查询词典 necessary condition

Firstly, we give a necessary and sufficient condition for a nonnegative square matrix to be decomposed into a product of a finite number of irreducible nonnegative matrices in chapter 1. We prove it by using Frobenius normal form in combinational matrix theory and associated directed graph in graph theory. In addition, we can limit the number of factors to three, and construct every factor.

首先，在第一章中，我们给出了一个非负矩阵可以分解成有限多个不可约非负阵的乘积的充要条件，证明过程利用了组合矩阵论中的Frobenius标准型和图论中的伴随有向图，并且将乘积中的因子个数限制到三个，具体地构造出了分解式中的每个不可约非负阵。

The necessary and sufficient condition for that the problem P〓 is nonsingular is derived.

利用原问题与P〓的等价性，给出了原系统二次指标最优控制器的设计，保证了闭环对给定的初值有唯一的光滑轨线且零解渐近稳定。

Keep on the development of the air condition, it is necessary to carry on the innovation .

为了使空调行业走可持续发展的道路，有必要对其技术进行创新。

The nose bleeding patients should strengthen the nursing the mentality after stopping the bleeding. It is necessary to take in oxygen persistently, to stop infection by observing the condition of disease carefully, and to strengthen the nursing of lying in bed and the nursing of mouth ,eyes,ordure and diet.

鼻出血患者在止血的同时应加强心理护理，必要时持续低流量吸氧，进行细致的病情观察，防止感染，加强卧位护理、口腔护理、眼部护理、排便护理及饮食护理等可促进康复。

Secondly, we investigate C°-flows on orientable closed surfaces having POTP, and obtain a necessary and sufficient condition of such flows.

剖析了这些轨道的邻域的轨线结构，还考虑了经过Poisson稳定点及几乎周期点的横截圈和相应的回归映射，其中本文讨论了可定向闭曲面上具有伪轨跟踪性质的C〓-流，得到了可定向闭曲面上C〓-流具有伪轨跟踪性质的较为简洁的充分必要条件；最后本文借助于从可定向的闭曲面到不可定向闭曲面的复叠投射，讨论了不可定向闭曲面上的C〓-流与其提升的轨线之间的联系，解决了不可定向闭曲面上C〓-流具有伪轨跟踪性质的判定问题。

The necessary and sufficient condition of separation for homogeneous Scalar Helmholtz equation is both the existence of Stackel determinant and h 1h 2h 3S=f 1(μ 1)f 2(μ 2)f 3(μ 3)in orthogonal curvilinear coordinates system.

讨论了在正交曲面坐标系中齐次标量Helmholtz 方程变量分离的充要条件是Stackel行列式存在且h1h2h3S＝ f1（μ1）f2（μ2）f3（μ3）成立。

Therefore,it is necessary to research diffusion equation for suspended sediment because it describes the sediment move process in the water body.The equation is a various coefficients second-order linear partial differential equa-tion,such equation under complex boundary condition is very difficult to get its analytical solution,while its numerical solution relative analytical solution is more easier and has the obvious superiority:simple,the computation convenience.but to get a kind of difference format which is good accuracy and stability is not easy.

泥沙扩散方程实际上是一个变系数的二阶线性偏微分方程，这样的方程在各种复杂边界条件下求解是十分困难的，求它的解析解在数学上存在着难以克服的障碍，无法求出其精确解，因此常用数值方法求它的近似解，相比较而言，数值方法有着明显的优势：即简单灵活、计算方便快捷，但要寻找一种精度高、稳定性好、计算方便的差分格式也并非易事。

From numerical analysis result obtained by abovementioned two methods (safety coefficient being less than 1.1) and combination with the geological evaluation in situ, the high rock slope of the left abutment downstream is considered as a potentially unstable one under natural condition and pondage cases. So it is necessary to be further studied.

根据上述两方法相结合的数值分析结果（安全系数小于1.1，并结合现场工程地质评价，认为在自然边坡及蓄水条件下，左坝肩下游高边坡属于潜在不稳定边坡，需进一步研究。

The necessary and the development of the society are the basic condition and strong power for the vocabulary expansion.

社会的需要和发展是词汇发展的基本条件和强大动力。

One-rank steam refrigeration system is researched in theory. In the condition of necessary hypothesis and predigestion,a kind of clear、simple、stable arithmetic is adopted.

本文对稳定工况下的单级蒸汽制冷循环系统的工作特性进行了理论研究，经过必要的假设和简化，采用了一种明确、简单、稳定的稳态仿真算法。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。