Correlation trends in the ground state static electric dipole polarizabilities of closed-shell atoms and ions

We employ the closed-shell perturbed relativistic coupled-cluster (RCC) theory developed by us earlier [Phys. Rev. A {\bf 77}, 062516 (2008)] to evaluate the ground state static electric dipole polarizabilities (\alpha s) of several atomic systems. In this work, we have incorporated a class of higher order many-body effects in our calculations that had not been taken into account in the above paper. We highlight their importance in improving the accuracy of $\alpha$. We also calculate the ground state \alpha s of the inert gas atoms and several iso-electronic singly and doubly charged ions in order to make a comparative study of the trends of the correlation effects. Furthermore, we have developed a method to construct intermediate diagrams that are required for the computation of the unperturbed singles and doubles coupled-cluster amplitudes. Our RCC results are compared with those of many-body perturbation theory at different orders to demonstrate the importance of higher order correlation effects for the accurate determination of (\alpha s) of the systems that we have considered.Comment: 11 pages, 15 figure

Economics of Sugarcane-based Farming System in Western Uttar Pradesh

Amongst 38 farming systems prevalent in the western Uttar Pradesh region, sugarcane–livestock– cereals–fodder has been found the major system being followed by a majority of the farmers. It has been found that sugarcane farmer keeps in general two dairy animals, largely for household milk consumption. The major income source of farmers in the area has been found sugarcane (58 per cent), followed by livestock and cereal crops. The study has revealed that marginal farmers take highest credit, while large farmers take minimum credit. It has also been observed that facility of Kisan Credit Card (KCC) is being availed by only 21 per cent farmers. Farming activity-wise analysis has revealed that sugarcane provides maximum employment, followed by livestock and wheat. In terms of income, the study has observed that a family worker earns Rs 41,270 per year in the study area, which is much lower than that in Punjab (Rs 74,080/year). The study has suggested that a combination of technology, policy and institutional innovations is needed for improvement in productivity and profitability of crops and livestock in the area.Crop Production/Industries,

Algorithms based on DQM with new sets of base functions for solving parabolic partial differential equations in (2+1)(2+1) dimension

This paper deals with the numerical computations of two space dimensional time dependent parabolic partial differential equations by adopting adopting an optimal five stage fourth-order strong stability preserving Runge Kutta (SSP-RK54) scheme for time discretization, and three methods of differential quadrature with different sets of modified B-splines as base functions, for space discretization: namely i) mECDQM: (DQM with modified extended cubic B-splines); ii) mExp-DQM: DQM with modified exponential cubic B-splines, and iii) MTB-DQM: DQM with modified trigonometric cubic B-splines. Specially, we implement these methods on convection-diffusion equation to convert them into a system of first order ordinary differential equations,in time which can be solved using any time integration method, while we prefer SSP-RK54 scheme. All the three methods are found stable for two space convection-diffusion equation by employing matrix stability analysis method. The accuracy and validity of the methods are confirmed by three test problems of two dimensional convection-diffusion equation, which shows that the proposed approximate solutions by any of the method are in good agreement with the exact solutions