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Regularity estimates for some free boundary problems of obstacle-type
We study regularity estimates for solutions to implicit constraint obstacle problems and penalized boundary obstacle problems. We first prove regularity estimates for the solution and the free boundary in the classical stochastic impulse control problem. We show that the free boundary partial {u < Mu}, where Mu is the implicit constraint obstacle, can be decomposed into a union of regular points, singular points, and degenerate points with corresponding regularity and measure theoretic estimates. We then turn to generalizing our analysis to the fully nonlinear problem with obstacles admitting a general modulus of semi-convexity omega(r). We prove that solutions to the fully nonlinear stochastic impulse control problem are C^{omega(r)} up to C^{1,1}. Finally we turn our attention to study both nonuniform and uniform estimates for the penalized boundary obstacle problem, Delta^{1/2}u^{epsilon} =beta_{epsilon} (u^{epsilon}). We obtain sharp estimates for the solution in both the nonuniform and uniform theory.Mathematic
Improvement in Th1/Th2 immune homeostasis, antioxidative status and resistance to pathogenic E. coli on consumption of probiotic Lactobacillus rhamnosus fermented milk in aging mice
Preparation and Evaluation of Tubular Micelles of Pluronic Lecithin Organogel for Transdermal Delivery of Sumatriptan
The present work focuses on the preparation and evaluation of lecithin organogel system of thermoreversible polymer pluronic F127, which would enhance the stability and absorption of sumatriptan succinate across the skin. Formulations were developed with and without co-surfactant (pluronic F127). The prepared organogels were evaluated for its appearance, organoleptic characteristics, and feel upon application, homogeneity, occlusivenes, washability, pH, viscosity, spreadability, gel transition temperature of formulations. The formulations were also evaluated for drug content, in vitro drug diffusion properties and skin irritation testing. In vivo evaluation of formulations was carried out by hot plate and writhing test method, and finally the optimized formulation was subjected to stability studies. The developed formulations were easily washable, smooth in feel, and showed no clogging which indicate superior texture of system. Formulation, containing pluronic showed greater spreadability and higher drug diffusion rate as compared to pluronic free organogel. Drug content of organogel formulations was in the range of 94–97%. The pH of the formulations was 6.48 ± 0.5 and 6.98 ± 0.1, reflecting no risk of skin irritation. Pluronic not only enhances the stability of organogel by increasing the viscosity (from 6,541 ± 234.76 to 7,826 ± 155.65 poise) but also increases the release of drug from 67.39 ± 1.53% to 74.21 ± 1.7%. The sumatriptan exhibits higher and long lasting antinociceptive effect as indicated by the persistent increase in reaction time in hot plate and inhibited abdominal contraction in acetic acid-induced writhing test (p < 0.05). The prepared optimized formulation was found to be stable without any significant changes at room temperature