Topic
Green's theorem
About: Green's theorem is a research topic. Over the lifetime, 610 publications have been published within this topic receiving 8337 citations.
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Book•
01 Jan 1933
TL;DR: The General Tauberian Theorem (GHT) as mentioned in this paper is a special Tauberians theorem which is based on the Plancherel's Theorem and the Special Tauberia Theorem.
Abstract: 1. Plancherel's Theorem 2. The General Tauberian Theorem 3. Special Tauberian Theorums 4. Generalized Harmonic Analysis.
746 citations
638 citations
Book•
01 Oct 1992
TL;DR: In this paper, the authors present guidelines for Element Meshes and Global Nodal Numbering, as well as a selection of approximate functions for the FE-method - Scalar Problems and Weight Function - Weighted Residual Methods.
Abstract: * Introduction. * Matrix Algebra. * Direct Approach. * Strong and Weak Formulations - One-dimensional Heat Flow. * Gradient - Gauss' Divergence Theorem - Green Theorem. * Strong and Weak Forms - Two-and Three-Dimensional Heat Flow. * Choice of Approximating Functions for the FE-method - Scalar Problems. * Choice of Weight Function - Weighted Residual Methods. * FE-formulation of One-Dimensional Heat Flow. * FE-formulation of Two-and-Three Dimensional Heat Flow. * Guidelines for Element Meshes and Global Nodal Numbering. * Stresses and Strains. * Linear Elasticity. * FE-formulation of Torsion and Non-circular Shafts. * Approximating Functions for the FE-method - Vector Problems. * FE-formulation of Three-and-Two Dimensional Elasticity. * FE-formulation of Beams. * FE-formulation of Plates. * Isoparametric Finite Elements. * Numerical Integration.
267 citations
TL;DR: In this paper, the authors focus on three fixed point theorems and an integral equation and prove a fixed point theorem which is a combination of the contraction mapping theorem and Schaefer's theorem which yields a T-periodic solution of (0.2) when / defines a contraction mapping, while D and g satisfy certain sign conditions independent of their magnitude.
Abstract: In this paper we focus on three fixed point theorems and an integral equation. Schaefer's fixed point theorem will yield a T-periodic solution of
(0.1) x(t)= a(t) + tt-h D(t,s)g(s,x(s))ds
if D and g satisfy certain sign conditions independent of their magnitude. A combination of the contraction mapping theorem and Schauder's theorem (known as Krasnoselskii's theorem) will yield a T-periodic solution of
(0.2) x(t) = f(t,x(t)) + tt-h D(t,s)g(s,x(s))ds
if f defines a contraction and if D and g are small enough.
We prove a fixed point theorem which is a combination of the contraction mapping theorem and Schaefer's theorem which yields a T-periodic solution of (0.2) when / defines a contraction mapping, while D and g satisfy the aforementioned sign conditions.
162 citations
TL;DR: An iterative algorithm is proposed for moment calculation which needs no multiplications, and the number of additions needed is reduced to O ( N ), which shows that the computational complexity is significantly reduced.
144 citations