A study of the effect of the loss function on Bayes Estimate,posterior risk and hazard function for Lindley distribution

In this paper, mathematical properties of Lindley distribution via Bayesian approach are derived under different loss functions. These properties include: Bayes Estimators, posterior risks and failure rate function for simulation scheme. Elicitation of hyperparameters is also discussed. A real life application to waiting time data at the bank is also described for the developed procedures (also using WinBUGS). Results are compared on the basis of posterior risk.     

A Facile Route for the Synthesis of 1-[5-Hydroxy-3-methyl-1-(2-thiazolyl)-4-pyrazolyl]-1,3-butanediones from Dehydroacetic Acid

Thiosemicarbazone (1) of dehydroacetic acid (DHAA) reacts smoothly with α-haloketones to yield corresponding thiazolylhydrazones (2) of DHAA, which on refluxing in EtOH-AcOH rearrange to the title compounds (3).     

Third-order iterative methods free from second derivatives for nonlinear equation

In this paper, we suggest and analyze a new two-step iterative method for solving nonlinear equations, which is called the modified Householder method without second derivatives for nonlinear equation. We also prove that the modified method has cubic convergence. Several examples are given to illustrate the efficiency and the performance of the new method. New method can be considered as an alternative to the present cubic convergent methods for solving nonlinear equations.     

Homogeneous Oxidation of Alcohols by Copper Permanganate

An improved protocol for the oxidation of sec. alcohols by copper permanganate is described by carrying out the reaction in a homogeneous medium (acetic acid), affording rapid and complete conversion to the ketones.     

Isolation of a flavonoid from Feronia limonia

The roots and leaves of Feronia limonia yielded a flavonoid characterized as 5-hydroxy-2-(4-hydroxyphenyl)-7-methoxy-6-(3-methylbut-2-enyl)chroman-4-one along with known imperatorin, bergapten and xanthotoxin. These isolated compounds were characterized by UV, IR, NMR and mass spectral studies.     

Modified variational iteration method for solving fourth-order boundary value problems

In this paper, we apply the modified variational iteration method (MVIM) for solving the fourth-order boundary value problems. The proposed modification is made by introducing He’s polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using the Adomian’s polynomials can be considered as a clear advantage of this algorithm over the decomposition method.     

Exp-function method for traveling wave solutions of nonlinear evolution equations

In this paper, we apply the exp-function method to construct generalized solitary and periodic solutions of nonlinear evolution equations. The proposed technique is tested on the modified Zakharov-Kuznetsov (ZK) and Zakharov-Kuznetsov-Modified-Equal-Width (ZK-MEW) equations. These equations play a very important role in mathematical physics and engineering sciences. The suggested algorithm is quite efficient and is practically well suited for use in these problems. Numerical results clearly indicate the reliability and efficiency of the proposed exp-function method.     

Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces

In this paper, we introduce a new system of general variational inequalities in Banach spaces. We establish the equivalence between this system of variational inequalities and fixed point problems involving the nonexpansive mapping. This alternative equivalent formulation is used to suggest and analyze a modified extragradient method for solving the system of general variational inequalities. Using the demi-closedness principle for nonexpansive mappings, we prove the strong convergence of the proposed iterative method under some suitable conditions.     

Some iterative methods for nonconvex variational inequalities

It is well known that the nonconvex variational inequalities are equivalent to the fixed point problems. We use this equivalent alternative formulation to suggest and analyze a new class of two-step iterative methods for solving the nonconvex variational inequalities. We discuss the convergence of the iterative method under suitable conditions. We also introduce a new class of Wiener – Hopf equations. We establish the equivalence between the nonconvex variational inequalities and the Wiener – Hopf equations. This alternative equivalent formulation is used to suggest some iterative methods. We also consider the convergence analysis of these iterative methods. Our method of proofs is very simple compared to other techniques.