目前，非线性泛函分析已经成为现代数学中的一个重要分支。
At present, nonlinear functional analysis has been one of the most important branch of learning in modern mathematics.
讨论了偏序线性空间的代数对偶空间上的端单调线性泛函的延拓性。
In this paper, our aim is to discuss the extension of an extremal monotonic linear functional in the algebraic dual space of a partially ordered linear space.
讨论了一类二阶非线性泛函微分方程的振动性，得到一些新的振动准则。
The oscillation of a class of second-order nonlinear functional differential equations is discussed, and some new oscillation criteria for the equations are obtained.
非线性泛函分析序集一般原理及其应用的研究是非线性泛函分析的重要研究课题。
The study for the general principle on ordered sets in nonlinear functional analysis and its applications is an important problem in nonlinear functional analysis.
拓扑线性空间的局部双序凸性，是该空间上连续线性泛函实现双序正分解的基础。
The Local biorder-convexity is a base of the biordering positive decomposition of linear functionals.
本文主要利用非线性泛函分析的拓扑度方法来研究时间测度上几类动力方程的正解存在性。
This thesis mainly investigates the existence of positive solutions for some class of dynamic equations on time scales by using topological degree of nonlinear functional analysis.
应用非线性泛函分析的理论和方法研究了一类二阶线性微分方程，证明了周期衰减解的存在性。
The second-order nonlinear differential equations are studied and the existence of the periodic degenerate solution is proved with the principle of the functional analysis.
利用拓扑度理论对一类非线性泛函差分方程周期解的存在性进行了讨论，得到该问题周期解的一个存在定理。
The existence of periodic solution to nonlinear functional difference equation is considered by using the topological degree, and a periodic solution of this problem is obtained.
本文利用拓扑矢量空间中的连续线性泛函导入最佳逼近定义，给出了最佳逼近元的特征定理、存在性定理和唯一性定理。
In this paper the author introduces the definition of the best approximation in topological vector Spaces by use of continuous linear functionals.
通常情况下，线性缩放密度泛函理论的应用还是很少的，而密度泛函理论只能计算成百、成千的原子电子结构。
In general though, linear scaling DFT is still quite rare and DFT calculations on a routine basis typically involve a few hundreds or thousands of atoms.
从稳定电流场基本方程出发，通过定义线性微分算子，推导出与之等价的泛函方程。
According to the fundamental equation of steady current field, the corresponding functional equation is obtained by use of the linear differential operator.
本文证明了关于对称泛函临界点的一个定理并用以研究非线性椭园型偏微分方程的多重解。
In this paper we prove a theorem for the critical points of symmetric functionals through which we research the multiple solutions of nonlinear elliptic PDE.
研究了一类非线性滞后型泛函微分方程周期解的存在性问题。
The existence problem for a class of nonlinear retarded functional differential equation is researched.
本文研究分段常数变量线性中立型泛函微分方程的振动性。
In this paper, we consider the oscillatory properties of neutral linear variable functional differential equation with piecewise constant delays.
随后，基于图像复原统一能量泛函的欧拉·拉格朗日方程，导出一种非线性数字滤波器的统一设计框架。
The unified designing framework for nonlinear digital filters is subsequently derived, through solving the Euler-Lagrange equation of the unified energy functional.
而灰色非线性规划，则将约束条件当作效益泛函，将一般的目标泛函当作消耗泛函，这二者都是含灰元的灰泛函。
In terms of grey nonlinear programming the restrictive condition is regarded as the profit functional, and the cost function is considered as the depleting functional.
把计算方法中的最小二乘法与泛函的抽象空间联系起来，得到最佳逼近问题的抽象提法，并在赋范线性空间探讨最小二乘法。
This article focuses on the topics that by connecting the the least-squares Minimization with the functional abstract space, the abstract definition of the best approximation problem is abtained.
本文把复变函数的围道积分应用于泛函分析，对一般的线性闭算子得到了算子值函数的中值定理。
In this paper, the author USES the contour integral in analytic function to functional analysis, and obtains the mean value theorem of operator-valued functions.
该分子材料具有较强的非线性光学性质，其分子的电子结构和电偶极矩是在密度泛函理论水平上利用从头计算方法得到的。
This kind of molecular material has strong nonlinear optical properties, and its electronic structures and dipole moments are calculated by use of density functional theory on ab initio level.
本文研究一阶非线性中立型泛函微分方程的振动性。得到了该方程振动的充分性判别法则。
This paper deals with the oscillation of the first order nonlinear neutral type functional differential equation, and obtains sufficient criterion of the equation oscillation.
与此同时，线性标度的密度泛函理论算法日趋成熟，使得通过密度泛函理论研究诸如生物大分子之类的体系成为可能。
Meanwhile, the linear scaling algorithms of DFT are getting mature, which makes the application of DFT to large systems such as biological macro molecules become possible.
建立了具泛函变元的拟线性偏微分系统解振动的充分条件。
Sufficient conditions are established for the oscillation of systems of second order partial differential equations with functional arguments.
利用泛函分析的技巧讨论了一类对具有连续时滞非线性积分微分方程周期解的稳定性。
The stability of periodic solutions of a kind of nonlinear integral-differential equations with continuous delay is discussed in this paper mainly by the method of functional analysis.
研究了间断非线性常微分方程奇摄动泛函边值问题。
The singularly perturbed functional boundary value problems for the discontinuous nonlinear ordinary di? Erential equations are considered.
研究一类具有连续分布滞量的偶数阶非线性中立型泛函微分方程解的振动性，得到了该类方程的若干新的振动准则。
We study the oscillation of solutions for a class of even order nonlinear neutral functional differential equations with continuous distributed delay.
我们使用了动态密度泛函理论对三杂臂星型共聚物以及线性均聚物的共混体系进行了研究。
Ordered microstructures assembled from the mixture of the ABC 3-miktoarm star terpolymers and the linear homopolymers have been investigated by using dynamic density functional theory.
我们使用了动态密度泛函理论对三杂臂星型共聚物以及线性均聚物的共混体系进行了研究。
Ordered microstructures assembled from the mixture of the ABC 3-miktoarm star terpolymers and the linear homopolymers have been investigated by using dynamic density functional theory.
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