Abstract:
The effect of radiation on the unsteady natural convection flow past an infinite vertical plate is presented, wherein the plate temperature is a ramped one. The fluid considered here is a gray, absorbing/emitting but a non-scattering medium. The influence of the various parameters entering into the problem on the velocity field, temperature field, skin friction and Nusselt number is studied.

Abstract:
An analysis is performed to study the heat and mass transfer on the flow past an infinite moving vertical cylinder, in the presence of first-order chemical reaction. The closed-form solutions of the dimensionless governing partial differential equations are obtained in terms of Bessel's functions and modified Bessel's functions by the Laplace transform technique. The transient velocity profiles, temperature profiles, and concentration profiles are studied for various sets of physical parameters, namely, the chemical reaction parameter, Prandtl number, Schmidt number, thermal Grashof number, mass Grashof number, and time. The skin friction, Nusselt number, and Sherwood number are also obtained and presented in graphs. It is observed that in presence of as well as increase in chemical reaction the flow velocity decreases. Also, in presence of destructive chemical reaction the concentration profile and Sherwood number tend to the steady state at large time. 1. Introduction Combined heat and mass transfer in natural convection flows along moving vertical cylinders has got considerable attention in the last few decades because of its wide engineering and industrial application such as in hot rolling, hot extrusion, nuclear reactor cooling system, and underground energy system. Sparrow and Gregg [1] first studied the heat transfer from vertical cylinders. Goldstein and Briggs [2] presented an analysis of the transient free convective flow past vertical flat plate and circular cylinder for the unit and variable Prandtl number by employing the Laplace transform technique. Ishak [3] studied mixed convection over a vertical cylinder in presence of heat flux, while Lien et al. [4] studied the effects of free convection and mass transfer on the flow past an impulsively moving infinite vertical circular cylinder. But, in nature, the presence of pure air or water is rather impossible. It is always possible that either foreign mass is present naturally in air or water, or foreign masses are mixed with air or water. A simple example is the naturally available water vapor that causes the flow of air. In many chemical engineering processes, there is chemical reaction between a foreign mass and the fluid in which the cylinder is moving. The rate of reaction, which is directly proportional to the concentration, is termed as first order chemical reaction. The effect of a chemical reaction depends on whether the reaction is homogeneous or heterogeneous. Chambré and Young [5] have analyzed a first order chemical reaction in the neighborhood of a horizontal plate. Das et al.

Abstract:
An exact solution to one-dimensional unsteady natural convection flow past an infinite vertical accelerated plate, immersed in a viscous thermally stratified fluid is investigated. Pressure work term and the vertical temperature advection are considered in the thermodynamic energy equation. The dimensionless governing equations are solved by Laplace Transform techniques for the Prandtl number unity. The velocity and temperature profiles as well as the skin-friction and the rate of heat transfer are presented graphically and discussed the effects of the Grashof number Gr, stratification parameter S at various times t.

Abstract:
The article intends to highlight folklore as an alternative source for the writing of history, particularly of the northeastern region of India, which is inhabited by numerous tribal communities, and where there is a dearth of written documents, archaeological and other evidences. Folklore as a source is important to explain and understand societies in the context of preserving cultural diversity and protecting minority cultures, especially those of indigenous peoples and marginalized social groups. With the increased growth of several ethnic identity crises in the region in recent times, the roots for their respective indigenous history are often traced to folklore.

Abstract:
This article examines density estimation by combining a parametric approach with a nonparametric factor. The plug-in parametric estimator is seen as a crude estimator of the true density and is adjusted by a nonparametric factor. The nonparametric factor is derived by a criterion called local L_2-fitting. A class of estimators that have multiplicative adjustment is provided, including estimators proposed by several authors as special cases, and the asymptotic theories are developed. Theoretical comparison reveals that the estimators in this class are better than, or at least competitive with, the traditional kernel estimator in a broad class of densities. The asymptotically best estimator in this class can be obtained from the elegant feature of the bias function.

Abstract:
We have studied the structure of mononuclear gold supported on acidic form of faujasite zeolite in two oxidation states, namely, 0 and +1, using density functional theory. The binding of the gold monomer to the zeolite support is stronger in the oxidation state +1 than in the oxidation state 0. For the oxidation state 0, the hydrogenated clusters AuH/(2H)-FAU, AuH2/H-FAU generated by stepwise reverse hydrogen spillover from bridging OH groups of zeolite are energetically preferred over the Au/(3H)-FAU structure. Reverse hydrogen spillover of all the three acidic protons from the zeolite to the Au monomer did not lead to a stable structure. The calculated reverse hydrogen spillover energy per hydrogen atom for zeolite supported AuH and AuH2 clusters are ？10.2 and ？5.1？kJ/mol, respectively, in the oxidation state 0, while in the oxidation state +1 it is 20.9？kJ/mol for zeolite supported Au+H cluster. 1. Introduction Oxide-supported transition metal clusters form an important class of system both for theoretical and experimental investigations mainly due to their very important applications as catalysts. The activity of supported metal clusters is found to be higher than bare clusters and these metal-support interfaces are believed to act as active sites for catalysis. The factors influencing the reactivity of supported clusters are the size, structure and oxidation state of the cluster, the nature of the support, and cluster support interaction. Zeolites form an important class of support material for nanoclusters because their pores and cavities facilitate the formation of size-selective clusters of nanometer and sub-nanometer dimensions. Also, the zeolite support enables the tuning of the charge state of the cluster, as it depends upon the concentration of the acidic centres on the support, which can be modified. Among the transition metals gold has been highly investigated due to its ability to catalyse a number of reactions like CO oxidation [1], water gas shift reaction [2], epoxidation of propylene, [3] vinyl chloride synthesis [4], and so forth. Spurt in research activities involving supported gold clusters began after the pioneering discoveries of Haruta et al. [5] and Hashmi and Hutchings [6] demonstrating strong catalytic activities of highly dispersed gold. The common metal oxide supports used for gold cluster catalysis are MgO, Al2O3, SiO2, TiO2, and so forth. It has been found by Vayssilov and R？sch [7] that transition metal clusters M6 with hydrogen impurity adsorbed on a zeolite support have more nearest neighbour M-O contacts than the

Abstract:
The problem of finding fermionic formulas for the many generalizations of Kostka polynomials and for the characters of conformal field theories has been a very exciting research topic for the last few decades. In this dissertation we present new fermionic formulas for the unrestricted Kostka polynomials extending the work of Kirillov and Reshetikhin. We also present new fermionic formulas for the characters of N=1 and N=2 superconformal algebras which extend the work of Berkovich, McCoy and Schilling. Fermionic formulas for the unrestricted Kostka polynomials of type $A_{n-1}^{(1)}$ in the case of symmetric and anti-symmetric crystal paths were given by Hatayama et al. We present new fermionic formulas for the unrestricted Kostka polynomials of type $A_{n-1}^{(1)}$ for all crystal paths based on Kirillov-Reshetihkin modules. We interpret the fermionic formulas in terms of a new set of unrestricted rigged configurations. Fermionic formulas for the N=1 and N=2 superconformal algebras are derived using the Bailey lemma by establishing new Bailey flows from the nonunitary minimal models to the superconformal models.

Abstract:
All electron scalar relativistic calculations have been performed to investigate the electronic structures of isomeric Au5Li binary clusters at the BLYP/DNP level of theory. The properties of these clusters are compared with the pristine Au6 clusters. As in case of the pure Au6 cluster, the minimum energy structure of the bimetallic Au5Li cluster is triangular with the lithium atom at the mid position. It is found that substitution of a gold atom by a lithium atom in the Au6 clusters leads to an increase in the binding energy per atom, the HOMO–LUMO gap and the chemical hardness of the structures. Thus, lithium substitution leads to stabilization of the Au6 clusters. Further, the response of various sites of the minimum-energy triangular Au5Li and Au6 clusters towards impending electrophilic and nucleophilic attacks has been determined using DFT-based local reactivity descriptors. It is found that lithium substitution leads to an increase in the number of sites prone to attack by nucleophiles like CO or H2O.

Abstract:
The transformation properties of irreducible tensor operators and the applicability of the Wigner-Eckart theorem to finite magnetic groups have been studied.