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φ-函数
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  φ-function
     In this paper,several properties of centroid φ-function and centroid Φ-function are discussed.
     讨论了形心φ-函数和形心Φ-函数的若干性质.
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  “φ-函数”译为未确定词的双语例句
     This paper studies the properties theφ-distortion function andη-distortion funition Schottky upper boundaries are established.
     文章用无穷乘积表示了Hersch-pflugerφ-函数与Agardη-偏差函数,得出它们的一些性质,由此给出了Schottky上界的估计。
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  相似匹配句对
     m) is Euler function.
     φ (m)是Euler函数
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     The Moments of the Function Φ(t)
     函数Φ(t)的矩
短句来源
     (H,φ)-monotone Mappings and its Characterizations
     (h,φ)-单调函数及其性质
短句来源
     The Euler φ-function in the quadratic number fields
     二次数域上Eulerφ-函数”的结构
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     The Lcm-sum Function
     最小公倍数的和函数
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  φ-function
It is demonstrated that we can represent Euler's φ-function by means of a Δ0-formula in such a way that the theory IΔ0 proves the recursion equations that are characteristic for this function.
      
For any pair of latticesL andL satisfying i)L?L and ii) the indexN ofL intoL is prime to 6, we construct from the usual φ-function ofL(cf.
      
It is shown by a simple induction that any square-free natural number is the square-free kernel of Euler's φ-function of infinitely many natural numbers.
      
Furthermore every square-free natural number >amp;gt;1 is the square-free kernel of Euler's φ-function of infinitely many square-numbers.
      
This paper is a comprehensive study of the set of totients, i.e., the set of values taken by Euler's φ-function.
      


In this paper the phase operator (?) is defined on the foundation of formulation of the classical radiation field,and then let it as one of field variable to obey the Heisenberg equation of motion.As a consequence of this procedure quantization of of the radiation field is carried out.It is different from[1][2][3],in which quantization of the field is a presupposition for the definition of phase operators. At the same time the problem on commutation relation of the func tions of phase operator is discussed adequately....

In this paper the phase operator (?) is defined on the foundation of formulation of the classical radiation field,and then let it as one of field variable to obey the Heisenberg equation of motion.As a consequence of this procedure quantization of of the radiation field is carried out.It is different from[1][2][3],in which quantization of the field is a presupposition for the definition of phase operators. At the same time the problem on commutation relation of the func tions of phase operator is discussed adequately.

本文以经典辐射场的表达为基础,定义了相位算符φ,并将它纳入Heisenberg运动方程,从而实现了辐射场的量子化,有别于文献[1][2][4]以场量子化为前提来定义相位算符。同时还适当地讨论了φ函数算符之间的对易性问题。

In this installment the authors present a study on the i=N/(N+1) epitrochoidal conjugate countour-pattern in light of the method of reversal. Some new concepts, such as "φ-function" and "contact graph", are established and their applications are discussed.

本文采用逆解法对i=N/(N+1)短幅外摆线线型进行理论分析,提出了“φ函数”等概念,建立了“接触图”,并从六个方面介绍了φ曲线和接触图在线型分析中的应用。

This paper is divided into four sections. Section 1 and 2 contain the following theorems. Theorem I. Let L_Φ~≠ and L_M~* be Orlicz spaces, Then the foll-owing are equivalent. (i) L_M~* and L_Φ~* have. the property(ii) L_Φ~* and L_M~* have the property(iii) Φ(u) is increasing more rapidly than M(u).Theorem Ⅱ. The following assertions are equivalent. Let L_(?)~* , L_(?)~* be Orlicz spaces with F-norms ||·||_φ,||·||_φgenera-ted by φ-functlons φ(u),(?)(u) respectively. In section 3 a conter-example is given to point...

This paper is divided into four sections. Section 1 and 2 contain the following theorems. Theorem I. Let L_Φ~≠ and L_M~* be Orlicz spaces, Then the foll-owing are equivalent. (i) L_M~* and L_Φ~* have. the property(ii) L_Φ~* and L_M~* have the property(iii) Φ(u) is increasing more rapidly than M(u).Theorem Ⅱ. The following assertions are equivalent. Let L_(?)~* , L_(?)~* be Orlicz spaces with F-norms ||·||_φ,||·||_φgenera-ted by φ-functlons φ(u),(?)(u) respectively. In section 3 a conter-example is given to point out that the second part of Lemma 1 inC.B.Lapin's paper [4] is false. And the following theorem hasbeen proved. Theorem Ⅲ. The following assertions are equivalent.

两个N-函数Ф(u)和M(u)有四种比较概念。本文§1和§2给出其中两种比较概念有关的Orlicz空间的五个补充定理。§3以一个反例指出C.B.Лапив一个引理的错误,详细讨论了两个φ-函数的“快于”比较概念,这补充了作者的文。

 
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