查询词典 equivalent functions

Weapply the kernel methods of regression functions and conditional density functions to obtain aseries ofβas the estimators ofβ.

回归函数核估计方法中，又分别提出了在选定连续样本点和离散样本点时的两种非参数估计模型，并对这两种模型做了详细的阐述。

We apply the kernel methods of regression functions and conditional density functions to obtain a series of as the estimators of . Then using Monte Carlo Analysis method , we can get the optimal choice of the unknown parametric that is . Examples illustrate the models and will show this estimation is effective.

应用回归函数核估计和条件密度函数的核估计方法估计未知量，将得到的一组估计值用Monte Carlo Analysis方法处理便得到最优的，并通过算例模拟讨论以上估计方法的优劣。

Based on censored data, a smoothing estimation method is proposed to estimate the parameter functions. Moreover, a consistent estimator for the asymptotic variance matrix of the estimators is provided. The limiting distribution of estimated functions and the estimator of variance matrix enable us to construct approximated regions.

根据截切资料，我们提供平滑估计法以便估计参数函数，接著，我们也对估计函数的变异矩阵提出一个估计式，利用估计式的常态分配逼近，其相对应的信赖区间建构法也被提出。

Furthermore, we define a convolution multiplication between characteristic functions of constructible subsets by using push-forward functor from the category of algebraic varieties over C to the category of spaces of constructible functions. We construct geometric model for "intrinsic symmetry" of the octahedral axiom in a triangulated category. Using it, we deduce the multiplication satisfies the Jacobi identity of Lie algebra and then realize infinite dimensional Lie algebras.

进一步，我们使用复代数簇范畴到可构函数空间范畴的pushforward函子，给出了可构集上特征函数的卷积乘法，并构造了三角范畴八面体公理的内蕴对称性的几何模型，最终证明了对于不可分解支撑有界可构集的特征函数，乘法满足李代数定义的Jacobi恒等式，从而给出了无限维李代数的实现。

The main aim of this thesis is to extend some results of classical convex analysis to notions of Carnot groups, which contain the inequalities of Hadamard type, the Lipschitz continuity, the comparison principle and the second order derivatives for convex functions on Carnot groups G and regularity of quasiconvex functions on G.

本文的主要目的是推广欧氏空间凸分析中的一些结果到Carnot群上凸分析的情形，其中包括Carnot群上凸函数的Hadamard型不等式、Lipschitz连续性、比较原理、二阶可微性及拟凸函数的正则性问题。

The techniques of computing the domain of convergence and sum function and expanding functions in several variables to power series of functions in several variables are mainly discussed by many examples.

引入了多元函数项级数的概念，给出了其收敛域及和函数的定义；通过详实的例子讨论了多元幂级数的收敛域、和函数及多元函数展开为多元幂级数的计算方法。

For a long time, it is a main factor to hamper the real-time application of SHET. The research is carried on aiming to quickening convergence speed. The automatic-changing Homotopy algorithm is proposed in the dissertation. The algorithm, which can change the solving method based on fundamental component, has the advantages of large convergence domain, high convergence rate and high precision. Many trigonometric functions are contained in the mathematical model, during solving equation, the calculated speed and the precision are affected by the calculations of trigonometric functions.

特定谐波消除技术的数学模型是一组非线性方程组，长期以来，方程的求解一直是限制该技术实时应用的关键因素，本文针对特定消谐方程组的快速求解进行细致的研究，提出自动变同伦算法，该算法可根据基波幅值的取值范围来决定采用的求解方法，其对求解方法的可选择性使该算法与其它算法相比具有计算速度快、收敛域宽、计算精度高等优点。

This paper introduces the definition of common quadratic Lyapunov functions and proves that the set which consists of all the common quadratic Lyapunov functions is a convex cone .

给出了共同二次Lyapunov函数的定义，并证明了全体共同二次Lyapunov函数所组成的集合是凸锥

There are a large number of non-convex functions in practical problems, and they have similar nature in the non-linear programming as convex functions.

实际问题中的大量函数都是非凸的，它们与凸函数在非线性规划中有一些相似的性质。

By the perturbation theorem of cosine operator functions,one perturbation result for C-cosine operator functions is obtained.

而对于扰动问题的研究向来是十分重要的，因为这类研究是获得丰富理论的基本途径之一。

We stopped by the old fashion ice cream parlor Manhattan Beach Creamery for some refreshment. The "No Shoes, No Shirt, No Problem" sign on the wall epitomizes the beach lifestyle.

我们去商店区的一家老式冰淇淋店坐坐，墙上挂著「没鞋，没上衣，没问题」的牌子完全捕捉了海滩生活的随性及风格。

"If therefore", argues Bellarmine we can offer our prayers and our satisfactions in behalf of those detained in purgatory, because we are members of the great body of Christ, why may not the Vicar of Christ apply to the same souls the superabundant satisfaction of Christ and his saints--of which he is the dispenser?

" "因此，如果"，认为贝拉明（德indulgentiis ，十四）"我们可以提供我们的祈祷和我们满意的代表那些被拘留在炼狱，因为我们是成员的伟大基督的奥体，为什麼可能不是牧师基督适用於同样的灵魂满意的过剩是耶稣和他的圣人-他是在配药？