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According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

First interpret it combinatorially, and then derive it algebraically from the multinomial theorem.

先用组合方法阐述，然后从多项式定理利用代数方法推导。

First interpret it combinatorially, and th derive it algebraically from the multinomial theorem.

先用组合方法阐述，然后从多项式定理利用代数方法推导。

It is from their celebrities that many Americans derive their sense of nationhood.

许多美国人正是从他们的精英身上找到了民族自豪感。

A function's Fourier transform is derive d by integrating the product of the function and a kernel function (an exponential function raised to a negative complex power) over the interval from －∞to +∞.

欲取得一个函数的傅立叶变换，可以在－∞与＋∞的间隔中把该函数与核函数(提升至负复数幂的指数函数)的结果整合起来。

In Locke the metaleptic reality and its noetic analysis is transFORMed into the acceptance of certain "common opinions" which still bear an intelligible relation to the experience from which they derive.

在洛克那里，转喻性的实在和它的理智分析被转形成对某些"普遍意见"的接受，这些意见仍然与导出它们的经验有着明显的联系。

Especially, we derive the Pohozaev identity for p-harmonic equation from which we obtain the corresponding nonexistence of nontrivial solution for p-harmonic equation with critical growth.

本文考虑了几类椭圆方程的Pohozaev恒等式，特别是对p-调和方程在两种边界条件下的恒等式作了详细的演算，并利用这些恒等式得到了一些解的非存在性结果。

A typical and e nti re money laundering process may be divided into three stages:placement,layeri ng and integration,and from which many common money laundering methods derive.

一个典型、完整的洗钱过程可以分为放置、培植以及融合三个阶段，围绕这三个阶段，衍生出许多常见的洗钱方法。

The word derive s from Rome's Palatine Hill, where the emperors built their residences.

该词源于罗马的帕拉蒂尼山，也就是罗马君王修建住所的地方。

The emission of light that does not derive energy from the temperature of the emitting body, as in phosphorescence, fluorescence, and bioluminescence.

发冷光：不是由于发光体的热量而来的光的发射，比如在磷光，荧光和生物性发光中。

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。