波函数

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

The wave function for the lion is hence a superposition of the gender eigenstate for a lion and that for a lioness.

因此狮子的波函数是雌雄狮子的性别因子本征态重叠的结果。

However, we can measure just the position alone of a moving free particle creating an eigenstate of position with a wavefunction that is very large at a particular position x, and zero everywhere else.

然而，我们可以仅单独测量一个运动的自由粒子的位置用多数情况下特别位置X和零其它地方的一波函数来产生一个特征态。

After we perform the measurement, obtaining some result x, the wavefunction collapses into a position eigenstate centered at x.

在我们完成测量后，获得某些结果x，波函数坍塌为以x为圆心的位置特征态。

In a quark model description of the nucleon, however, such time-derivative term might contribute because it is hard to construct a true Hamiltonian eigenstate of relativistic interacting quarks.

我们同样也注意到在一个复合粒子的现象模型中这一项可能是非零的，因为这个模型中的波函数可能不是真实的Hamiltonian本征态。

The single-particle electronic eigenstates are expressed as a linear combinations of slightly excited PAO's positioned at the atomic coordinates

本征波函数用激发的PAO的线性组合表示

On the basis of the concept of perfect quantum gas, a physical model of extreme relativity is established for perfect quantum gas, and also according to the conclusions of the state density of the extreme theory of relativity, the densities of quantum statistics′ particle numbers and energy, the extreme relativity′s result of the enthalpy、internal energy and heat capacity of the perfect quantum gas is obtained under the high temperature by strict theory inference.

在理想量子气体概念的基础上，首先建立极端相对论理想量子气体的物理模型；再根据极端相对论的态密度和量子统计的粒子数、能量的密度结论，通过严格的理论推导，得出理想量子气体在高温条件下的极端相对论性的焓、内能和热容量的结果，并将其热容量与高温条件下的理想量子气体、经典理想气体的热容量对比，指出极端相对论与非相对论两种模型、理想量子气体与经典理想气体两种模型的热容量之间的差异，同时分析这些差异的物理原因在于各自气体模型的态密度以及对应体系的波函数的对称性；最后阐明高温条件下极端相对论理想量子气体的热容量在量子统计方面的先进性及应用前景。

Finally it clarifies the advance in quantum statistics and the practical prospect of heat capacity of the extreme relativity's perfect quantum gas under high tamperature.

摘 要：在理想量子气体概念的基础上，首先建立极端相对论理想量子气体的物理模型；再根据极端相对论的态密度和量子统计的粒子数、能量的密度结论，通过严格的理论推导，得出理想量子气体在高温条件下的极端相对论性的焓、内能和热容量的结果，并将其热容量与高温条件下的理想量子气体、经典理想气体的热容量对比，指出极端相对论与非相对论两种模型、理想量子气体与经典理想气体两种模型的热容量之间的差异，同时分析这些差异的物理原因在于各自气体模型的态密度以及对应体系的波函数的对称性；最后阐明高温条件下极端相对论理想量子气体的热容量在量子统计方面的先进性及应用前景。

By defining several localindices which can be easily calculated from these ground-state wavefunctions, we first succeeded in explaining bond lengths, orientation ofelectrophilic aromatic substitution, and local aromaticity of these benzenoidhydrocarbons within the VB theory. Moreover, the energy splittings betweenthe ground state and first excited state are applied to correlate with theiroverall aromatic characters, the results are also in good agreement withrelated predictions from MO theory.

通过定义一些可由基态波函数直接计算的局域指标，首次在VB模型下成功地解释了苯型烃的键长、亲电取代反应的方向及局域芳香性，并用基态与第一激发态的能量差讨论了这些分子的整体芳香性，得到了与分子轨道理论的预测基本平行的结果。

In the present work, usingFCPC method, we have performed systematically the theoretical investigationsfor the electronic charge density, high-order Zeeman effect and hyperfinestructure.

本文通过研究这些物理量的收敛性质发现，波函数第二项对这些物理量的合理描述起着重要的作用，特别是对高阶Zeeman效应和超精细结构参数的影响。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。