Existence of an optimal control for stochastic control system with nonlinear cost functional

Abstract We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate convexity assumptions on the coefficients of the forward and the backward equations we prove the existence of an optimal control on a suitable reference stochastic system. The proof is based on an approximation of the stochastic control problem by a sequence of control problems with smooth coefficients, admitting an optimal feedback control. The quadruplet formed by this optimal feedback control and the associated solution of the forward and the backward equations is shown to converge in law, at least along a subsequence. The convexity assumptions on the coefficients then allow to construct from this limit an admissible control process which, on an appropriate reference stochastic system, is optimal for our stochastic control problem

STUDY OF THE ANTIOXIDANT ACTIVITY OF FLAVONOIC EXTRACT OF A MEDICINAL PLANT (CALOTROPIS PROCERA) OF AHAGGAR TAMANRASSET

Calotropis procera (family Lamiaceae) is a famous medicinal plant in the region of Hoggar Tamanrasset in southern Algeria. In this study, will have undertaken the study of the antioxidant activity of the flavonoid extract of this plant using several solvents (diethylether, ethyl acetate and N-butanol), the potential antioxidant extracts was determined on the based on their scavenging activity of the stable 1.1-Diethyl-2, hydrazylpyrryl (DPPH) free radicals. The values ​​of IC50 (mg / ml) were for the extract of 0.020 g / l, 0.014 g / l and 0.029 g / l successively for diethyl ether, ethyl acetate and N-butanol. Compared to the salts of ascorbic acid (VC) and tocopherol acid (VE) which were 0.011g / l and 0.015 g / l respectively. In addition the FRAP (Fenic antioxidant power reduction) effective acetate test on the same extract. By using VEAC (Vit E equivalent antioxidant capacity) it is found that the ethyl acetate extract has a higher reducing power than the other extracts equal to 1.115 g / l. diethyl ether 0.956g / l and n-butanol 0.987 g / l and ascorbic acid (VC) was considered a positive test with a VEAC is equal to 2.031g /

Ideas and perspectives: Microorganisms in the air through the lenses of atmospheric chemistry and microphysics

Microorganisms in the atmosphere comprise a small fraction of the Earth's microbiome. A significant portion of this aeromicrobiome consists of bacteria that typically remain airborne for a few days before being deposited. Unlike bacteria in other spheres (e.g., litho-, hydro-, phyllo-, cryospheres), atmospheric bacteria are aerosolized, residing in individual particles and separated from each other. In the atmosphere, bacteria encounter chemical and physical conditions that affect their stress levels and survival. This article goes beyond previous overviews by placing these conditions in the context of fundamental chemical and microphysical concepts related to atmospheric aerosols. We provide ranges of water amounts surrounding bacterial cells both inside and outside clouds and suggest that the small volumes of individual cloud droplets lead to nutrient and oxidant limitations. This may result in greater nutrient limitation but lower oxidative stress in clouds than previously thought. Various chemical and microphysical factors may enhance or reduce microbial stress (e.g., oxidative, osmotic, UV-induced), affecting the functioning and survival of atmospheric bacteria. We illustrate that these factors could impact stress levels under polluted conditions, indicating that conclusions about the role of pollutants in directly causing changes to microbial abundance can be erroneous. The perspectives presented here aim to motivate future experimental and modeling studies to disentangle the complex interplay of chemical and microphysical factors with the atmospheric microbiome. Such studies will help to comprehensively characterize the role of the atmosphere in modifying the Earth' microbiome, which regulates the stability of global ecosystems and biodiversity.</p