ஜர்னல் ஆஃப் அப்ளைடு & கம்ப்யூட்டேஷனல் கணிதம்

The article proposes a mathematical method that permits to treat numbers with more than 2 dimensions. The sums and the products must be done by two distinct definitions. Despite this little limitation you have the same algebra of the standard complex numbers. The limitations occur only when you have to really compute the sums and the products between numbers, not in the symbolic algebra. The product and the sum are commutative

An initial value problem concerning the motion of an incompressible electrically conducting viscoelastic Oldroyd-B fluid in a channel bounded by two infinite rigid non-conducting plates in presence of an external transverse magnetic field when both the fluid and the plates are in a state of solid body rotation with constant angular velocity about an axis normal to the plates is solved. The unsteady motion is generated impulsively from rest in such a fluid when the upper plate is subjected to velocity tooth pulses with the lower plate held fixed. It is assumed that no electric current exists in the basic state and the magnetic Reynolds number is very small. Exact solutions of the problem are obtained by utilizing two methods, of them, one is the method of Fourier analysis and the other is the method of Laplace transforms. The enquiries are made about the velocity field and the skin-friction on the walls. It is shown that both the methods give the same exact solution of the problem. The influence of rotation, the magnetic field and the elasticity of the fluid on the components of fluid velocity and the wall skin-frictions are examined quantitatively. Some known results are found to emerge as special cases of the present analysis.

In this paper, we derive new method for solving particular solution of linear second order ordinary differential equations whenever one solution of their associated homogeneous differential equations is given. Also, we construct second solution of the associated homogeneous differential equation from this new method. Moreover, we have general solution method of linear second order ordinary differential equations without applying the two famous methods, undetermined coefficients method and variation of parameters method, for solving their particular solution

In this paper, we present and discuss issues related to volume estimation of various brain components using MR brain images. We discuss pre-processing techniques to remove elements such as skull, blood vessels and fats from the MR images since these are non-essential to the volume calculations. The volume estimation is based on image segmentation. A challenge in MR brain image segmentation is to distinguish central gray matter from surrounding matters. This paper provides a frame work from pre-processing stage through volume estimation for white matter, gray matter and cerebrospinal fluid (CSF). The main contribution of this paper contains two parts. First, it provides a software-based method for interactive image pre-processing; second, it introduces a software-based, supervised interactive image segmentation method to deal with the segmentation of different matters, especially the central gray matter. Experiments with real data demonstrate the efficiency of our frame work.

In this communication, we proved that the parametric general nonlinear nonconvex variational inequalities are equivalent to the parametric general Wiener-Hopf equations. We use this alternative equivalence formulation to studied the sensitivity analysis for general nonlinear nonconvex variational inequalities without assuming the differentiability of the given data.