对偶的

It is proved in this paper that R/ is a principal ideal domain, where R=F+uF+…+u(superscript k-1)F, n is odd, and p is a prime number, and some necessary and sufficient conditions for the cyclic codes over R to be self-dual are given.

该文证明了R/是主理想环，其中R=F+uF+…+u(上标 k-1)F，n是奇数，p为素数，给出了环R上循环码是自对偶码的充要条件。

The sufficient and necessary conditions which Fuzzy subalgebra of direct product Boolean algebra can be decomposed as direct product of two Fuzzy subalgebras are obtained.

进而分别定义了在对偶模意义下直觉模糊群的外直积与内直积。

The order of differential equation is reduced when the dual variable s of Hamilton system are used in mechanical problems.

力学中的Hamilton体系采用对偶变量描述问题。

Moreover, we develop corresponding duality theory and related saddle point theory.

同时，我们还建立了对偶理论及相关的鞍点理论。

Using duality theory to the economic analysis is applying the"shadow price"to realize the optimal allocation of resources〓.

利用对偶理论进行经济分析主要是应用"影子价格"实现资源的最优配置〓。

Effects of main reaction conditions such as reaction time to the coupling reaction and the yield of squalene were studied primarily.

初步探索了主要反应条件如反应时间等对偶联反应中产物角鲨烯得率的影响。

Optimization; parametric quadratic convex programming; set-valued map; directional derivative; linear stability; solution-set map; parametric linear programming; error bound; subdifferential map; lower locally directionally Lipschitzian; upper locally di-rectionally Lipschitzian; locally directionally Lipschitzian; convex function; quasidiferential; kernelled quasidiferential; quasi-kernel; star-kernel; star-diferential; Penot diferential; subderivative; superderivative; epiderivative; set-valued optimization; set-valued analysis; subdifferential; optimization condition;ε-dual; scalization; generalized subconvexlike-cone;ε-Lagrange multiplier

基础科学，数学，运筹学最优化；集值映射；方向导数；线性稳定；最优解集映射；参数线性规划；参数凸二次规划；误差界；次微分映射；下局部方向Lipschitzian；上局部方向Lipschitzian；局部方向Lipschitzian；凸函数；拟微分；核拟微分；拟核；星核；星微分； Penot-微分；上导数；下导数； Epi-导数；集值优化；集值分析；集值映射的次微分；最优性条件；广义锥次类凸；ε-对偶；数乘；ε-Lagrange乘子

With the aid of the adjoint relationship of symplectic ortho-normalization and integral transformation, solutions of duality equations were obtained, or Saint-Venant solutions and local solutions, reducing the original problem to finding zero eigenvalue solutions and non-zero eigenvalue solutions.

利用辛正交归一关系和积分变换得到了对偶方程的解，即圣维南解和局部解，从而将原问题转化为寻找零本征值本征解和非零本征值本征解问题。

Based on dual variable principle, a symplectic algorithm for solving optimal control problem of nonlinear dynamic system was proposed.

基于对偶变量变分原理提出了求解非线性动力学系统最优控制问题的一种保辛数值方法。

Tensor of the dual space and in the "Linear Algebra"(version 2) At the same time to explain, which is "Linear Algebra"(version 2) is a major feature.

对偶空间和张量在《线性代数》(第2版)同时讲解，这也是《线性代数》(第2版)的一大特色。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐