泛函性

Secondly, using the relation between the weighted modified K-functional, the weighted modulus of smoothness ,the weighted main-part modulus of smoothness . we get the pointwise direct and inverse approximation theorem with Jacobi weight for Szdsz-Kantorovich operator. Thus some results on w = 0w(x denotes the weight function, Ditzian-Totik modulus and classic modulus are extend.

其次，引入一种改变的带权K-泛函，利用带权光滑模和带权主部光滑的关系及带权光滑模与改变带权K-泛函的等价性，关于Szász-Kantorovich算子，讨论了一阶矩不为零的算子的点态带Jacobi权逼近正定理及等价定理，推广了已有的权为零及Ditzian-Totik光滑模和古典光滑模的结果。

Unfortunately, it has been shownthat these methods are not suitable to study about chemical bonds due to not involvingchemical bonds. In order to consider chemical bonds obviously, we have proposed an atom-bondelectronegativity equalization model on the basis of density-functionaltheory and electronegativity equalization principle. The main contents of our atom-bond electronegativity equalization model contain:(1)Considering the fact that there are varies of chemical bonds in molecules andpartitioning the molecular electron density as summations of atomic electron densitiesand chemical bond's electron densities, we obtained the basic equations of atom-bondelectronegativity equalization model: the expression of the total energy 〓, theexpression of the atom electronegativity 〓 and the expression of the bondelectronegativity 〓.

为了明确地考虑和处理分子中存在的化学键，以便能够更好地描述体系中的电荷分布进而准确地描述分子体系中的有关物理化学性质，尤其是与化学键有关的物理化学性质，我们在密度泛函理论和电负性均衡原理基础上提出了原子-键电负性均衡模型，原子-键电负性均衡模型的主要内容是：(1)考虑到分子体系中存在各种化学键这个事实，将分子空间看成是由原子区和化学键区组成的，将分子的单电子密度表达成为分子中各组成原子的单电子密度和各化学键的单电子密度的加和，从而得到了原子-键电负性均衡模型的基本方程：分子体系总能量〓和分子中原子电负性〓和化学键电负性〓表达式。

According to that Caristi fixed point theorem is equivalent to Ekeland variational principle, we weaken the condition that the functional is bounded from below in Ekeland variational principle, then we enlarge the area of the applicable functionals.

鉴于Caristi不动点定理和Ekeland变分原理的等价性，我们对Ekeland变分原理中泛函的下方有界的要求作了相应的削弱，从而扩大了适用泛函的范围。

The fact that solution of wave equation is equivalent to the extreme value of quadratic function solution was verified, and the existence and uniqueness of the quadratic function solution was also proved.

证明了波动方程的解和二次泛函极值解的等价性，以及二次泛函极值解的存在唯一性，为其在液压传动中流体瞬变分析的进一步应用提供了理论依据。

Some sufficient criteria were obtained for oscillation of all solutions of such systems under first boundary value conditions by employing Gauss＇ divergence theorem, the integral inequalities and some results of the functional differential equations.

研究一类具非线性扩散系数的中立型双曲泛函偏微分方程组的振动性，利用Gauss散度定理、积分不等式和泛函微分方程的某些结果，获得了该类方程组在第一类边值条件下所有解振动的若干充分判据，结论充分表明振动是由时滞量引起的，同时也揭示该类方程组与普通双曲型偏微分方程组质的差异。

Then, the system is linearized by variational approach, the local null controllability is proved by applying a generalized implicit function theorem and combining the good property of the solution mapping.

首先通过对系统线性化，构造泛函，利用对偶方程，给出控制函数具体形式的办法得到系统的逼近能控性；然后采用变分方法对系统线性化，再结合解映射好的性质，应用推广的隐函数定理，证明系统的局部零能控性；最后利用局部零能控性和逼近能控性结合给出系统零能控的结论。

Limit theorems for the integration of function sequence with respect to weak convergence probability measure sequence are proved under the condition of the weak tight, which have been used to research the some convergence of expectant functional sequence,and a sufficient condition for the epi-convergence of expectant functional sequence is obtained.

提出了弱胎紧的概念，并在弱胎紧的条件下证明了函数序列关于弱收敛概率测度序列积分的极限定理，用其研究了期望泛函序列的若干收敛性，得到了期望泛函序列的、上图收敛的一个充分条件。

Aim at the shortage of vertically additive method by which we can't discuss forced oscillations of systems of partial functional differential equations,we directly use the oscillatory definition,Green's formula and boundary condition of homogeneous Neumann to change the oscillatory problem of solutions to a class of systems of quasilinear parabolic equations of neutral type into the problem of which functional differential inequality haven't eventually positive solution.

针对垂直相加法无法讨论泛函偏微分方程组的强迫振动性的不足，直接利用振动的定义、Green公式以及齐次Neumann边界条件把中立型抛物微分方程组的振动问题转化为泛函微分不等式不存在最终正解的问题，然后利用最终正解的定义及上下极限得到了在齐次Neumann边界条件下判别其所有解振动或全振动的充分条件。

Euler-Lagrange equations of the functionals defined on the unit sphere S〓 with more general form is also educed, which is beneficial to the discussion of the behavior of those functionals in chromaticity diffusion.

我们还导出了球面上的较一般形式的泛函的Euler-Lagrange方程，为进一步研究不同泛函用于色彩扩散的性态打下了基础。

We get the sufficient and necessary conditions for the reaction process to be stochastic monotonic under certain conditions e.g.

第三部分推广了[29]中的结果，对较广的有限系统证明了若干泛函不等式与底过程对应的泛函不等式的等价性以及不等式常数之间的关系。

Since historical times,England ,where the early inhabitants were Celts, has been conquered three times .

从有历史以来，英国，在此地早期居住的是凯尔特人，已经被征服了三次。

Bluetooth OBEX File Transfer Enables the sending and receiving of files on your phone via Bluetooth.

蓝牙OBEX文件移动允许经过蓝牙传送和接受文件。。。。