Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

Pico Cell Integration to Operator’s Incident Management Process

Mobile network coverage is traditionally provided by outdoor macro base stations, which have a long range and serve several of customers. Due to modern passive houses and tightening construction legislation, mobile network service is deteriorated in many indoor locations. Typically, solutions for indoor coverage problem are expensive and demand actions from the mobile operator. Due to these, superior solutions are constantly researched. The solution presented in this thesis is based on Small Cell technology. Small Cells are low power access nodes designed to provide voice and data services.. This thesis concentrates on a specific Small Cell solution, which is called a Pico Cell. The problem regarding Pico Cells and Small Cells in general is that they are a new technological solution for the mobile operator, and the possible problem sources and incidents are not properly mapped. The purpose of this thesis is to figure out the possible problems in the Pico Cell deployment and how they could be solved within the operator’s incident management process. The research in the thesis is carried out with a literature research and a case study. The possible problems are investigated through lab testing. Pico Cell automated deployment process was tested in the lab environment and its proper functionality is confirmed. The related network elements were also tested and examined, and the emerged problems are resolvable. Operators existing incident management process can be used for Pico Cell troubleshooting with minor updates. Certain pre-requirements have to be met before Pico Cell deployment can be considered. The main contribution of this thesis is the Pico Cell integrated incident management process. The presented solution works in theory and solves the problems found during the lab testing. The limitations in the customer service level were solved by adding the necessary tools and by designing a working question pattern. Process structures for automated network discovery and pico specific radio parameter planning were also added for the mobile network management layer..

Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.

Invertibility characterization of Wiener-Hopf plus Hankel operators on variable exponent Lebesgue spaces via even asymmetric factorization

We obtain invertibility and Fredholm criteria for the Wiener-Hopf plus Hankel operators acting between variable exponent Lebesgue spaces on the real line. Such characterizations are obtained via the so-called even asymmetric factorization which is applied to the Fourier symbols of the operators under study.

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

Strictly singular operators in pairs of L (p) space

Let E and F be Banach spaces. A linear operator from E to F is said to be strictly singular if, for any subspace Q aS, E, the restriction of A to Q is not an isomorphism. A compactness criterion for any strictly singular operator from L (p) to L (q) is found. There exists a strictly singular but not superstrictly singular operator on L (p) , provided that p not equal 2.

Rota's universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In particular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

The significant role of third-party logistics (3pl) operators as fosterers of organizational performance in colombian companies

La eliminación de barreras entre países es una consecuencia que llega con la globalización y con los acuerdos de TLC firmados en los últimos años. Esto implica un crecimiento significativo del comercio exterior, lo cual se ve reflejado en un aumento de la complejidad de la cadena de suministro de las empresas. Debido a lo anterior, se hace necesaria la búsqueda de alternativas para obtener altos niveles de productividad y competitividad dentro de las empresas en Colombia, ya que el entorno se ha vuelto cada vez más complejo, saturado de competencia no sólo nacional, sino también internacional. Para mantenerse en una posición competitiva favorable, las compañías deben enfocarse en las actividades que le agregan valor a su negocio, por lo cual una de las alternativas que se están adoptando hoy en día es la tercerización de funciones logísticas a empresas especializadas en el manejo de estos servicios. Tales empresas son los Proveedores de servicios logísticos (LSP), quienes actúan como agentes externos a la organización al gestionar, controlar y proporcionar actividades logísticas en nombre de un contratante. Las actividades realizadas pueden incluir todas o parte de las actividades logísticas, pero como mínimo la gestión y ejecución del transporte y almacenamiento deben estar incluidos (Berglund, 2000). El propósito del documento es analizar el papel de los Operadores Logísticos de Tercer nivel (3PL) como promotores del desempeño organizacional en las empresas colombianas, con el fin de informar a las MIPYMES acerca de los beneficios que se obtienen al trabajar con LSP como un medio para mejorar la posición competitiva del país.

O desenvolvimento do texto dissertativo em crianças da 4ª série

This reaserch analysed the developmental stage of fourth grade (primary school) children in ability of writting argumentative texts joint with their context. The reason of this reaserch is the lack of new studies in linguistical area and high ratio of unable students to make this kind of text. It will be showed the analysis of making text by public schools children for three months. These data were analysed trying identify argumentative operators, the kinds of arguments used and the stage of the argumentative ability of these children. The study showed that the introduction of argumentative text in first grades give them more chances of succeed, preparing these pupils in their finishing high school. This fact obviously will make easier the development of their critical point of view, helping the students to think about their living social reality.

Sistema de sincronismo entre a colhedora de cana-de-açúcar e o veículo de transbordo

One of the problems found in mechanical harvest of sugar cane is the lack of synchronism between the harvest machine and the infield wagon, causing crop losses as well as operational capacity. The objective of the present research was to design a system capable of helping to synchronize the sugar cane harvest machine with the wagon. The communication between tractor and harvest machine is wireless. Two ultrasound sensors coupled to the elevator and a microprocessor manage such information, generating a correct synchronization among the machines. The system was tested in laboratory and on field performing its function adequately, maintaining the two machines in synchronization, indicating and alerting the operators their relative positions. The developed system reduced the sugar cane lost in 60 kg ha-1 comparing to the harvest with the system turned off.

Proposição e avaliação de um método baseado em projeção de luz para reconstrução e análise da superfície do tronco durante a respiração

Universidade Estadual de Campinas . Faculdade de Educação Física

Comparasion of two minimally invasive methods on the longevity of glass ionomer cement restorations: short-term results of a pilot study

The purpose of this study was to evaluate the clinical performance of glass ionomer cement (GIC) restorations comparing two minimally invasive methods in permanent teeth after 12 months. Fifty pregnant women (second trimester of pregnancy), mean age 22 ± 5.30 years, were treated by two previously trained operators. The treatment approaches tested were: chemomechanical method (CarisolvTM; MediTeam) and atraumatic restorative treatment (ART). A split-mouth study design was used in which the two treatments were randomly placed in 50 matched pairs of permanent teeth. The chemomechanical method (CM) was the test group and the ART was the control group. The treatments were performed in Public Health Centers. The tested restorative material was a high-strength GIC (Ketac Molar; 3M/ESPE). The restorations were placed according to the ART guidelines. Two calibrated independent examiners evaluated the restorations in accordance with ART criteria. The inter-examiner kappa was 0.97. Data were analyzed using 95% confidence interval on the binomial distribution and Fisher's exact test at 5% significance level. In a 12-month follow-up, 86% of the restorations were evaluated. In the test group (CM), 100% (CI=93.3-100%) of the restorations were considered successful. In the control group (ART) 97.6% (CI=87.4-99.9%) of the restorations were considered successful and 2.4% unsuccessful (marginal defect >0.5 mm). There was no statistically significant difference between the 12-mounth success rate for both groups (Fisher's exact test: P=0.49) and between the two operators (Fisher's exact test: P=1.00). Both minimally invasive methods, chemomechanical method and ART, showed a similar clinical performance after 12 months of follow up.

Use of flowable composite as intermediary layer in non-carious cervical lesions restored with composite resin: 48-month follow-up

PURPOSE: In this case report, the clinical performance of a microhybrid resin composite placed with or without a flowable resin composite was compared, over a 48-month period. CASE DESCRIPTION: The patient of this case report presented 2 pairs of equivalent cervical abfraction lesions, under occlusion. Four restorations were placed in teeth 34, 35, 44 and 45. The restorations were divided into groups (Single Bond + Filtek-Flow + Filtek Z250 or Single Bond + Filtek Z250) and the materials were applied according to the manufactures instructions. Two previously calibrated operators placed the restorations and two other independent examiners evaluated the restorations at baseline and after 48 months, according to the USPHS criteria and modified criteria for color match. CONCLUSION: After 48 months of evaluation the lesions restored with Filtek-Flow as a liner under Filtek Z250 did not show better clinical performance than the restorations without Filtek-Flow. All restorations showed a trend toward dark yellowing after 48 months.