55 resultados para System of differential equations

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During time-resolved optical stimulation experiments (TR-OSL), one uses short light pulses to separate the stimulation and emission of luminescence in time. Experimental TR-OSL results show that the luminescence lifetime in quartz of sedimentary origin is independent of annealing temperature below 500 °C, but decreases monotonically thereafter. These results have been interpreted previously empirically on the basis of the existence of two separate luminescence centers LH and LL in quartz, each with its own distinct luminescence lifetime. Additional experimental evidence also supports the presence of a non-luminescent hole reservoir R, which plays a critical role in the predose effect in this material. This paper extends a recently published analytical model for thermal quenching in quartz, to include the two luminescence centers LH and LL, as well as the hole reservoir R. The new extended model involves localized electronic transitions between energy states within the two luminescence centers, and is described by a system of differential equations based on the Mott–Seitz mechanism of thermal quenching. It is shown that by using simplifying physical assumptions, one can obtain analytical solutions for the intensity of the light during a TR-OSL experiment carried out with previously annealed samples. These analytical expressions are found to be in good agreement with the numerical solutions of the equations. The results from the model are shown to be in quantitative agreement with published experimental data for commercially available quartz samples. Specifically the model describes the variation of the luminescence lifetimes with (a) annealing temperatures between room temperature and 900 °C, and (b) with stimulation temperatures between 20 and 200 °C. This paper also reports new radioluminescence (RL) measurements carried out using the same commercially available quartz samples. Gaussian deconvolution of the RL emission spectra was carried out using a total of seven emission bands between 1.5 and 4.5 eV, and the behavior of these bands was examined as a function of the annealing temperature. An emission band at ∼3.44 eV (360 nm) was found to be strongly enhanced when the annealing temperature was increased to 500 °C, and this band underwent a significant reduction in intensity with further increase in temperature. Furthermore, a new emission band at ∼3.73 eV (330 nm) became apparent for annealing temperatures in the range 600–700 °C. These new experimental results are discussed within the context of the model presented in this paper.

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In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.

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INTRODUCTION Despite important advances in psychological and pharmacological treatments of persistent depressive disorders in the past decades, their responses remain typically slow and poor, and differential responses among different modalities of treatments or their combinations are not well understood. Cognitive-Behavioural Analysis System of Psychotherapy (CBASP) is the only psychotherapy that has been specifically designed for chronic depression and has been examined in an increasing number of trials against medications, alone or in combination. When several treatment alternatives are available for a certain condition, network meta-analysis (NMA) provides a powerful tool to examine their relative efficacy by combining all direct and indirect comparisons. Individual participant data (IPD) meta-analysis enables exploration of impacts of individual characteristics that lead to a differentiated approach matching treatments to specific subgroups of patients. METHODS AND ANALYSIS We will search for all randomised controlled trials that compared CBASP, pharmacotherapy or their combination, in the treatment of patients with persistent depressive disorder, in Cochrane CENTRAL, PUBMED, SCOPUS and PsycINFO, supplemented by personal contacts. Individual participant data will be sought from the principal investigators of all the identified trials. Our primary outcomes are depression severity as measured on a continuous observer-rated scale for depression, and dropouts for any reason as a proxy measure of overall treatment acceptability. We will conduct a one-step IPD-NMA to compare CBASP, medications and their combinations, and also carry out a meta-regression to identify their prognostic factors and effect moderators. The model will be fitted in OpenBUGS, using vague priors for all location parameters. For the heterogeneity we will use a half-normal prior on the SD. ETHICS AND DISSEMINATION This study requires no ethical approval. We will publish the findings in a peer-reviewed journal. The study results will contribute to more finely differentiated therapeutics for patients suffering from this chronically disabling disorder. TRIAL REGISTRATION NUMBER CRD42016035886.

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In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

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CYP17A1 plays a pivotal role in the biosynthesis of androgens in the adrenals and the gonads. Although this enzyme catalyzes two different reactions on one single active site, its specific activities are regulated independently. Although the 17alpha-hydroxylase activity is rather constant and regulated by gene expression, the 17,20-lyase activity varies significantly with the amount of cofactors or by protein phosphorylation. cAMP increases CYP17A1 expression, P450c17 phosphorylation, and androgen production. However, the exact mechanism(s) and the specific regulators of CYP17A1 remain unknown. Therefore, we studied the regulation of adrenal androgen biosynthesis in human adrenal H295R cells focusing on CYP17A1. We analyzed androgen production and P450c17 activities in H295R cells grown under normal and serum-free conditions and/or after stimulation with 8-bromoadenosine-cAMP. H295R cells grown in starvation medium produced more androgens and had decreased HSD3B2 expression and activity but increased P450c17-17,20-lyase activity and serine phosphorylation. Although starvation increased serine phosphorylation of P450c17 specifically, cAMP stimulation enhanced threonine phosphorylation exclusively. Time-course experiments revealed that a short cAMP stimulation augmented threonine phosphorylation of P450c17 but did not increase 17,20-lyase activity. By contrast, long cAMP stimulation increased androgen production through increased P450c17 activities by enhancing CYP17A1 gene expression. We conclude that serum withdrawal shifts steroidogenesis of H295R cells towards androgen production, providing a suitable model for detailed studies of androgen regulation. In addition, our study shows that starvation and cAMP stimulation regulate P450c17 phosphorylation differentially and that an increase in P450c17 phosphorylation does not necessarily lead to enhanced enzyme activity and androgen production.