数学系论文翻译英文文献

Proposition . For xo 属于P to be primal optimal it is sufficient that f(x) and the active components of g(x) at Xo are Type I functions with respect to a common rl(X ) at Xo and conditions ()-() hold at x o .for some Yo. We note that if r(x) is identically zero then () and () imply that xo is primal optimal. It follows that if a primal constraint qualification holds, then for xo属于P to be primal optimal it is necessary as well as sufficient that conditions ()-() hold at xo for some Y0 and that f(x) and g(x) are Type I functions with respect to a common r(x) at x0. However in the following theorem we see that for optimality, under an additional qualification on the constraints there must exist a vector r(x) which is not identically zero for each feasible x. Theorem . If x0 属于 P and the number of active constraints at Xo is k, where k < n, then for Xo to be optimal in the primal problem it is necessary that f(x) and g(x) are Type I functions with respect to 命题 。为XO笔记本电脑属于磷是原始最佳它是足够的F （ x ）和活性成分的G （十）在厂是I型职能方面的一个共同的北京（十）在XO和条件（ ） - （ ）保持在XO笔记本电脑。一些哟。 我们注意到，当R （ x ）是相同的零然后（ ）和（ ）意味着原始XO笔记本电脑是最佳的。因此，如果原持有资格限制，那么为XO笔记本电脑属于磷是原始最优这是必要的，也是充分的条件 （ ） - （ ）举行XO笔记本电脑的一些Y0和函数f （ x ）和g （ x ）的是I型职能方面的共同住宅（十）在x0 。然而在下列定理，我们看到的最优化，根据附加资格的限制，必须存在一个矢量住宅（十）这是不相同的每个可行零十定理 。如果x0属于P和积极的数目限制在XO笔记本电脑却钾，其中k “氮，然后厂为最优的原始问题是必要的函数f （ x ）和g （ x ）的是I型职能方面

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The Relationship among Green Formula, Gauss Formula and Stokes FormulaAbstract: Green Formula, Gauss Formula and Stokes Formula are three important formulae of calculus, they connected diffierent calculuses together, and have very important applications in the research field. In the paper, several formula relations are discussed, and from the exterior differential angle, three formulae are expressed uniformly and some applications of three-formula are enumerated.

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