查询词典 equivalent functions

This article uses the implicit function theorem and the properties of analytic functions,with less limitations for the uniqueness,continuity,continuous differentiability of the implicit functions,and gets the sufficient and necessary conditions of the existence of implicit functions by simplifying them.

从常用隐函数存在性定理出发，放宽对隐函数唯一、连续、连续可微等性质的限制，利用解析函数的性质将其展拓，得到广义隐函数存在的充分必要条件和广义隐函数的分布特征。

Properties of measurable functions; approximation by simple functions and by continuous functions; convergence in measure; Egoroff's theorem; Lusin's theorem; Jensen's inequality.

可测函数。可测函数的性质；简单和连续函数逼近；测度收敛；叶果洛夫定理；鲁津定理；詹森不等式

For radians, these functions are found in boost/units/cmath.hpp These behave as one expects, with trigonometric functions taking an angular quantity and returning a dimensionless quantity, while the inverse trigonometric functions take a dimensionless quantity and return an angular quantity

对于弧度，这些函数定义在 boost/units/cmath.hpp 。这些函数就像你想的那样，三角函数以弧度数量为参数返回一个无量纲数量，反三角函数以无量纲数量为参数返回一个弧度数量

System is divided into five subsystems : party management subsystems : major achievement for the party members and activists dynamic change process; Party official system : achieving document handling, information dissemination, e-mail management functions; Public information system : the achievement of notice information processing, integration, and other functions, the party's theoretical study and explore information processing; party analysis systems integrated operations management system for statistical computing, statements editing, modification, and export management functions; party management subsystems : the main party organizations to achieve integrated data management, and the party's domestic and foreign party overall control and management decision-making aids.

系统分为五个子系统：党员管理分系统：主要实现预备党员、积极分子动态变动过程；党务公文系统：实现文件的收发、信息发布、电子邮件管理功能；公用信息系统：实现对公告信息处理、整合等功能，党组织对党的理论研究和探讨的信息处理；党务管理分析系统综合业务系统实现统计计算、报表的编辑、修改及输出等功能管理；党务管理分系统：主要是实现党组织的综合数据管理，以及党的对内对外的党务全程控制和辅助决策管理。

In particular, for recurrent event data, we proposed a novel nonparametric estimator of the survival function and obtained an efficient estimator of the expected total number of events for counting processes. Also we established asymptotic properties of these estimators and investigated nonparametric estimation of survival functions, density functions and hazard functions under various types of incomplete data.

在重复事件发生的情况下，创新地提出了一种生存函数的非参数估计，获得了计数过程中预期事件总数的估计以及这些估计的大样本性质，并在其他各种不完全数据下对生存函数，概率密度和失效率函数等非参数估计进行了深刻研究。

We can not apply Galerkin methods with radial basis functions to the first boundary value problem (the Dirichlet boundary value problem) of the second-order elliptic equation, because it requires that the approximate functions should fit the essential boundary condition, while the spaces spanned by the radial basis functions fails to satisfy this kind of boundary condition, and it is the same for the higher-order elliptic equation.

我们不能直接应用这样的无网格算法求解二阶椭圆型方程的第一类边值问题(Dirichlet边值问题)，因为第一类边界条件是本质边界条件(对二阶椭圆型方程为Dirichlet边界条件)，而径向基函数的支集通常是全空间，由它们所生成的近似函数空间一般不满足这样的条件。

Interval slope method is proposed for a class of unconstrained min-max-min problems, in which the objective functions are factorable functions. An interval algorithm is given by interval slope discard tests and interval extension of objective functions. Numerical results are also presented.

讨论目标函数为因子函数的离散无约束min-max-min问题，利用区间斜率，构造目标函数的区间扩张和区问斜率删除原则，建立了求解离散无约束min-max-min问题的区间斜率算法，并给出了数值算例。

Jinri Group, a Hong Kong pharmaceutical enterprise, made a survey on Zhejiang Province that is a key-consuming province of health-caring products. The result indicated that among 30 main products, 80% emphasized on the functions while 16.7% on kinship and the rest are 3.3%. And of 24 brands focusing on functions, many concentrated on functions of anti-fatigue, anti- caducity and blood fattiness adjustment that occupied 26.7%, 23.3% and 20% respectively, thus, obviously, a similarity appeared.

根据香港一家制药企业——金日集团对中国内地消费品重点消费省份浙江省的调查显示，主要的30种保健品品牌中，在传播中强调功效的占80%，强调亲情的占16.7%，其它3.3%。24种强调功效的保健品品牌中，大多将功效集中在缓解疲劳、抗衰老和调节血脂三个方面，分别占所调查品牌数的26.7%、23.3%和20%，出现明显雷同的现象。

Based on a kind of orthogonal complete functions in L2[0,1], another one (called V-system) which has equivalence relation with U-system is created. It is a kind of new and effective mathematical tool on signal multi-resolution analysis. Besides that V-system keeps the favorable properties of U-system and can accurately reconstruct geometry information which expressed in piecewise polynomials by finite sum of functions in V-system, it has more special properties, such as simple construction, abundant levels, convenience of application, quick calculation, local support, and so on. V-system is the generalization of Haar orthogonal functions, and to be a class of wavelet base. It has a good future for some applications in the fields of wavelet analysis and signal processing.

从L2[0，1]空间的一类正交完备函数系U系统出发，构造了另一类与之等价的正交完备函数系，称之为V系统，它是信号多分辨分析方面的一种新型的、有效的数学工具。V系统不仅保持了U系统的优良特性，对多项式表达的几何信息能够做到有限项精确重构，并且较之U系统，它更有结构简单、层次分明、计算快捷、局部支集等特点，应用起来将更加灵活方便。V系统可以看作是Haar函数系的推广，是一类小波基，在某些数字信号处理及小波分析问题中有良好的应用前景。

This paper provides the analytic method to calculate the value of Green"s functions in space domain at the zero distance by the discrete complex image theory,that is ,to express the finite progressional sum of Green"s functions detained with DCIT into Taylor expansion and deduce the analytic expression of the singularities at the zero distance with the help of the specific subdomain base functions.

对此，本文在讨论采用离散复镜象理论计算空间域Green函数时，提出了采用该镜象理论计算空间域Green函数零距离处奇异值的解析方法，即，采用Taylor公式展开镜象理论得到的空间域Green函数的有限级数和形式，并结合特定的分域基函数来得到零距离处Green函数奇异值的解析计算式进行计算。

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？