等式

A general super memory gradient projection method was generalized to solve the nonlinear programming problems about the nonlinear equality constraints and in equality constraints by using general projection matrix.

利用广义投影技术，将求解无约束规划的超记忆梯度算法推广，建立了求解带非线性等式和不等式约束优化问题的一种超记忆梯度广义投影算法，并证明了算法的收敛性。

By using generalized projection matrix, conditions are given on the scalars in the three term-memory gradient direction to ensure that the three term-memory gradient projection direction is a descent direction. A new three term-memory gradient projection method for nonlinear programming with nonlinear equality and in-equality constraints is presented.

利用广义投影矩阵，对求解无约束规划的三项记忆梯度算法中的参数给一条件，确定它们的取值范围，以保证得到目标函数的三项记忆梯度广义投影下降方向，建立了求解非线性等式和不等式约束优化问题的三项记忆梯度广义投影算法，并证明了算法的收敛性。

By this equality,we prove that the amplitude of a compact DG module M over a cohomologically bounded DG algebra A is just the sum of the amplitude of A and the projective dimension of M.

对于一个同调有界的连通DG代数上的紧的DG模，我们由此等式可得其振幅与DO代数的振幅的差恰是它的投射维数。

The basic steps of this method are as follows.The firststep is to derive a necessary condition such that the families of quasipolynomials withone parameter,corresponding to the edges of the polytope,have pure imaginary rootsby using the Dixon's resultant for polynomials.Then to check that the casescorresponding to the parameters obtained in the first step are in fact impossible byusing the generalized Sturm criterion and some stability criteria.

其基本思路是先利用多项式方程组的Dixon结式理论导出使各棱边对应的单参数特征拟多项式有纯虚根时，参数值应满足的一个等式条件，即所谓的Dixon结式等于零，然后由广义Sturm判别法验证对所有参数值，Dixon结式不等于零，或使结式等于零的解不产生特征拟多项式的纯虚根。

In the model, the non-sensitive loss function was replaced by quadratic loss function and the inequality constraints were replaced by equality constraints.

在该模型中，用二次损失函数取代支持向量机中的不敏感损失函数，将不等式约束条件变为等式约束，从而将二次规划问题转换为线性方程组的求解，并提出对核函数的盯参数进行动态选取。

The non-sensitive loss function is replaced by quadratic loss function and the inequality constraints are replaced by equality constraints. Consequently, quadratic programming problem is simplified as the problem of solving linear equation groups.

用二次损失函数取代支持向量机中的不敏感损失函数，将不等式约束条件变为等式约束，从而将二次规划问题转变为线性方程组的求解。

Considering the fat-tail phenomenon that may exist in practical data, we have also studied the PTLE for the multi-t distribution model based on the three large sample tests above. Performances of the estimators according to the quadratic bias and mean square error are similarly compared in detail.

考虑到实际数据可能存在的厚尾情况，本文研究了文献中讨论颇多的多元t分布模型的基于大样本检验的等式约束预检验Liu估计，并同样在平方偏差和均方误差两个准则下对其优良性进行了详细比较。

The purpose of this paper is to estimate the eigenvalues of square quaternion matrices.

估计定理，在估计定理的基础上提出了对角线元素是实数的四元数方阵的特征值。等式

In 45/3=15, 15 is the quotient.

在45÷3＝15这个等式中，15是商

The paper prices bond and bond option, analyzing dynamic interest rate, regime-switching and option pricing. According to the affection of regime-switching to interest rate derivative pricing, the paper deduces the partial differential equation of bond pricing with Ito lemma, and obtains characteristic function and recursion equation of bond option.

从利率动态变化、结构转换和期权定价三个方面进行分析，对结构转换下的债券和债券期权进行定价，考虑了结构转换对利率衍生物定价的影响，利用Ito引理获得债券定价的偏微分方程，并得到债券期权定价的特征函数与递归等式。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。