数值常数

In chapter three,we have derived a generalized dual London equation for the Abelian "electric" field A_μfrom the effective dual Abelian-Higgs model.The approximative result and the numerical simulation result as well as their figs were shown via solving the dual Abelian-Higgs model with different methods.Hereby the vortex solution of the chromo-electric field and the vortex energy density were also discussed.Finally,we have studied the dual Abelian-Higgs model with additional vacuum constant,and have unpuzzled the vacuum constant corresponding to the bag model.When the quark sources is introduced, the vacuum constant in the MIT bag model is proportional to the quartic of the monopole mass.

利用不同方法求解该方程，给出了该方程的近似结果和数值模拟结果，并分别对两种情形画出图像作了比较，据此还讨论了色电场的涡旋解及能量密度，最后讨论了含有附加真空常数的对偶阿贝尔-黑格斯模型并对应口袋模型给出了附加真空常数的物理解释，引入夸克源之后还预言麻省口袋模型中的真空常数正比于单极质量的四次方。

We present an analytic expression for the energy of this extended state which is negative of the strength of the nearest coupling over the strength of the next-nearest coupling.

我们得到了系统处于扩展态时电子能量的解析表达式，它的数值为负的最近邻耦合常数与次近邻耦合常数的比值。

The angular distribution of the scattering coefficient of the HH polarization is obtained by numerical implementation, the influence of the fractal dimension, the special fundamental frequency, the scale interval, the permittivity of substrate medium, the permittivity and the mean layer thickness of intermediate medium, the root mean square of rough surface, and the frequency of the incident wave on the bistaticscattering coefficient is discussed.

通过数值计算得到了HH极化下双站散射系数随散射角的变化曲线，讨论了分维、空间基频、标度区间、底层介质介电常数、中间介质介电常数和厚度、粗糙面高度起伏均方根及入射波频率对双站散射系数的影响，得到了平面波入射一维带限Weierstrass分形分层介质粗糙面散射系数的分形特征、基本特征、分区特征和随频率变化的特征。

A large uumber of numerical calculations using the analytic formula and the dispersion equation have been candied out on the relations of the attenuation and phase constant with wave frequency, thickness and conductivity of the lossy layer.

此式适用于截止频率附近，通过解析表达式和波导模式色散方程，对衰减常数和相位常数进行了大量数值计算，得到了它们随损耗层厚度、频率以及损耗层电导率的变化规律，两种方法所获得的结果有较好的一致性，研究表明，损耗强度和损耗层厚度的变化会改变波导中电磁模式的色散和简并特性，对于改善高功率回旋行波放大器中注波互作用带宽和模式竞争非常有益。

Energy distribution function and chemical reaction rate coefficient s were calculated through Boltzmann equation analysis and collision theory.

应用碰撞理论和波尔兹曼方程分析，对能量分布函数及反应速率常数进行数值模拟，得到离解反应速率常数与温度的曲线，分析预报各反应过程及表现。

Based on this model, the age of the universe, and the Hubble constant value can be accurately determined by the Velocity of light,and the mode indicates the reasons of Hubble constant becoming smaller with farther observation of celestial body and changing trends of Gravitational constant.

依据此模型，可以通过光速值准确测定宇宙的年龄、哈勃常数值，揭示哈勃常数随所测天体距离越远越小的原因和引力常数变化的趋势。

Physical reality can be seen as grounded in the numerical values of a handful of dimensionless constants, the best known of which are the fine structure constant and the ratio of the rest mass of the proton to the electron.

自然实在被视为基于少数无量纲常数的数值，其中最有名的常数是"精细结构常数"和"质子与电子静止质量的比率"。

In which T k is the mean kinetic temperature; D H is the heat of activation, 83.144 kJ·mole 1 (unless more accurate information is available from experimental studies); R is the universal gas constant, 8.3144 × 10 3 kJ·mole 1 ·degree 1; T 1 is the value for the temperature recorded during the first time period, e.g., the first week; T 2 is the value for the temperature recorded during the second time period, e.g., second week; and T n is the value for the temperature recorded during the nth time period, e.g., nth week, n being the total number of storage temperatures recorded (minimum of 52 weekly entries) during the annual observation period.

公式中Tk代表平均动力温度；⊿H代表激活的热能，83.144KJ.mole-1（除非从试验研究中能得到更精确的信息）；R代表气体常数，8.3144×10-3KJ.mole-1.degree-1；T1为第一时间段记录的温度数值，例如，第一周；T2为第二时间段记录的温度数值，例如，第二周；Tn为第n时间段记录的温度数值，例如，第n周，n为记录的贮存温度的总数（每周一次记录，在每年的监测周期内最小为52次）【注释：所有温度T，为绝对温度，单位为开尔文。

In the first part, it was investigated the interaction between Pb2+ and La4Ti9O24 ceramic bulk. The result shows that a significant Pb2+ diffusion into La4Ti9O24 ceramic bulk and a significant crystallization of the La2/3TiO3-type phase is clearly observed in the Pb2+ diffusion layer. The reacted zone consists of the La2/3TiO3-type phase exhibits the linear dependence of the square of the thickness, x, on the heat-treated time, t, in excellent agreement with the parabolic law x2 = kt, where k is the growth rate coefficient. The kinetic study thus indicates that the Pb2+/La4Ti9O24 interaction strictly obeys the theory of the reactive diffusion. Furthermore, the experimental k values were used to determine the associated activation energy, Ea, for the formation of La2/3TiO3-type phase using the Arrhenius plot and the following least-square equation, ln =-Ea/RT + A, where T is the annealing temperature, R is the universal gas constant, and A is a constant, resulting in Ea ~ 607 ?b 60 kJ/mol.

首先， 以巨观的方式观察PbO与La4Ti9O24陶瓷体介面的反应现象；利用X-ray绕射分析以及扫描式电子显微镜来观察不同的热处理温度以及不同的持温时间所制作的样品，研究结果发现， Pb2+离子会渗入到La4Ti9O24陶瓷内，同时在Pb2+离子所渗入的区域内会产生新的La2/3TiO3-type钙钛矿斜方晶相；藉由量测不同温度与时间之样品，其因Pb2+离子渗入而产生之La2/3TiO3-type相层厚度之关系，符合反应式扩散机制中 x2 = kt 之关系式(其中 x：扩散层厚度； k：反应速率常数； t：反应时间)；进一步将不同实验条件所得到之反应速率常数值代入Arrhenius方程式ln (k =-Ea/RT + A ，其中Ea：活化能； T：绝对温度； R：气体反应常数； A：常数，可以求得Pb2+离子与La4Ti9O24陶瓷发生反应式扩散所需之活化能为607 ± 60 kJ/mol。

The flow-field around a hemisphere and a flat-nosed cylinder in the shock tube is simulated numerically by using non-equilibrium Navier-Stokes equations with an air chemical model of 5 species 17 reactions, and the catalytic rate constant of surface materials such as Pt, SIC:, Ni and a flight vehicle materials is determined by using the heat transfer rate of testing in the shock tube and the distribution of heat transfer rate along with the catalytic rate constants.

用5组分17个化学反应Durm-Kang空气化学模型和轴对称热化学非平衡Navier-Stokes方程，对激波管中球头和平头圆柱模型绕流流场进行了数值模拟，给出了驻点热流随催化速率常数变化的分布，并根据激波管实验测量的热流值确定了表面材料Pt、SiO2、Ni和某种飞船材料的催化速率常数，建立了数值分析高焓流动边界层催化特性的软件。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。