证得

本文证得若EC00那么SE是（E，d）的一个闭线性子空间。

Is a closed linear subspace of ( E , d ) .

证得：在Banach空间中，相对紧集上的恒等算子可由一列有限秩连续拟线性投影算子一致逼近。

It is proved that the identity mapping on every precompact set in Banach space can be approximated uniformly by a sequence of finite rank continuous quasilinear projectors .

对于渐近性质，我们则利用二阶Bessel方程和最速下降法，证得分数阶奇异扩散方程是否为延伸的高斯分布。

By using the second-order Bessel equation and the method of steepest descent , we obtain the asymptotic behavior of the diffusion equation .

通过理论推导及事例分析证得含平直单边缘图像子块，其DCT变换系数能量并不总是集中分布在与其空间边缘走向垂直的方向上。

It is proved that for a image subblock with a single straight edge , the DCT coefficient . energy compaction orientation and the spatial edge orientation are not always orthogonal .

证得非交换主理想整环R上右齐次线性方程组基础解系存在定理，给出R上右线性方程组解的表示。

This paper proves the existence theorem of the system of basic solutions for the right homogeneous linear equation sets over a non-commutative principal ideal domain R and gives the representation of the solutions for the right linear equation sets over R.

本文用广义Laguerre多项式的母函数表达式，证得文献〔1〕中，计算ρn次幂的类氢原子径向波函数Jd平均值的通式。

This paper reported that the parent function representation of Laguerre 's generalized multinomial proved the general formula of J d average value of like-ness of hydrogen atmo radial wave function in Literature ( 1 )

考虑一类非线性退化抛物型方程初边值问题，利用特征函数和Jensen不等式，在一定条件下，证得方程的解在有限时刻爆破。

A nonlinear degenerate parabolic equation subject to Dirichlet initial-boundary conditions is considered . Using eigenfunction and Jensen inequation , under certain assumptions , it is proved that the blowup of solution occurs at finite time .

从而我们只需验证初始值就可证得该等式。

Thus , the identity is proved by checking the initial values .

愿祈这两本中英版的《大圆融》一书得以协助许多的行者在此生中证得正等正觉。

May these two books on Great Harmony help many practitioners to attain enlightenment in this life !

从这些新定义出发，证得一些系数不等式，模和幅角的估计。

From these new definitions we obtain some coefficient inequalities and the estimates of module and argument .

如果今天谷歌的中文搜索服务许可证得不到续期，那么百度将获得更多市场份额。

It stands to gain more market share if Google fails to renew its Chinese licence today .

同理，懂得根本真理的人可以证得《吠陀》经典里所描述的全部内容。

Similarly all the purposes in all Vedic scriptures are realized to he who knows the Ultimate Truth .

研究了D-共调和变换，证得D-共调和变换事实上就是恒等变换。

We study the property of D-conharmonic transformation and obtain that the D-conharmonic trans-formation is actually the identity transformation .

在适当的假设下，证得解的存在并给出任意阶的一致有效的渐近展开式。

Under suitable conditions we proved existence of solution and its uniformly valid asymptotic expansion of arbitrary order is given .

给出多项式软化子的几个性质，并由此证得用多项式一致逼近连续函数的结论。

Some properties of polynomial mollifier are presented and the conclusion that polynomial can consistently approximate continuous function is proved .

一般而言，喜心是好的。但是，就这方法而言，喜心却是证得苦灭的障碍。

In general , Piti is good but according this method , Piti is the obstacle of attaining the End of Suffering .

在适当的假设下，证得摄动问题解的存在性并导出其解关于ε的高阶近似。

Under appropriate assumptions we proved existence of solution of perturbation problem and derived higher order approximation of its solution with respect to ε .

借助积分变换定理构造了过程的一个耦合算子，利用ITO^公式证得所构造耦合的成功性。

Using the theory of integral transformation a coupling of the processes is constructed . By the IT O ^ formula the successful coupling is proved .

进一步分析系统算子和其生成半群的谱性质，可证得该半群是拟紧的，并且0是孤立的代数重数为1的简单特征值。

In terms of the spectral properties , the C0-semigroup can be proved to be quasi-compactness and 0 is an isolated eigenvalue with algebra multiplicity one .

学校即将开始性课程，每个学生都要先回去证得父母的同意，方能学习此课程。

A unit in sex education was about to begin , and each student had to bring in a permission slip in order to take it .

然后从预解算子的全连续性证得在正则情形下其谱是离散的结论。

Finally , we give an estimation for Green function and obtain the results that the resolvent operator is complete continuity operator and its spectrum is discrete .

我们现代证得圣道的很少很少，现在为了能供养到一个圣者阿罗汉得供千僧斋。

For this , there are four types of Sangha – the sage and saints , the approximate ones , the titular ones , and the ones without shame .

为克服这一困难，引入伪解的概念，并证得伪解的存在性与唯一性。本文继续这一工作，证得伪解关于强制项是连续相依的，从而使问题成为适定的。

To overcome this difficulty , the Concept of pseudo-solution is introduced , and continuous dependence of it is proved in this paper , so that the problem becomes well-posed .

本文证得（1）若λ具有弱滑脊性，那么λ-数乘收敛级数具有对偶不变性。

In this paper , the main results are : ( 1 ) If λ has the weak gliding hump property , then λ - multiplier convergent series has the dual-invariant .

但是，当你观照身心现象的时候，只能通过深的定力，你才能经由正见的三个层次体证得这些。

However , it is only through deep concentration , when you are mindful of bodily and mental phenomena , that you are able to realize them with the three levels of Right Understanding .

佛陀，在外在层次上，指的是悉达多-乔达摩，那位舍弃了王族头衔，进入丛林禅修，最终证得觉醒的印度王子。

The Buddha , on the external level , refers to Siddhattha Gotama , the Indian prince who renounced his royal titles and went into the forest , meditating until he ultimately gained Awakening .

本文在行波解意义下，利用作者的向量场同胚映射证明了广义Sine&Gordon方程具有极限异宿轨，从而证得孤波的存在性。

This paper shows the existence of solitary waves of generalized sine-Gordon equation by proving the existence of limit heteroclinic orbit via the author 's vector field homeomorphism in the sense of traveling waves .

流遍他的身体，直到每一个脚趾的下降福佑，和到达他的头顶光环的上升福佑把他带到证得福佑最高境界。

The descending bliss flowing through his body down to his very toes , and the ascending bliss reaching up to the crown of his head , brought him to the ultimate bliss of fruition .

深思大师的偈诵，然后超越他的喜悦，瓦库拉当时当地证得阿罗汉，于色心二法完全地领悟了。

Pondering the Master 's verse , and then transcending his rapture , Vakula then and there realized Arhatship together with a full grasp of the Dharma , both in the spirit and in the letter .

研究一类高阶积分微分方程的周期边值问题，利用上下解和单调迭代法证得最大解和最小解的存在性。

This paper deals with the periodic boundary value problems for a class of higher order integro differential equations . By means of upper and lower solutions and monotone iterative method , the existence of maximal and minimal solutions is obtained .