A new theoretical method of evaluating polarizabilities of liquid crystals is presented and applied to the liquid crystalline compounds, namely n-alkyl-p-(4-ethoxy benzylidene amino)-α-methyl cinnamates, which exhibit smectic A and nematic phases. In the present method, vibrational frequencies are used to evaluate force constants, mean amplitude of vibration and hence bond polarizabilities. From mean polarizabilities, polarizability anisotropies and mean diamagnetic susceptibilities are also estimated. A close agreement is found between the values estimated from the present molecular vibration method and the reported data, which confirms the applicability of this method to the liquid crystals exhibiting smectic A and nematic phases. In addition, the variation of the order parameter with temperature is also studied.

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Mean Molecular polarizabilities, polarizability anisotropies and order parameters are evaluated in members of three homologous series, using two theoretical models. The variation of polarizabilities and their anisotropies with number of carbon atoms in the alkyl chain is studied. The temperature dependence of order parameter is also presented. The results are compared with the reported values and the merits of the different models are discussed.

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We study the risk-sensitive exponential cost MDP formulation and develop a trajectory-based gradient algorithm to find the stationary point of the cost associated with a set of parameterized policies. We derive a formula that can be used to compute the policy gradient from (state, action, cost) information collected from sample paths of the MDP for each fixed parameterized policy. Unlike the traditional average-cost problem, standard stochastic approximation theory cannot be used to exploit this formula. To address the issue, we introduce a truncated and smooth version of the risk-sensitive cost and show that this new cost criterion can be used to approximate the risk-sensitive cost and its gradient uniformly under some mild assumptions. We then develop a trajectory-based gradient algorithm to minimize the smooth truncated estimation of the risksensitive cost and derive conditions under which a sequence of truncations can be used to solve the original, untruncated cost problem.