查询词典 difficult problem

Combustion control and performance evaluation for scramjets need effective measurement information, therefore it is important to choose the optimal location and number of sensors. This problem is a combinatorial optimization problem which is difficult to solve.

超燃冲压发动机的燃烧控制和性能评估需要有效的燃烧室测量信息，而如何确定传感器的最佳位置和数量是非常重要的，要求选择最小的传感器数目和最佳的测量位置来较准确的描述燃烧室工作特性，这是一个组合优化问题，直接求解比较复杂。

This problem is generally NP-hard and its deterministically equivalent problem is also difficult to be found.

这样的一个问题一般是NP-难，而且其确定性等价问题一般很难导出。

One of the most important, most difficult, and most exasperating unsolved problem s of operator theory is the problem of invariant subspaces

算子理论中最重要、最困难也最令人烦恼的未解决问题之一就是不变子空间问题。

Several combining with middle school mathematics teaching Abstract: combining the number is the number of more abstract corresponding relation and the geometrical graph, combine to solve the problem of abstract concepts to materialize and intuitive, intuitive, abstraction, and systematic problem to reduce the difficulty of the problem, and to help students thinking transformation and training students' ability.

数形结合与中学数学教学摘要：数形结合就是把较为抽象的数量关系和与其对应的几何图形相互结合起来解决问题，使抽象的概念直观化、具体化，使直观的问题系统化、抽象化，从而达到降低难题的难度、帮助学生思维转换、培养学生能力的作用。

Finally by constructing an auxiliary problem, using addition theorem and applying an iterative process based on results obtained for the linear problem, the existence and uniqueness of the weak generalized solution of the nonlinear problem is proved.

解决了线性问题后，本文构造了辅助问题，利用迭加原理，并基于线性问题的主要结论运用迭代过程，最终证明非线性问题存在唯一广义弱解。

As for mixed problem with integral boundary conditions for a certain nonlinear pseudo-parabolic partial equation, the existence and uniqueness of a strong solution to the corresponding linear problem is established and so the nonlinear problem can be solved by using addition theorem.

对于一类非线性伪抛物型方程的带积分边值条件的混合问题，本文通过相应的线性方程利用迭加原理来解决。

Basing on the Graf′s addition theorem, two expessions, interior and exterior expression, are deduced and the suitable problems for them are discussed. It has been found that the interior expression is the main point for sovling the scattering problem of circular inclusion in half-space. It also has been found that the exterior expression is the key for the scattering problem of circular arc canyon and circular arc alluvial valley, and is one of the main points for scattering problem of circular arc hill as well.

从Graf原有加法公式出发，本文给出了其内域型和外域型两种表达形式并讨论了这两种表达的适用范围，同时指出：内域型表达是求解半空间内含夹塞区出平面散射问题的要点，而外域型表达是解决任意圆弧型凹陷地形和任意圆弧型沉积盆地出平面散射问题中求解难点的关键，同时也是克服任意圆弧型凸起地形出平面散射问题求解困难的要点之一。

First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按"序"最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

It consists of the next three aspects: firstly, we study Murthys' open problem whether the augmented matrix is a Q0-matrix for an arbitary square matrix A , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the Graves algorithm can be used to solve linear complementarity problem with bisymmetry Po-matrices; Secondly, we study Murthys' conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix, we also study Pang's conjecture , obtain two conditions when R0-matrices and Q-matrices are equivelent and some properties about E0 ∩ Q-matrices; Lastly, we give a counterexample to prove Danao's conjecture that if A is a Po-matrix, A ∈ E' A ∈ P1* is false, point out some mistakes of Murthys in [20] , obtain when n = 2 or 3, A ∈ E' A ∈ P1*, i.e.

本文分为三个部分，主要研究了线性互补问题的几个相关的公开问题以及猜想：(1)研究了Murthy等在[2]中提出的公开问题，即对任意的矩阵A，其扩充矩阵是否为Q_0-矩阵，给出了肯定的回答，得到充分矩阵的扩充矩阵是充分矩阵，并讨论了Graves算法，证明了若A是双对称的P_0-矩阵时，LCP可由Graves算法给出；(2)研究了Murthy等在[6]中提出关于半正定矩阵的猜想，给出了半正定矩阵的一些充分条件，并研究了Pang~-猜想，得到了只R_0-矩阵与Q-矩阵的二个等价条件，以及E_0∩Q-矩阵的一些性质；(3)研究了Danao在[25]中提出的Danao猜想，即，若A为P_0-矩阵，则，我们给出了反例证明了此猜想当n≥4时不成立，指出了Murthy等在[20]中的一些错误，得到n=2，3时，即[25]中定理3.2中A∈P_0的条件可以去掉。

However, there are visible directions in research of this problem, which is either external analysis academically, thinking consumerism as neutral problem, such as sociology, or extensive praise, thinking consumerism as boundless beneficence to promoting economical increase, such as economics, or new exploration on advancing technical problem of consumption, so as to help the sustaining increase of consumerism, such as marketing, or as agent provocateur of consumerism, so as to research psychology of consumers, and to find out psychological weakness in human nature, such as consumption psychology.

但各个学科对这个问题的研究也明显存在着方向性的问题：它们或者从纯学术的意义上对消费问题进行客观的分析，对消费主义的盛行采取中性的态度；或者对消费主义的兴起兴高采烈，把消费主义看作是促进经济增长的有功之臣；或：耆对促进消费的技术性问题进行新的探索，以便助消费主义持续增长的一臂之力；或者充当消费主义的密探，对消费者的心理进行偷窥，为消费主义寻找人性的心理弱点，以便进行攻击。

The circulation, consumption and reproduction of the trilogy have not only testified to its historical significance and literariness, but also invested it with new meanings.

该三部曲的流通、消费与再生产不仅验证了其历史意义及文学性，而切还赋予它以新的意义。

If he thought that he could buy me off, he would be wrong.

如果他认为他可以收买我，那他就大错特错了。