Straight-forward systematic derivations of the weakly singular boundary integral equations (BIEs) are presented, following the simple and directly-derived approach by Okada, Rajiyah, and Atluri (1989b) and Han and Atluri (2002). A set of weak-forms and their algebraic combinations have been used to avoid the hypersingularities, by directly applying the “intrinsic properties” of the fundamental ...

We consider the problem of extracting the morphology of a terrain represented as a Triangulated Irregular Network (TIN). Our reference framework to model terrain morphology is given by the descending and the ascending Morse complexes, which define a decomposition of the terrain through its critical points and integral lines. We review several algorithms proposed in the literature to extract des...

The objective of our work is to explore the potential of parallel computers in numerical simulation of viscoelastic flows. Viscoelastic flow simulations often result in ill-conditioned algebraic systems and, therefore, direct solution methods have been in vogue. But the main disadvantage of direct methods is their excessive storage requirements for large matrices, especially for three-dimension...

In this paper, we propose a new modified recursion scheme for the approximate solution of higher-order, multipoint, nonlinear boundary value problems with higher-order Robin-type boundary conditions by the Adomian decomposition method. Our new approach utilizes all of the boundary conditions to derive an equivalent nonlinear Fredholm-Volterra integral equation before establishing the new modifi...

We prove that if R is a domain with many units, then the natural inclusion E2(R) → E2(R[t]) induces an isomorphism in integral homology. This is a consequence of the existence of an amalgamated free product decomposition of E2(R[t]). We also use this decomposition to study the homology of E2(Z[t]) and show that a great deal of the homology of E2(Z[t]) maps nontrivially into the homology of SL2(...

We investigate topology change in 3D. Using Morse theory and handle decomposition we find the set of elementary cobordisms for 3-manifolds. These are: (i) Ø ↔ S 2 ; (ii) Σ g ↔ Σ g+1 ; (iii) Σ g 1 ⊔ Σ g 2 ↔ Σ g 1 +g 2 , and they have appealing physical interpretations, e.g. Big Bang/Big Crunch, wormhole creation/annihilation and Einstein-Rosen bridge cre-ation/annihilation, respectively. This de...

Since 2001, Laplace decomposition algorithm (LDA) has been one of the reliable mathematical methods for obtaining exact or numerical approximation solutions for a wide range of nonlinear problems. The Laplace decomposition algorithm was developed by Khuri in [2] to solve a class of nonlinear differential equations. The basic idea in Laplace decomposition algorithm, which is a combined form of t...

The crystal base of the modified quantized enveloping algebras of type A+∞ or A∞ is realized as a set of integral bimatrices. It is obtained by describing the decomposition of the tensor product of a highest weight crystal and a lowest weight crystal into extremal weight crystals, and taking its limit using a tableaux model of extremal weight crystals. This realization induces in a purely combi...

ion paradigm or approach KBS defined in terms of Source Heuristic classification Feature abstraction, heuristic match, solution refinement Clancey 1985 Deep and shallow knowledge Deep knowledge, causal relations, shallow knowledge Keravnoe and Washbrook 1989 Problem-solving method Problem decomposition, domain independent strategies, sequencing inferences McDermott 1988 Generic tasks Problem ty...

We prove that if R is a domain with many units, then the natural inclusion E2(R) → E2(R[t]) induces an isomorphism in integral homology. This is a consequence of the existence of an amalgamated free product decomposition of E2(R[t]). We also use this decomposition to study the homology of E2(Z[t]) and show that a great deal of the homology of E2(Z[t]) maps nontrivially into the homology of SL2(...