数值函数

An explicit formula for the enhancement factor in gas-liquid absorption with irreversible chemical reactions is presented.

提出气液化学吸收增大因子β的显函数式，并分别同膜理论、渗透理论模型以及可vanKrevelen—Hoftijzer隐函数式的数值解比较，证明显函数式相当逼近该二理论模型，同时在准确性和方便性方面都优于隐函数式。

At first, the examples are given to explain a new method in signal processing, in which functions are defined from the viewpoint of multi-scale analysis. Then the authors present "coordinate heft separate" method, discover self-similar structure of points set on plain area; based on this self-similar structure, construct orthogonal complete 2-value function system of high-dimension simplicity; enrich and extend the theory and application of Rademacher function and Walsh function.

首先，举例说明在多尺度分析观点下，信号处理中某些函数定义的新方法；进而提出"坐标分量分离方法"，并由此发现了平面区域上点集坐标数值的自相似结构；在揭示了如此自相似结构的基础上，构造了高维单纯形上的正交完备的二值函数系统；丰富与推广了Rademacher函数及Walsh函数的理论及应用。

The gamma function calculation of Pearson type III distribution is investigated,a new approximation method by using cone curve is put forward,and neither numerical integral nor series expansion may be used.

对皮尔逊Ⅲ型分布公式中伽玛函数的计算问题进行了研究，提出了一种新的数值逼近方法，在一定范围内对伽玛函数用圆锥曲线表示，利用递推公式扩大参数范围，免去了数值积分和用级数展开计算的麻烦。

The following are the major work in this thesis which has been studied and still needs to be studied further in the future: 1 An improved adjoint variational method is developed, thus it can be applied to the LAGFD-WAM Wave Numerical Model for data assimilation; 2 A linear evolution equation of spectral perturbation is derived in order to analyze its increasing or decreasing mechanism.

本论文主要完成了以下几个方面的研究： 1）建立了推广形式的共轭变分同化方法，使之能够应用于LAGFD-WAM海浪数值模式； 2）导出了扰动谱线性演化方程，分析了扰动谱增长、衰减机制，考察了涌浪情况下扰动谱的持续时效问题及风浪情况下扰动的演变过程； 3）利用波谱共轭方程初步分析了同化模型中距离泛函的敏感性及敏感区域空间分布； 4）将推广的共轭变分方法应用于海浪谱能量平衡方程，建立了连续形式的海浪同化模型，特别是严格导出了风输入、破碎、底摩擦、波波非线性相互作用和波流相互作用各源函数的共轭源函数表示式； 5）分别进行了波谱层次上和有效波高层次上的同化试验，并对数值结果进行了分析。

The constructing process of the algorithms itself indicate that they are brevity and have definite geometric meaning, scientific iterative terminal criterions and no strict requirement to function. Finally, some digital experimentation is presented to indicate the algorithms application in solving the problem of maximum of function, transcendental equation,integer programming and so on. The results indicate that the algorithms have more global and more adaptability compared to traditional algorithms and have more calculating efficiency and more scientific iterative terminal criterions compared to some present popular artificial intelligence algorithms.

算法的构造过程本身表明了该算法简单明了、几何意义明确、迭代终止准则科学、对函数的要求较低；最后举了几个数值试验的例子以说明该类算法在求函数的最值，解超越方程以及整数规划等问题中的应用；数值试验的结果标明该算法比单纯由"微分"思想演化而来的传统算法有更好的全局性和对问题的更广泛的适应性，比现在流行的一些人工智能方法有更高的运算效率和更适当的迭代中止准则。

Based on the dynamic equation, the transport and acceleration of out-flowing ionospheric ions in the magnetosphere are studied by means of finding the ion distribution function. They include two parts: the study of static ion distribution with analysis and numerical compute; the study of ion acceleration by induced electric feild in the period of dipolarization of taillike geomagnetic lines in the substorm expansion phase with the numerical simulation of the ion distribution function.

本文在磁层中上行离子的加速与传输理论研究领域中，采用动力论方程，用求解离子分布函数的方法来研究问题：(1)用解析求解和数值计算的方法，对上行离子在不同Kp指数条件下磁场位形中的定态分布进行了研究；(2)用数值模拟计算分布函数的方法，对上行离子在亚暴膨胀相磁场向偶极形驰豫过程中受磁尾的感应电场加速进行了研究。

The results of numerical analysis show that the elastic modular and the poisson ratio have no effect on two-dimensional bearing capacity, but can affect the ultimate bearing capacity of three-dimensional foundations and control the convergence and precision of finite element calculation; the earth pressure coefficient controls the geostatic stress of foundation, sequentially affects the ultimate bearing capacity of foundations and the convergence of numerical calculation. When calculating the ultimate bearing capacity of undrained saturated foundation, the complete formulation exists shear locking, and reduce formulation exists hourglassing, so the hybrid formulation is suitable to imitate the geomaterial. When the soil obeys nonrelevent flow rule, the yielding function is different from potential function, and the elastic-plastic matrix of soil is asymmetric, so the unsymmetry numerical solver and appropriate finite element mesh is required.

研究结果表明，土体弹性模量和泊松比对二维基础极限承载力没有影响，但是影响着三维矩形基础的极限承载力，控制着ABAQUS数值算法的计算精度与收敛速度；地基土压力系数控制着地基土体中的地应力平衡，从而影响着二维条形基础和三维矩形基础的极限承载力和地基破坏包络面；对于不排水饱和软黏土地基，常规的完全积分单元会造成剪力自锁现象，而减缩积分单元则存在过于柔化的现象，故采用杂交单元来模拟较合适；当土体服从非关联流动法则时，屈服函数与塑性势函数之间存在差异，从而导致土体弹塑性矩阵呈现非对称性，在有限元计算中必须采用非对称数值解法，并且合理地划分单元才能对极限承载力进行准确求解。

It is found thatthe fractal dimension D=1.25 corresponds to the lowest criticalcoupling constant αc=1.9,D=1.73 corresponds to the highest criticalratio of dielectric constants ηc=0.163,and when D≤1.145 bipolaronscan not exist at any rate.In chap,4,we will propose a novelapproach to the calculation of the exciton ground-state energy for thestrong-coupling case.Different from all previous methods,the wavefunction of the phonon part is assumed to take a form related to thewave function of the relative motion.We obtain the exciton energy bysolving the derived integrodifferential equation rather than select ahydrogen-like form to minimize the energy expectation.

结果发现，分数维的维数D＝1.25对应最小的临界的电-声耦合常数(αo＝1.9)，D＝1.73对应最大的临界的介电常数比(ηc＝0.163)，当分数维的维数D≤1.145时，双极化子无论如何也不可能存在，在第四章中，我们将提出一种新颖的变分方法来计算强耦合的激子-声子系统的基态能，不同于以前所有的方法，我们取声子的波函数与相对运动波函数有关的形式，而不是假定一个固定的关于相对运动坐标r的函数形式，得到相对运动波函数所满足的非线性的微分积分方程，我们数值求解这个微分积分方程得到系统基态能，而不是选择一个类氢原子的波函数变分使得能量的期待值最小。

The mechanism of instability wrinkling in the process based on minimum energy principle is revealed, uniform mathematic description of the wrinkling wave on the strip of in-plane bending is established, the internal and external energy is deduced by energy method, and a uniform criteria of internal and external wrinkling is established; then how to combine the criteria with the FEM simulation system to make the numerical prediction of wrinkling into reality is also resolved in the paper. The effects of the forming parameters on the deforming result are analyzed by the uniform predict criteria. The results show as follows: as the compress width increase, external wrinkling first come into being, then internal winkling do, and finally in-plane bend occur; the loading wedge angle increase, internal winkling first come into being, thenin-plane bend do, and finally external wrinkling occur; in-plane bend is possible to occur with a increase of the strain-hardening exponent and the strength coefficient; and the effect of the friction factor may be ignored.

2揭示了板带不均匀压下面内弯曲成形过程基于能量原理的失稳起皱机理，提出了统一的描述内外缘起皱波形的函数，采用变分法推导了服从该波形函数的内外缘起皱能，建立了统一的起皱预测准则；将新建立的统一的起皱预测准则引入到数值模拟系统IBS中，数值预测结果与实验结果的吻合较好；分析了成形过程各参数对起皱的影响规律：随着接触变形区宽度的逐渐增大，先是发生外缘起皱，然后发生内缘起皱，进而才出现稳定成形；随着实际加载楔角的增大，先是发生内缘起皱，然后发生稳定成形，进而出现外缘起皱；硬化指数和强化系数增大，易于稳定成形；摩擦因子对起皱的影响不明显；而且接触变形区宽度对起皱的影响最大。

In the third chapter, using the methods of nonlinear feedback functions and Lyapunov functions and combining analytical with numerical methods, the nonlinear feedback methods are introduced and the synchronizations of chaos in Hadley system of aerographs and LFRBM system of physics are realized. Some of nonlinear feedback functions are constructed.

第三章在介绍非线性反馈方法原理的基础上，应用非线性控制的基本思想及Lyapunov函数方法，将解析法与数值法相结合，分别对气象学中著名的Hadley环流和物理学中的LFRBM系统进行研究，找到了一类非线性反馈函数，实现了混沌自同步，并利用Mathematica软件进行仿真实验，数值结果说明了该方法的有效性。

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。