Optimal control of a one-dimensional storage process

We consider the discounted and ergodic optimal control problems related to a one-dimensional storage process. The existence and uniqueness of the corresponding Bellman equation and the regularity of the optimal value is established. Using the Bellman equation an optimal feedback control is constructed. Finally we show that under this optimal control the origin is reachable.This work was supported by the National Science Foundation under Grant No. MCS 8121940.     

Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs

For a d‐dimensional diffusion of the form dX_t = μ(X_t)dt + σ(X_t)dW_t and continuous functions f and g, we study the existence and uniqueness of adapted processes Y, Z, Γ, and A solving the second‐order backward stochastic differential equation (2BSDE) If the associated PDE has a sufficiently regular solution, then it follows directly from Itô's formula that the processes solve the 2BSDE, where ?? is the Dynkin operator of X without the drift term. The main result of the paper shows that if f is Lipschitz in Y as well as decreasing in Γ and the PDE satisfies a comparison principle as in the theory of viscosity solutions, then the existence of a solution (Y, Z,Γ, A) to the 2BSDE implies that the associated PDE has a unique continuous viscosity solution v and the process Y is of the form Y_t = v(t, X_t), t ∈ [0, T]. In particular, the 2BSDE has at most one solution. This provides a stochastic representation for solutions of fully nonlinear parabolic PDEs. As a consequence, the numerical treatment of such PDEs can now be approached by Monte Carlo methods. © 2006 Wiley Periodicals, Inc.     

Special Issue: Optimization and Stochastic Control in Finance,Journal of Optimization Theory and Applications

In this paper, we study the near-optimal control for systems governed by forward–backward stochastic differential equations via dynamic programming principle. Since the nonsmoothness is inherent in this field, the viscosity solution approach is employed to investigate the relationships among the value function, the adjoint equations along near-optimal trajectories. Unlike the classical case, the definition of viscosity solution contains a perturbation factor, through which the illusory differentiability conditions on the value function are dispensed properly. Moreover, we establish new relationships between variational equations and adjoint equations. As an application, a kind of stochastic recursive near-optimal control problem is given to illustrate our theoretical results.     

Clairaut Anti-invariant Submersions from Sasakian and Kenmotsu Manifolds

We investigate new Clairaut conditions for anti-invariant submersions from Sasakian and Kenmotsu manifolds onto Riemannian manifolds. We prove that there do not exist Clairaut anti-invariant submersion admitting vertical Reeb vector field in case of the total manifold is Sasakian. Several illustrative examples are also included.     

Transition-metal-free regioselective thiocyanation of phenols,anilines and heterocycles

An expedient direct and regioselective thiocyanation of phenols, anilines and heterocycles is described. Transformation is realized via the direct CH functionalization under transition metal free conditions at ambient temperature in excellent yields. Method proved to be monoselective and variety of functional groups tolerated the reaction conditions. The practicality of the protocol is demonstrated in gram scale synthesis of a precursor of PPAR δ agonist in excellent yield.     

Synthesis of 1-Aryl-3-phenethylamino-1-propanone hydrochlorides as possible potent cytotoxic agents

1-Aryl-3-phenethylamino-1-propanone hydrochlorides 1-10, which are potentialpotent cytotoxic agents, were synthesized via Mannich reactions using paraformaldehyde,phenethylamine hydrochloride as the amine component and acetophenone, 4'-methyl-, 4'-methoxy-, 4'-chloro-, 4'-fluoro-, 4'-bromo-, 2',4'-dichloro-, 4'-nitro-, 4'-hydroxyacetophenone or 2-acetylthiophene as the ketone component. Yields were in the87-98 % range. Of the compounds synthesized, compounds 2, 6-8 and 10 were new. Theoptimum reaction conditions were investigated by changing the mol ratios of the reactants,the solvents and the acidity levels using 1 and 10 as representative targets. It was observedthat the best mol ratio of the ketone, paraformaldehyde and phenethylamine hydrochloridewas 1:1.2:1 (compared with a 2:2.1 ratio), and the most suitable reaction medium wasethanol containing concentrated hydrochloric acid (compared with only ethanol or nosolvent). This study may serve as a guide for the conditions of the reactions to synthesizecompounds having similar chemical structures.     

Higher Dimensional Plane Symmetric Cosmological Models with Two-Fluid Source in General Relativity

We consider anisotropic, homogeneous two-fluid plane symmetric cosmological models in higher dimensions. Here one fluid represents the matter content of the universe and another fluid is chosen to model the CMB (cosmic microwave background) radiation. The radiation and matter content of the universe are in interactive phase. Also we have discussed the behaviour of fluid parameters and kinematical parameters.