A NEW ENGINEERING CALCULATING MODEL FOR A LINEAR INCLUSION AND ITS APPLICATIONS

By using the hypothesis of the deformation of the straight bar and beamin mechanics of materials,a new engineering calculating model for a linear inclusion inplane is presented.Through the Kelvin's solution of a concentrated force,the inclusionproblem is reduced to solving a set of uncoupled singular integral equations which canbe solved by the numerical method of singular integral equation.Based on theseresults,several applicable examples including an inclusion-crack problem are calculatedand the results are quite satisfactory.     

Orientations of Hamiltonian cycles in bipartite digraphs

The main result of the paper is the following Theorem. Let D=(X,Y,A) be a bipartite, balanced digraph of order 2n and size at least 2n²–2n+3. Then D contains an almost symmetric Hamiltonian cycle (i.e. a Hamiltonian cycle in which at least 2n–1 arcs are symmetric edges), unless D has a vertex which is not incident to any symmetric edge of D.This theorem implies a number of results on cycles in bipartite, balanced digraphs, including some recent results of N. Chakroun, M. Manoussakis and Y. Manoussakis.     

Are linear algorithms always good for linear problems?

We exhibit linear problems for which every linear algorithm has infinite error, and show a (mildly) nonlinear algorithm with finite error. The error of this nonlinear algorithm can be arbitrarily small if appropriate information is used. We illustrate these examples by the inversion of a finite Laplace transform, a problem arising in remote sensing.     

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