This paper discusses the numerical solution of Fredholm integral equations of the second kind which have weakly singular kernels and inhomogeneous terms. Global convergence estimates are derived for the Galerkin and iterated Galerkin methods using splines on arbitrary quasiuniform meshes as approximating subspaces. It is observed that, due to the singularities present in the solution being appr...

In this study, efficacy of two hernia mesh implants viz. conventional Prolene and a novel Prolene-Vicryl composite mesh was assessed for experimental ventral hernia repair in dogs. Twelve healthy mongrel dogs were selected and randomly divided into three groups, A, Band C (n=4). In all groups, an experimental laparotomy was performed; thereafter, the posterior rectus sheath and peritoneum were ...

We consider scattering of a time-harmonic acoustic incident plane wave by a sound soft convex curvilinear polygon with Lipschitz boundary. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the number of degrees of freedom required to achieve a prescribed level of accuracy grows at least linearly with respect to the frequency of the incident wave. ...

We consider scattering of a time-harmonic acoustic plane wave by a sound-soft convex polygon. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we recently proposed a novel Galerkin boundary element method, for which the approximation space consists of piecewise polynomials supported on a graded mesh, with smaller elements adjacent to the corn...

When used for visualization of high-dimensional data, the self-organizing map (SOM) requires a coloring scheme, such as the U-matrix, to mark the distances between neurons. Even so, the structures of the data clusters may not be apparent and their shapes are often distorted. In this paper, a visualization-induced SOM (ViSOM) is proposed to overcome these shortcomings. The algorithm constrains a...

Let G be a group with identity e. Let R be a G-graded commutative ring and let M be a graded R-module. The graded classical prime spectrum Cl.Specg(M) is defined to be the set of all graded classical prime submodule of M. The Zariski topology on Cl.Specg(M); denoted by ϱg. In this paper we establish necessary and sufficient conditions for Cl.Specg(M) with the Zariski topology to be a Noetherian...

Let $G$ be a finitely generated abelian group and $M$ be a $G$-graded $A$-module. In general, $G$-associated prime ideals to $M$ may not exist. In this paper, we introduce the concept of $G$-attached prime ideals to $M$ as a generalization of $G$-associated prime ideals which gives a connection between certain $G$-prime ideals and $G$-graded modules over a (not necessarily $G$-graded Noetherian...