比较函数

We show the different properties between covariance risk allocation function and relative risk allocation function and prove that the commonly used risk budgeting model is a special form of risk allocation function.

我们证明并比较了在标准差风险度量下，协方差风险分配函数与相对风险分配函数性质上的差异，并证明风险预算也是一种特殊形式的风险分配函数。

This thesis analyzes the energy eigenvalue and of the Harmonic oscillator with a one-dimensional δ-function, makes a comparative study of those of the one-dimensional harmonic oscillator, and analyzes the reason which causes their different quality and the different influences to the eigenvalue of the even parity energy and to the wave function when the number of the "Z" is different.

本文研究了一维δ势场中的谐振子的能量本征值及其本征波函数，并与一维谐振子的能量本征值和波函数进行了比较，分析了它们的性质不同的原因以及取不同势参数Z值时对偶宇称能量本征值和波函数的不同影响。

The higher mathematics curriculum is a college engineering course undergraduate course each specialized student's compulsory important basic theory class, through this curriculum study, causes the student to obtain: Circular function calculus study, the space analytic geometry and the vector algebra, the function of many variables calculus study, the infinite series, aspect and so on ordinary differential equation basic concepts, the elementary theory and the fundamental operation skill, and further obtain mathematics knowledge for the study successor curriculum to lay the essential mathematics foundation,During instruction knowledge, must train the student through each teaching link to have the abstract thinking ability, logic reasoning ability, spatial imagination ability gradually and studies independently ability, but also must pay attention specially trains the student to have the quite skilled operational capability and the synthesis utilization studies the knowledge to analyze the question and to solve the question ability.

高等数学课程是高等学校工科本科各专业学生的一门必修的重要基础理论课，通过本课程的学习，使学生获得：一元函数微积分学，空间解析几何与向量代数，多元函数微积分学，无穷级数，常微分方程等方面的基本概念、基本理论和基本运算技能，为学习后继课程和进一步获得数学知识奠定必要的数学基础，在传授知识的同时，要通过各个教学环节逐步培养学生具有抽象思维能力、逻辑推理能力、空间想象能力和自学能力，还要特别注意培养学生具有比较熟练的运算能力和综合运用所学知识去分析问题和解决问题的能力。主要是其中的一些专有名词查不到，比如一元函数等

The interpolation formula can be compiled into standard computer code.

在此，我们首先论述了保单调性的插值方法，根据分布函数的逆函数具有单调性的特点，用保单调的插值曲线去逼近分布函数的逆函数，进而用得到的插值公式进行随机变量的抽样，这样做可以节省抽样的时间，并且在分布函数具有一定的光滑性条件时，插值公式具有比较好的收敛阶。

In this paper, the Lagrange interpolation formula asked a class function expression question, the determination function to the higher mathematics in the elementary mathematics in some value scope question, the equality proof question, the multinomial factorisation question, to ask to have the Finite series to pass the formula question, the certificate any n function at will n+1 different spots function value maximum value minimal problem and so on six aspects should serve as the simple introduction, and has separately made the comparison with these six aspects elementary mathematics method, thus solved some operation problems in elementary mathematics.

摘要本文对高等数学中Lagrange插值公式在初等数学中的求一类函数表达式问题、确定函数在某点的取值范围问题、恒等式的证明问题、多项式的因式分解问题、求有穷数列的通项公式问题、证明任一n次函数的随意的n+1个两两不同点的函数值的最大值的最小值问题等六个方面的应用作了简单介绍，并与这六个方面的初等数学方法分别作了比较，从而解决一些初等数学中的运算问题。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

The paper establishes the standard fuzzy systems with partition of normal quadratic polynomial membership functions and normal trigonometric membership functions. The comparison problems of fuzzy system with normal triangle membership functions and the two fuzzy systems are put forward.

摘要在标准模糊系统的基础上建立了正规二次多项式和正规三角函数为基函数的两类新模糊系统，进而提出了以正规三角形函数为基函数的标准模糊系统与所提出模糊系统的比较问题。

The AF3 scheme has been used in the adjoint solution for potential flow.

在设计问题中，需要定义的形状函数能够表达一个丰富的设计空间，文中比较了分别使用Hicks-Henne函数和B-样条作为形状函数时，设计过程的不同。

Examples have been calculated by use of parameter optimization inverse program.

根据田间实测数据采用开发的参数优化反求程序进行了实例计算，分析比较了采用不同目标函数的结果，结果表明，采用第三种目标函数进行计算，优化结果最理想；并用这些结果与设置相同目标函数的离散变量算法和试算法的结果进行了对比，结果显示，三种算法所得结果没有明显差异。

By the iterative functional equation we usually mean an equation containing at leastan n-th iterate〓of an unknown function.A relatively general form of it is〓(1)where〓is a given integer,J is a connected closed subset of the real number axis R,G is a given〓function from〓to R,and f is an unknown function to be solved.

迭代函数方程通常是指含有未知的函数并含有它的至少2次迭代的方程，它的一个比较广泛的形式是〓，对任〓，（1）其中〓是个给定的整数，J是实数轴R的一个连通闭子集，G是个给定从〓到R的〓映射，f是个未知而待求的函数。

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。