查询词典 problem

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。

If fractional equation into Interdisciplinary equations into algebraic geometry problem, the problem will be transformed into quadrilateral triangle problem.

如将分式方程化为整式方程，将代数问题化为几何问题，将四边形问题转化为三角形问题等。

In addition, we also prove that solutions for the Stokes problem, Dirichlet problem and Neumann problem are all particular cases of the satellite altimetry.

同时证明了常用的Stokes问题、Dirichlet问题、Neumann问题可以看成卫星测高问题的特殊情况。

Since the problem of GVT with two primes restricted in arithmetic progressionsof the same moduli k is actually the same as the previous problem(2),we consideredthe problem of GVT with exactly one prime in an arithmetic progression.

两个素数取值于相同模的算术级数中的GVT问题实际上和前面的的问题（2）是一样的，于是只需考虑一个素变数在算术级数中取值的奇数Goldbach问题。

In this period, the rural land problem contains land assignment problem and land use problem.

该时期，农村土地问题讨论的重心主要集中于"土地分配"和"土地利用"问题。

Life. But the intrinsic way of the Internet by wire confines accessing and using of the network information.

然而，Internet固有的有线连接方式大大限制了人们对网络信息的访问和使用。

I have a strong persuasion that this is true .

我坚信这是正确的。