比较函数

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。

The identity and difference in the expressional patterns between distribution functions of discrete random variables and distribution functions of continuous random variables are elaborated,and the main expressional patterns of distribution functions of continuous random variables are summarized,and the derivability of distribution functions of continuous random variables is discussed.

0引言在概率论中，连续型随机变量分布函数的表达形式及其可导性是一难点。其一，离散型随机变量的分布函数有较明显的性质和统一的表达形式，而连续型随机变量，由于其概率密度函数一般为分段函数，根据其分段区间的差异，表达形式差异较大，不容易总结其规律，本文主要比较连续型随机

Functions are provided to support input in latitude and longitude, to support output of latitude and longitude, to calculate the great circle distance between two points and to easily specify a bounding box usable for index searches.

提供了几个支持以经纬度输入的函数、支持输出经纬度的函数，以及计算大圆上两点距离的函数以及可以比较简单地声明一个外包框用于索引搜索的函数。

Shows several familiar methods to call external function by PowerBuilder and their definition format,and gives a comparision of call effici ency between external and internal functions.

给出了PowerBuilder的几种常见的外部函数调用方法及外部函数的定义形式，并对外部函数和内部函数的调用效率作了比较。

Results show that radial basis function and point interpolation methods possess Kronecker Delta function property, but the robustness is poor in some cases; the MLS approximation function does not possess Kronecker Delta function property, but it has good robustness. Differences among the three discretization schemes of meshless method are as follows:the collocation method requires no numerical integration and very little computational time while its robustness is poor; Galerkin method is not a truly meshless method due to the background meshes required for integration; the Petrov-Galerkin method is a truly meshless method and need numerical integration in each sub-domain, so it needs more computational time.

分析结果显示：径向基函数和点插值法均具有d 函数属性，但计算稳定性差；移动最小二乘近似函数不具有d 函数属性，但计算比较稳定；无网格方法中的3种离散方法不同之处在于：配点法不需要积分，计算量小，计算稳定性差；Galerkin方法需要借助背景网格进行积分，它不是真正的无网格方法；Petrov-Galerkin方法，是一种真正的无网格方法，它需要对每个子域进行积分，计算工作量较大。

The third aspect: we consider comparison of Minimum Norm Quadratic Unbiased Estimator and ordinary least squares estimator of in the multivariate normal linear model Y ~ N{XB, V, where the design matrix A' need not have full rank and the dispersion matrix V can be singular.

使用的损失函数有二次损失函数、嫡损失函数和对称损失函数。论文基于以下三个准则：二次损失风险准则、嫡损失风险准则和对称损失风险准则，将MINQUE和LSE进行比较。

Keywords: Machine discovery,recursive function,primitive recursive formula,goal restraint.

递归函数法，该方法把待求函数本身作为唯一的理论项，从而保证了理论项的合适性；其发现能力也有所提高，该方法采用原始递归式定义函数，递归函数在理论上比较完善，故该方法具有很好的理论依据并且便于计算机实现。

The spectral curve vs invariant mass is becoming wider and the peak is shifted towards the high invariant mass region with the increase of temperature. However, in ultra high temperature or density envi- ronment, the peak is shifted towards lower region and the curve is changed narrower with the increase of temperature. In the invariant mass region M 憕.-?0.4 GeV?.6 Ge1~, the spectral function is enhanced very much. which contributes to the interpretation of dilepton enhancement results in relevant experi

结果显示高温高密强子物质环境对其有非常重要的影响：ρ谱函数在温度或密度不太高时谱函数曲线变宽，并且峰朝不变质量高的方向移动；在极端高温或高密情况下谱函数却变窄，并且峰朝不变质量低的方向移动，在不变质量M～0.4-0.6 GeV区间谱函数有比较明显的增强，这有助于解释双轻子产生的相关实验现象。

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

Tangent sine function with the function, structure and the cosine function linear structure, The results showed tangent curve smoothing function fitting, bending loss smaller, more optimization of the optical path.

正切函数与正弦函数、余弦函数结构以及直线结构进行比较，结果表明正切函数拟合曲线平滑，弯曲损耗较小，更优化了光路径。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。