有界性

Based on general orthogonal polynomials and general hybrid orthogonal functions, a new linear, continuous and bounded operator has been proposed in the dissertation. The definitions and properties of PGOPO are given, a various operational rules of the operator have been set up in a systematic way, the convergence of approximate solutions has been discussed. After introducing PGOPO and discussing its main properties and operational rules, a systematic methodology for solving various control problems via PGOPO has been developed.

本文在广义正交多项式及广义混合正交函数的基础上，提出了一种新的线性、连续、有界算子—分段广义正交多项式算子，探讨了这种算子的基本性质，并系统地建立了与该算子有关的各种运算规则及收敛性结论，给出了它在控制理论中的各种应用。

The discussion produces some useful result:theconvergence of bounded subfeasible solution sequence and the convergence to zero of thesubfeasible dual gap.

在引入摄动的思想下，针对受摄动KKT系统，首先证明了以上四个规划问题中线性规划及其Wolfe对偶问题解的存在性，在此基础上得到一个关于其有界次可行序列收敛和次可行对偶间隙收敛到0的重要结论。

And we also prove the existence theorem of minimizer for the new model by means of Poincares inequality and the lower semi-continuity of bounded variation functions.

根据有界变差泛函中的Poincare不等式和下半连续性，证明了该模型极小值的存在性。

And we also prove the existence theorem of minimizer for the new model by means of Poincare's inequality and the lower semi-continuity of bounded variation functions.

根据有界变差泛函中的Poincare 不等式和下半连续性，证明了该模型极小值的存在性。

Under some reasonable assumptions of the'Distribution Matrix', the Riemann Problem with piecewise constant initial data is proved to have a unique Riemann Solver; furthermore, using'Wave Front Tracking Method'and properties of the'Generalized Characteristics', we prove the existence of weak entropy solution to the Riemann Problem with arbitrary initial data of bounded Total Variation.

在"分布矩阵"满足合理的假设前提下，证明了具有分片常值初始条件的黎曼问题的黎曼解算子的存在唯一性；并进一步运用"波前追踪法"和"广义特征"等得到了具有任意有界全变差初值条件的广义黎曼问题的弱熵解的存在性。

Using the change of variable and fixed point method andmethod of approximation, we obtain some interesting and new results on the existenceand uniqueness of bounded solutions and almost periodic solutions of these equations.

利用变量替换和不动点方法及逼近法，我们得到了此类方程有界解和概周期解的存在性及唯一性的一些有趣的新结果。

We have studied a model of a non-Newtonian viscous compressible fluid in 3D bounded domains, in which the viscous part of the stress tensor satisfies the coerciveness condition and the values of the growth condition ., are positive constants. Here is the tensor of the velocity gradient, is the strain tensor and ,which depends on the tensor of the velocity gradient, is the hefts of .

对满足强制性条件，以及增长性条件的非牛顿粘性可压缩流体在三维有界区域中的流动进行了研究，其中和为正常数，为速度梯度张量，是偏应力张量，为的分量，它依赖于速度梯度张量。

The aim of this paper is to study the existence of solution and multiply results for quasilinear elliptic system in bounded domain and the whole space, semilinear elliptic equation in two dimension space, second order nonlinear difference equation by variational methods. The main results are listed in the following:1. An abstract compactness theorem is proved, and then, under weak Boccardo and De.

本文主要利用变分法，分别研究了有界区域和全空间上拟线性椭圆型方程组、二维空间上半线性椭圆型方程和二阶非线性差分方程问题的解与多重解的存在性，具体内容如下： 1。

Does research in a common fixed point theorem of fuzzy mapping s in inequality conditions and the cut set is the nonempty closed bounded subsets of,while is complete metric space.

2，研究了在完备度量空间中一对模糊映象满足一些特定不等式条件，以及当其截集是中非空有界闭集时，该对模糊映象的公共不动点的存在性问题。

By means of deriving the approximate solution and a process of approaching iteration, we have shown that a general solution exists for a non-Newtonian compressible fluid in 3D bounded domains. The proof is based on an elementary energy method.

文章利用构造近似解和极限的过程证明了三维有界区域中非牛顿可压缩流体广义解的存在性，所用的证明方法为能量方法。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。