查询词典 generalized function

In the study of the stochastic chaos in simple pendulum, the random Melnikov process is derived and the mean-square criterion is used to determine the threshold amplitude of the bounded noise excitation for the onset of the chaos or random chaos in the system. For the coupled simple pendulum and harmonic oscillator, the Melnikov function is used to determine the condition for the onset of chaos in the case of Hamiltonian perturbations. In the case of non-Hamiltonian perturbation, the generalized random Melnikov process and mean-square criterion are used to determine the threshold amplitude of the bounded noise for the onset of random chaos.

在随机混沌研究中，应用随机Melnikov过程的均方准则研究了单摆在有界噪声激励下发生混沌或随机混沌时有界噪声激励的临界幅值；对于耦合的单摆-谐振子系统，先用Melnikov函数研究了在哈密顿扰动下发生混沌的必要条件；然后用推广的随机Melnikov过程方法研究了在非哈密顿扰动下发生随机混沌的必要条件；用最大Lyapunov指数及Poincaré截面方法结果与上述理论结果作了对比。

Keywords Sobolev space;generalized function;Galerkin method;nonlinear elastic bar;existence and uniqueness of solution

Sobolev空间；广义函数； Galerkin法；非线性弹性杆；解的存在性和唯一性

The approximate stationary probability density function for the response of multi-degree-of-freedom dissipated Hamiltonian systems to Poisson white noises are obtained by solving the four-order generalized Fokker-Planck-Kolmogorov equation using perturbation approach.

通过用摄动法求解四阶广义福克－普朗克方程，得到泊松白噪声激励的多自由度耗散的哈密顿系统的近似平稳响应概率密度函数。

Optimization; parametric quadratic convex programming; set-valued map; directional derivative; linear stability; solution-set map; parametric linear programming; error bound; subdifferential map; lower locally directionally Lipschitzian; upper locally di-rectionally Lipschitzian; locally directionally Lipschitzian; convex function; quasidiferential; kernelled quasidiferential; quasi-kernel; star-kernel; star-diferential; Penot diferential; subderivative; superderivative; epiderivative; set-valued optimization; set-valued analysis; subdifferential; optimization condition;ε-dual; scalization; generalized subconvexlike-cone;ε-Lagrange multiplier

基础科学，数学，运筹学最优化；集值映射；方向导数；线性稳定；最优解集映射；参数线性规划；参数凸二次规划；误差界；次微分映射；下局部方向Lipschitzian；上局部方向Lipschitzian；局部方向Lipschitzian；凸函数；拟微分；核拟微分；拟核；星核；星微分； Penot-微分；上导数；下导数； Epi-导数；集值优化；集值分析；集值映射的次微分；最优性条件；广义锥次类凸；ε-对偶；数乘；ε-Lagrange乘子

This method can be generalized to simulate the transmission network with unknown transfer function.

该方法可以推广到传递函数未知的传输网络的仿真应用中。

In this paper,several quasi-Newton algorithms are generalized to a class of new quasi-Newton equation,several modified quasi-Newton algorithm s are obtained and their global convergence are proved under the objective function is uniformly convex.

将几个拟牛顿算法推广到一类新拟牛顿方程，得到几个修正拟牛顿算法；在目标函数为一致凸的条件下，证明了它们都具有全局收敛性。

The design of output feedback H(subscript ∞) controllers is discussed for nonlinear discrete singular systems. First of all, by means of generalized Lyapunov function and linear matrix inequalities, zero solution E-asymptotically stable is studied for the system, a sufficient condition is given such that the system is zero solution E-asymptotically stable and a H(subscript ∞) norm constraint. And the output feedback H(subscript ∞) controller is designed to guarantee the performance of the resulting closed-loop system.

主要对非线性离散广义系统的输出反馈H控制器的设计问题进行讨论，首先利用广义Lyapunov函数和线性矩阵不等式，对系统的零解E-渐近稳定性问题进行分析，在此条件基础上给出系统零解E-渐近稳定且具有H范数约束的充分条件，然后设计系统的输出反馈H控制器，使得闭环系统具有同样的性能。

In chapter 4, by AREELS, the Generalized Oscillator Strength Density Spectra were measured in the energy region from 56 to 66eV, with the incident energy 2. 5 keV and energy resolution 80 meV, at scattering angles from 0°to 6°, corresponding to the momentum transfer K〓=0.03~2. 01 a. u. The Fano profile parameters f〓 and q for the optically allowed transition 〓(0, 1)〓P°and the optically forbidden transitions 〓(1, 0)〓S〓and 〓(1, 0)〓D〓 were obtained as a function of K〓. With the hyperspherical coordinate wavefunctions, the dynamical correlation are discussed qualitatively. So, a new experimental way to study dynamical electron correlation effect is opened.In chapter 5, the widely used R-matrix theory was introduced. Then, the GOSDS for the optically allowed excitation series (1s〓)〓S〓→〓(0, 1)〓P°(n=2-4) were calculated by this method, and the Fano profile parameters f〓 and q were obtained sequently. So the electron correlation effect can be described by these parameters quantitatively, and the theoretical results were compared with our AREELS experimental results.

在第四章中，实验上，同样使用角分辨的高能量分辨快电子能量损失谱仪，在2.5keV电子入射能量和80meV的能量分辨下，测量了0°到6°散射角下的He原子双电子激发态在56~66eV的广义振子强度密度谱，这种情况，0°~6°对应的动量转移范围K〓=0.03~2.01a.u。，得到了光学允许跃迁的双电子激发态〓（0，1）〓P〓和光学禁戒跃迁的双电子激发态〓（1，0）〓S〓、〓（1，0）〓D〓的Fano线形参数f〓，q等随动量转移变化的曲线；观测到了几个强度很弱、能级很窄的光学允许和禁戒跃迁双电子激发态，用前人准确的理论结果进行了标识；通过比较弱共振〓（1，0）〓S〓和〓（-1，0）〓S〓的强度随动量转移K〓的变化规律，结合超球坐标理论计算的波函数，定性地阐述了在电子碰撞散射过程中它们各自不同的动力学电子关联效应，发展了一套在实验上研究电子关联效应的新方法。

Deduced the analytical structure of the Mamdani fuzzy system whose input sets were with generalized linear membership function and manifested that the output of the fuzzy systems were monotonical, decreasing, continuous and bounded.

设计了一种将三角形和梯形隶属函数作为特例的广义线性隶属函数，推导了输入采用广义线性隶属函数的典型Mamdani模糊系统的解析结构，证明了典型模糊系统是单调、递减的有界连续函数；在此基础上证明了该类模糊系统能以任意精度逼近任意连续实函数，最后仿真实例证明了本设计的有效性。

Aim Based on the generalized Bose-Einstein distribution function in nonextensive statistical mechanics, thermodynamical quantities of the two-dimensional Bose gas such as internal energy, entropy, free energy, heat capacity, etc., are calculated.

目的 应用非广延统计力学中的广义玻色－爱因斯坦分布函数，计算出了广义二维玻色气体的内能、熵、自由能、热容量等热力学量。

Pachomius manual labour was organized as an essential part of the monastic life; and since it is a principle of the monks as distinguished from the mendicants, that the body shall be self-supporting, external work of one sort or another has been an inevitable part of the life ever since.

根据圣pachomius体力劳动组织作为一个重要组成部分寺院生活；以来，这是一个原则的和尚，作为有别于乞丐，该机构应自支撑，对外工作的这种或那种已一个必然的一部分，生活至今。

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。