in this paper, a new numerical method is presented for solvingthe optimal control problems of bang-bang type with free or xed terminaltime. the method is based on bezier polynomials which are presented inany interval as [t0; tf ]. the problems are reduced to a constrained problemswhich can be solved by using lagrangian method. the constraints ofthese problems are terminal state and conditions....

We propose a framework for sensitivity analysis of linear programs (LPs) in minimization form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact, convex uncertainty set. This framework unifies and extends multiple approaches for LP sensitivity analysis in the literature and has close ties to worst-case li...

In this paper, using the best proximity theorems for an extensionof Brosowski's theorem. We obtain other results on farthest points. Finally, wedene the concept of e- farthest points. We shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (X; ||.||). If z in W is a e-farthest point from an x in X, then z is also a-best approximati...

Using a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — arf < c, r(q — fir) < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals a and /3, provided that c > 1/2.6394. This improves an earlier result of Davenport, who shows that the same conclusion holds if c > 1/46"" = 1/2.6043 • • •.