloud. Various types of evolutionary algorithms have also been developed in addressing the problems where these contribute to the evolutionary computation field. The algorithms provide solutions for efficient resource management of composite SaaS in Cloud that resulted to a low total cost of ownership for users while guaranteeing the SaaS performance.

Supersonic flutter of composite skin panels of repeated-sublaminate layup

In high-speed aerospace vehicles, supersonic flutter is a well-known phenomenon of dynamic instability to which external skin panels are prone. In theory, the instability stage is expressed by the 'flutter critical parameter' Q(crit), which is a function of the stiffness-, and dynamic pressure parameters. For a composite skin panel, Q(crit) can be maximised by lay-up optimisation. Repeated-sublaminate lay-up schemes possess good potential for economical lay-up optimisation because the corresponding effort is limited to a family of sublaminates of few layers only. When Q(crit) is obtained for all sublaminates of a family, and the sublaminates ranked accordingly, the resulting ranking reveals not only the optimum lay-up, but also the near-optimum lay-ups, which are useful design alternatives, and the inferior lay-ups which should be avoided. In this paper, we examine sublaminate-ranking characteristics for a composite panel prone to supersonic flutter. In particular, we consider a simple supported midplane-symmetrical rectangular panel of typical aspect ratio alpha and flow angle psi, and for four-layered sublaminates, obtain the Q(crit)-based rankings for a wide range of the number of repeats, r. From the rankings, we find that an optimum lay-up can exist for which the outermost layer is oriented wide of, rather than along, the flow. Furthermore, for many lay-ups other than the optimum and the inferior, we see that as r increases, Q(crit) undergoes significant change in the course of converging. To reconcile these findings, eigenvalue-coalescence characteristics are discussed in detail for specific cases.

Some studies on free vibration of composite laminates

Free vibration analysis is carried out to study the vibration characteristics of composite laminates using the modified shear deformation, layered, composite plate theory and employing the Rayleigh-Ritz energy approach. The analysis is presented in a unified form so as to incorporate all different combinations of laminate boundary conditions and with full coverage with regard to the various design parameters of a laminated plate. A parametric study is made using a beam characteristic function as the admissible function for the numerical calculations. The numerical results presented here are for an example case of fully clamped boundary conditions and are compared with previously published results. The effect of parameters, such as the aspect ratio of plates, ply-angle, number of layers and also the thickness ratios of plies in laminates on the frequencies of the laminate, is systematically studied. It is found that for anti-symmetric angle-ply or cross-ply laminates unique numerical values of the thickness ratios exist which improve the vibration characteristics of such laminates. Numerical values of the non-dimensional frequencies and nodal patterns, using the thickness ratio distribution of the plies, are then obtained for clamped laminates, fabricated out of various commonly used composite materials, and are presented in the form of the design curves.