Green tea glycolic extract-loaded liquid crystal systems: development, characterization and microbiological control

ABSTRACT Liquid crystal systems (LCSs) have interesting cosmetic applications because of their ability to increase the therapeutic efficiency and solubility of active ingredients. The aim of the present research was to develop green tea glycolic extract-loaded LCSs, to characterize and to perform microbiological control. The ternary phase diagram was constructed using polysorbate 20, silicone glycol copolymer (SGC) - DC 193(r), and distilled water with 1.5% glycolic green tea extract. The systems were characterized by polarized light microscopy. Formulations selected were characterized as transparent viscous systems and transparent liquid system indicated mesophases lamellar structure. The results of the microbiological analysis of mesophilic aerobic microorganisms (bacteria and fungi) revealed that the above formulation showed a biologic load <10 CFU/mL in all samples. In conclusion, liquid crystalline systems that have presented formation of a lamellar mesophases were developed. Furthermore, the formulation and products tested presented the adequate microbiological quality in accordance with official recommendations

Extension Of Gkb-fp Algorithm To Large-scale General-form Tikhonov Regularization

In a recent paper an algorithm for large-scale Tikhonov regularization in standard form called GKB-FP was proposed and numerically illustrated. In this paper, further insight into the convergence properties of this method is provided, and extensions to general-form Tikhonov regularization are introduced. In addition, as alternative to Tikhonov regularization, a preconditioned LSQR method coupled with an automatic stopping rule is proposed. Preconditioning seeks to incorporate smoothing properties of the regularization matrix into the computed solution. Numerical results are reported to illustrate the methods on large-scale problems. © 2013 John Wiley & Sons, Ltd.213316339Tikhonov, A.N., Solution of incorrectly formulated problems and the regularization method (1963) Soviet Mathematics Doklady, 4, pp. 1035-1038Morozov, V.A., (1984) Regularization Methods for Solving Incorrectly Posed Problems, , Springer: New YorkHansen, P.C., O'Leary, D.P., The use of the L-curve in the regularization of discrete ill-posed problems (1993) SIAM Journal on Scientific Computing, 14, pp. 1487-1503Golub, G.H., Heath, M., Wahba, G., Generalized cross-validation as a method for choosing a good ridge parameter (1979) Technometrics, 21, pp. 215-222Regińska, T., A regularization parameter in discrete ill-posed problems (1996) SIAM Journal on Scientific Computing, 3, pp. 740-749Bazán, F.S.V., Fixed-point iterations in determining the Tikhonov regularization parameter (2008) Inverse Problems, 24. , DOI: 10.1088/0266-5611/24/3/035001Engl, H.W., Hanke, M., 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and Discrete Ill-posed Problems, , SIAM: PhiladelphiaKirsch, A., (1996) An Introduction to the Mathematical Theory of Inverse Problems, , Springer: New YorkHansen, P.C., Regularization tools: a MATLAB package for analysis and solution of discrete ill-posed problems (1994) Numerical Algorithms, 6, pp. 1-35Bazán, F.S.V., Francisco, J.B., An improved fixed-point algorithm for determining the Tikhonov regularization parameter (2009) Inverse Problems, 25. , DOI: 10.1088/0266-5611/25/4/045007Golub, G.H., Van Loan, C.F., (1996) Matrix Computations, , The Johns Hopkins University Press: BaltimorePaige, C.C., Saunders, M.A., Solution of sparse indefinite systems of linear equations (1975) SIAM Journal on Numerical Analysis, 12, pp. 617-629Hansen, P.C., The discrete picard condition for discrete ill-posed problems (1990) BIT, 30, pp. 658-672Castellanos, J.J., Gómez, S., Guerra, V., The triangle method for finding the corner of the L-curve (2002) Applied Numerical Mathematics, 43, pp. 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Résultats préléminaires sur le besoin en protéine et en lysine des porcelets de race Alentejana

International audienc

O método de Galerkin estocástico e a equação ao diferencial de transporte linear com dados de entrada Aleatórios

We use the stochastic Garlekin method to solve a linear transport equation with random data. Following the ideias of the method, the statiscal solution is projected on the space generated by generalized Polynomials Chaos, a basis for the space of random functions. Numerical simulations compare our results with the Monte Carlo simulations.Apresentamos o método de Garlekin estocástico para resolver equações diferenciais com dados de entrada aleatórios. O método de Galerkin estocástico produzido é uma extensão simples do método de Galerkin clássico usado em problemas determinísticos. Especificamente, o método consiste em projetar a solução estatística sobre o espaço gerado pelos Polinômios de Caos generalizados que formam uma base para o espaço de funções aleatórias. Introduziremos o método sobre uma equação de transporte linear aleatória. Faremos o tratamento numérico e comparamos com as simulações de Monte Carlo.23324