等式

A proper k total colouring of a graph G is a colouring to its vertices and edges using k colours such that no two adjacent or incident elements of G may be assigned the same colour.

利用梯度投影与罚函数相结合的技巧，将带不等式和等式约束的优化问题化成一个无约束问题，提出了初始点可任意的求解不等式、等式约束优化问题的摄动梯度投影算法；参数δk取不同的数还可以得到一类梯度投影算法，从而得出了在搜索方向和步长不精确条件下的梯度投影法，保证了在实际应用中更容易实现；在较弱条件下，证明了该算法的全局收敛性。

There exits several MDO algorithms. But they are in our opinion either nonefficient or complicated. So we devised an algorithm called Subspace Approximation Optimization . In the SAO algorithm, the whole system is decomposed into one system-level optimization and several disciplinary optimizations so that a large and complicated problem can be divided into several easy-solving sub-problems. The coupling relationships and the coordination among disciplines are presented by equality constraints and these equality constraints are assigned to relevant disciplines. The optimums of design variables in system level optimization are transferred to discipline level optimization. The optimums of design variables in discipline level correspond to the point that is the nearest to the optimums of design variables in system level. If the optimums of design variables in system level are out of feasible region of discipline 1eve1, linear constraints can be built in the system level optimization using the design variable optimums obtained by the discipline level optimization. The system level optimization would improve the design of the whole system with these linear constraints.

目前，国内外已经发展出了多种飞机多学科设计优化算法，本文的重点是针对协同优化算法的不足，提出了子空间近似优化算法(Subspace ApproximatingOptimization，SAO)，SAO算法中，整个系统的优化问题被分解成一个系统级优化和若干学科级优化，而各个学科之间的耦合与权衡关系则被当作等式约束，这些等式约束将被分配到各个学科级优化中去，系统级优化的任务是寻找整个系统的最优解，而学科级优化的目标函数是以系统级优化分配下来的设计点为圆心的超球半径的平方，因此，如果系统级优化分配下来的设计点在学科级优化可行域内，则学科级优化目标函数为0，反之，则学科级优化的最优点是系统级优化当前设计点距离可行域最近的点。

The unity current gain frequency fT of a BJT is related to the collector current IC by Equation (2) predicts that the fT would rise unrestrictedly with a rising IC.

一个双机型晶体管的单位电流增益fT和集电极电流IC的关系表达为等式(2)，该等式预测在IC上升时fT会无限上升。

Of variable bindings is called a closure. Closures turn out to be useful in a widevariety of applications.

因此，标题的等式显然是不成立的，而以下的等式是成立的

Of course this way of showing that the propositions of logic are tautologies is not at all essential to logic, if only because the propositions from which the proof starts must show without any proof that they are tautologies.

意义。但是对于等式来说，具有根本意义的一点是：为了显示用等号连接的两个表达式有相同的指谓，等式并非必要，因为这一点从两个表达式本身即可以看出来。

The equity (liabilities and owner's equity) on the right side of the equation show the legal and economic claims against the assets.

等式左边是资产，等式右边的权益则表明对资产拥有的法律和经济的求偿权。

The paper expounds the connotation of the three accounting equalities.

本文通过对我国使用过的三个会计等式，分别解析各等式的基本内涵。

In such a situation, the equalities s = u = v will be derived, but the equalities x = y and y = t will not be.

在这种情况下，等式商S =ü= V将派生，但等式x = y和y =吨不会。

It analyzes the meaning of the equalities and their difference in figure and structure when reflecting capital items. It studies the application of the equalities in account setting, accounting and trail balance.

即各等式所显示的实际意义与它们在反映资金项目时表现在数量与结构方面上的差异，以及等式在账户设置、会计处理与试算平衡中的具体运用。

Based on meshing principle of involutes gears, this paper deduces proper engagement equations for transmission mechanism with dual-idle gears .

根据渐开线齿轮啮合原理，推导出双惰轮传动机构的正确啮合条件等式，并根据等式编程求解，设计悬索桥主缆缠丝机的双惰轮传动机构。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。