密度定理

In this article the usual method of determining the distribution density of function of one-dimensional continuous random variable——distribution function method.

本文给出了求一维连续型随机变量函数分布密度的一般方法：分布函数法，并用分布函数法对现有文献中的计算公式进行了理论探讨，对现有的定理进行修正拓展，扩大了应用范围。

This statement of the Hohenberg-Kohn theorem of Density Functional Theory plays an exceptionally important role among all the fundamental relations of molecular physics.

这Hohenberg科恩职能理论在的全部分子物理学的基本关系中起异常重要作用的密度的定理的陈述。

According to the Logistic Equation and the impact of stochastic factors, a stochastic nonlinear dynamical model had been presenred. The max Lyapunov exponent was calculated by Oseledec multiplicative ergodic theory, the local stability conditions had been obtained; the global stability conditions had also been obtained by judging the modality of the singular boundary; the stochastic Hopf bifurcation was analyzed using the invariant measure of stable probability density, and the condition of stochastic Hopf bifurcation had been discussed. The key parameter impacting the urban domestic water consumption had been found by numerical emulation.

根据Logistic阻滞增长模型原理，考虑到诸多随机因素的影响，本文建立了一个城市生活用水量的随机非线性模型，运用Oseledec乘性遍历定理计算了模型的最大Lyapunov指数，得到了局部稳定性的条件；通过对扩散边界性态的分析，得到了全局稳定性的条件；通过分析系统平稳状态概率密度的不变测度，得到了模型随机Hopf分岔的条件，结合实际进行了数值仿真，得到了影响用水量的关键参数。

When the generalized uncertainty relation is considered the new equation of quantum state density is obtained based on Liouville's theorem.

当考虑了广义不确定关系后，在刘维定理的基础上采取了新的量子态密度方程，我们发现黑洞视界附近的量子态数目变成了有限。

By using center manifold theorem and normal form of maps, we also present formal proofs of the supercritical flip bifurcation at the bifurcation point. Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behavior of the single species model with birth pulses are very complex.

利用单参数族映射的中心流形定理、正规型和指数积分函数的性质，得到了具非线性出生率或具密度依赖成熟率的混杂矩阵模型正平衡态的存在性和稳定性、超临界分支以及各种复杂现象甚至混沌。

We mainly investigate the influence of different covariant representations on the satisfiable extent of the Hugenholtz-Van Hove theorem in the nuclear medium in the framework of DBHF.

结果表明：不同的协变表示对核子自能各分量的动量相关性和密度依赖性均有重要影响，进而对核介质中HVH定理的满足程度产生重要影响。

The empirical Bayes estimation for parameters of the one-side truncated distribution family with convergence rate which can close to 1 arbitrarily is investigated using NA samples and an example that satisfies the conditions of theorem is given.

运用NA样本密度函数核估计构造了一类截断型分布族参数的经验Bayes估计，建立了它的收敛速度，证明了在适当条件下该收敛速度可以任意接近于1，文中还给出了适合定理条件的例子。

Gr\ochenig and Balan, Casazza, Heil, and Landau introduced the concepts of localization.

Gr\ochenig 和 Balan， Casazza， Heil， Landau 等人提出了两种框架局部化的概念，这两种局部化在近几年被应用到了Gabor框架，小波框架和采样定理，得出了许多关于框架的超完备性、冗余度、框架界和密度的关系以及局部化框架的对偶框架的结构方面的重要结果。

A stochastic model with initial stochastic conditions and stochastic coefficients for surge calculation was developed for the typical hydraulic system of a surge tank .

针对典型调压室水力系统，建立了具有随机初始条件和随机系数的涌波分析随机模型，从数学上严格证明了调压室涌波随机模型存在唯一的均方解，并进一步利用Liouville定理求解了其解过程的联合概率密度函数，最后给出了调压室涌波的均值解曲线

He and Nina moved to California and lived at 2005 Ivar Street, Apt.

他和Nina搬到加州，并在2005年伊瓦尔街，公寓生活。

Droperidol （ potently inhibits transfected HERGchannels and this is the probable mechanism for QT prolongation.

氟哌利多有效地抑制了转染的 HERG 钾通道，可能是 QT 间期延长的机制。