Aplicação do Método de TAU a um modelo de descontaminação de água subterrânea

Neste trabalho são apresentados alguns resultados obtidos com o método de TAU implementado sobre um modelo dinâmico de transferência de massa em colunas com enchimento desordenado. A solução do sistema de equações em derivadas parciais que traduz o modelo em estado transiente revelou-se ajustada com resultados neméricos muito interessantes.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

Metacognitive and social cognition training (MSCT) in schizophrenia: a preliminary efficacy study

Psychosocial interventions have proven to be effective in treating social cognition in people with psychotic disorders. The current study aimed to determine the effects of a metacognitive and social cognition training (MSCT) program, designed to both remediate deficits and correct biases in social cognition. Thirty-five clinically stable outpatients were recruited and assigned to the MSCT program (n = 19) for 10 weeks (18 sessions) or to the TAU group (n = 16), and they all completed pre- and post-treatment assessments of social cognition, cognitive biases, functioning and symptoms. The MSCT group demonstrated a significant improvement in theory of mind, social perception, emotion recognition and social functioning. Additionally, the tendency to jump to conclusions was significantly reduced among the MSCT group after training. There were no differential benefits regarding clinical symptoms except for one trend group effect for general psychopathology. The results support the efficacy of the MSCT format, but further development of the training program is required to increase the benefits related to attributional style.

On a generalized Laguerre operational matrix of fractional integration

A new operationalmatrix of fractional integration of arbitrary order for generalized Laguerre polynomials is derived.The fractional integration is described in the Riemann-Liouville sense.This operational matrix is applied together with generalized Laguerre tau method for solving general linearmultitermfractional differential equations (FDEs).Themethod has the advantage of obtaining the solution in terms of the generalized Laguerre parameter. In addition, only a small dimension of generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the proposedmethod is very effective and convenient for linear multiterm FDEs on a semi-infinite interval.

Numerical solution of a PDE system with non-linear steady state conditions that translates the air stripping pollutants removal

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

Spectral solution for the air stripping pollutants removal dynamic model with non linear steady state conditions

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

Commercial squids: Characterization, assessment of potential health benefits/risks and discrimination based on mineral, lipid and vitamin E concentrations

The most consumed squid species worldwide were characterized regarding their concentrations of minerals, fatty acids, cholesterol and vitamin E. Interspecific comparisons were assessed among species and geographical origin. The health benefits derived from squid consumption were assessed based on daily minerals intake and on nutritional lipid quality indexes. Squids contribute significantly to daily intake of several macro (Na, K, Mg and P) and micronutrients (Cu, Zn and Ni). Despite their low fat concentration, they are rich in long-chain omega-3 fatty acids, particularly docosahexaenoic (DHA) and eicosapentanoic (EPA) acids, with highly favorable ω-3/ω-6 ratios (from 5.7 to 17.7), reducing the significance of their high cholesterol concentration (140–549 mg/100 g ww). Assessment of potential health risks based on minerals intake, non-carcinogenic and carcinogenic risks indicated that Loligo gahi (from Atlantic Ocean), Loligo opalescens (from Pacific Ocean) and Loligo duvaucelii (from Indic Ocean) should be eaten with moderation due to the high concentrations of Cu and/or Cd. Canonical discriminant analysis identified the major fatty acids (C14:0, C18:0, C18:1, C18:3ω-3, C20:4ω-6 and C22:5ω-6), P, K, Cu and vitamin E as chemical discriminators for the selected species. These elements and compounds exhibited the potential to prove authenticity of the commercially relevant squid species.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.