Journal of Prime Research in Mathematics

Abstract: Brajinskii’s equations are the fundamental relations governing the behavior of the plasma produced during a fusion reaction, especially ICF plasma. These equations contains six partial differential coupled together. In this paper we have tried to give analytical solutions to these equations using a one dimensional method. Laplace transform technique is the main tool to do that with an arbitrary boundary and initial conditions for some special cases.

Abstract: For \(K\) a valued subfield of \(\mathbb{C}_{p}\) with respect to the restriction of the p-adic absolute value | | of \(\mathbb{C}_{p}\) we consider the \(K\)-algebra \(IK[[X]]\) of integral (entire) functions with coefficients in \(K\). If \(K\) is a closed subfield of \(\mathbb{C}_{p}\) we extend some results which are known for subfields of \(C\) (see [3] and [4]). We prove that \(IK[[X]]\) is a Bezout domain and we describe some properties of maximal ideals of \(IK[[X]]\).

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Abstract: In this paper, we establish the weak and strong convergence theorems for strictly pseudo-contractive mappings in the framework of quniformly smooth Banach spaces. Our results improve and extend the corresponding ones announced by Reich, Acedo, Marino, Xu and some others.

Abstract: A Cauchy problem for a two-dimensional ultra-parabolic model of filtration through a porous ground of a viscous incompressible fluid containing a solute (tracer) is considered. The fluid is driven by the buoyancy force. The phenomenon of molecular diffusion of the tracer into the porous ground is taken into account. The porous ground consists of one dimensional filaments oriented along some smooth non-degenerate vector field. Two cases are distinguished depending on spatial orientation of the filaments, and existence of generalized entropy solutions is proved for the both. In the first case, all filaments are parallel to the buoyancy (gravitational) force and, except for this, the equations of the model have rather general forms. In the second case, the filaments can be nonparallel to the buoyancy force and to each other, in general, but their geometric structure must be genuinely nonlinear. The proofs rely on the method of kinetic equation and the theory of Young measures and H-measures.

Abstract:  Current surface construction methods in CADCAM use parametric polynomial equations in the form of a NURBS. This representation is ideal for computer-based implementations, allowing efficient interrogation. However, issues exist in constructing and manipulating such surfaces. When constructing a NURBS surface there are difficulties in determining constraints such as parameterisation, tangent magnitudes and twist vectors. Controlling the geometric features like curvature profiles of sectional/longitudinal curves on a NURBS surface is problematical as is joining several such surfaces together. A cause of these difficulties in control is that the control points do not lie on the surface itself. An alternative approach to surface construction is to specify the curvature and construct the surface so that it satisfies the curvature constraints. Since NURBS does not directly allow this, a fundamentally different approach is required. The key is to adopt a point-based approach where the surface is defined by a small number of points lying on the surface. Intermediate points are then constructed using a recursive approach which is defined to ensure that the curvature profile between adjacent points is of a very  high quality. A case study is presented that illustrates the point-based approach.