Applied Mathematics

In this paper we present a new method to compute the determinants of matrices of order 4. This method computes the determinant of matrices of order 4 by using the schemes.

We investigate the simultaneous effects of soret and ohmic heating on MHD free convective heat and mass transfer flow for a micro polar fluid bounded by a vertical infinite surface. Approximate solutions have been derived for the velocity, angular velocity, temperature field, concentration profiles, skin friction and rate of heat transfer using multi-parameter perturbation method. The effects of various pertinent parameters on flow, heat and mass transfer properties are discussed numerically and explained graphically. Also the velocity profiles of micropolar fluid is compared with the corresponding flow problem for a Newtonian fluid and found that the polar fluid velocity is decreasing

The Expectation-Maximization (EM) algorithm is a parameter estimation method which performs to the general data frame of maximum-likelihood estimation, including some applications to data analysis and statistics. There is the work by Dempster, Laird and Rubin (1977) on the key features of defining the EM algorithm. Logistic mixtures, unlike normal mixtures, have not been studied for the EM algorithm. In this paper, we express the theorem about a relationship between the gradient of the log likelihood and the step in parameter space taken by the EM algorithm in their multivariate extension for the mixture logistic distribution (see Malik and Abraham (1973)). The literature on determination of the number of modes in logistic mixture models has focused primarily on univariate mixtures. In fact, there is a simple description of modality when one is mixing two univariate components. In particular, an analogue of the techniques such as the paper written by Robertson and Fryer (1969) allows to attain the results in the case of the convex combination of two item response functions (IRFs) for the unidimensional dichotomous 1-parameter to 4-parameter logistic (1PL to 4PL) item response theory (IRT) models.

In this paper we introduce some properties and definition of the new integral transform, called ZZ transform. Farther, we use ZZ transform to solve systems of ordinary differential equations. The results indicate these methods to be very effective and simple.

This paper presented a trust region method with memory, which retained the individuals with secondary high fitness. What’s more, we brought in the most decline direction and conjugate direction to keep the method going on and even joined it in genetic algorithm for enhancing search efficiency in the middle-late time. We find the trust region with memory had higher search ability than trust region comparing results and the algorithm was an effective method on solving multi-peak problems proved by examples.

Distribution theory is powerful tool for dealing with pseudo-functions including impulsive phenomena, absolutely divergent integrals and their Fourier transforms. A new theory of generalized functions which is an extension of classical theory of distributions has been introduced and various properties have been generalized. The purpose of this paper is two dimensional fractional cosine transform is extended in the distributional generalized sense. Operators on the testing function E and its dual space E^* are obtained.

Dufour effect on unsteady MHD flow through porous medium past an impulsively started inclined oscillating plate with variable temperature and mass diffusion is studied here. The fluid considered is gray, absorbing-emitting radiation but a non-scattering medium. The Governing equations involved in the present analysis are solved by the Laplace-transform technique. The velocity profile is discussed with the help of graphs drawn for different parameters.

The motion of an infinitesimal body with variable mass is studied. The equations of motion of the restricted three body problem with infinitesimal body of variable mass are introduced. The Jeans' law of mass change is applied. To tackle the dynamical problem, the Hamiltonian of the problem is formed with the time as independent variable. The solution of the equations of motion is formulated based on Lie series developments. Numerical representation of coordinates and momenta are given.

This paper is concerned with the existence of solutions for some partial functional integrodifferential equations with state-dependent delay in Banachspaces. The results are obtained by using Leray-Schauder’s alternative fixed point theorem. Finally, an example is provided to illustrate the main results.

The aim of this paper is to prove that the infinite family of pure octic field L = Q( ?8 m) is non-monogenic if m ? 1 (mod 4), ultimately, to complete the classification of pure octic fields L = Q( ?8 m) with respect to monogenity. We prove our results by considering the relative norms of the partial differents ? ? ? ?j of an integer ? from the Galois closure L˜ of L to Dirichlet optimum subfields of L, ˜ where ? is the isomorphism which maps ?8 m to ?8 ?8 m of L with ?8 = e 2?i/8 , i = ? ?1 and j = 4, 2, 1