有界性

In this paper,with the aid of the w~*- sequential compactness of bounded closed balls in the conjugate space of a separable space,we proved that the convex hull of a finite union of bounded closed balls in l~∞ is closed.

借助可分空间的共轭空间中有界闭球的弱星序列紧性，证明在无穷维数列空间l∞中有限个闭球之并的凸包仍为闭集

Then we use Lebesguge s dominated convergence theorem to obtain some sufficient conditions for (2) and study the existence of a bounded positive solution.

接着，利用Lebesgue单调收敛定理给出了方程(2)振动的若干充分必要条件并且研究了正有界解的存在性。

Then the satisfiability of DTITL is equivalently transformed to the same problem for SFO. Since the decidability of SFO can be transformed to the satisfiability of the propositional interval temporal logic, so SFO is decidable.

利用多个命题变量等价表示有界整数，把SFO的可满足性判定问题等价转换为可判定的命题区间时序逻辑的判定问题。

The existence,uniqueness and globally exponential stability of the equilibrium point of a dynamic neural network with distributed delay s were studied without assumption of boundedness and differentiability of activation functions.

在没有假定激励函数有界、可微的情况下，研究包含分布时滞的动态神经网络平衡点的存在性、唯一性和全局指数稳定性。

In Chapter 3, The existence of a bounded global attactor for Olmstead model with homogeneous Dirichlet boundary condition is proved under some condition on the parameters.

第三章讨论了带齐次Dirichlet边界条件的Olmstead模型的有界吸引区域的存在性。

Using the method of blow up lower and upper solutions, the existence and boundary behavior of positive boundary blow up solutions for some elliptic systems of competitive type with singular weight functions are obtained, here the singular weight functions are permitted to be bounded in some parts of the boundary, and to go to infinity or even oscillate in other parts.

利用爆破上、下解方法，本文建立了带奇异权函数的竞争型椭圆方程组正的边界爆破解的存在性和边界行为，这里奇异权函数可以在边界的某一部分有界，而在其他的部分趋于无穷或者震荡。

In particular, it is difficult to prove the Frechet differential for the semigroup {S}_(t≥0) in L~(2p) directly.

R~n(n≥3)是有界光滑区域，p≥2，初始值u(0)∈L~2，外力项g∈L~2，且非线性项f∈C~2满足我们在空间L~(2p)证明了指数吸引子的存在性。

The sufficient condition of stochastic delay population system with diffusion is obtained in Hilbert space.

利用Ito公式和Burkholder-Davis-Gandy定理及Gronwall-Bellman不等式，通过构造一个有界的柯西列，给出了Hilbert空间中随机时滞种群扩散系统解的存在性和唯一性的充分条件，文章所得到的结论是目前现有结果的推广。

Supposing the nonlinear term bounded, by using homotopy invariance theorem, we proved the existence of solutions of boundary value problems for a class of nonlinear ordinary differential equations.

在假设一类常微分方程边值问题中的非线性项有界的条件下，运用同伦映射不变性定理，得出了解的存在性结论。

This paper makes use of a Lyapunov function and a nonlinear integral inequality of Gronwall-Bellman-Bihari type to study the asymptotic hehaviors of solutions of a second-order nonlinear functional differential equation.

本文利用李雅普诺夫函数及一个Gronwall—Bellman—Bihari型的非线性积分不等式，研究一类二阶非线性泛函微分方程解的渐近性态，在第一部份，给出一组方程的全体解可延展到t=+∞的充分条件及三组方程的全体解有界的充分条件。

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。