查询词典 abelian summation

Via generalizing the Cauchy method we obtain a new method,called the modified Cauchy method.By means of this method we establish two bilateral _3ψ_3 and _4ψ_4 series summation formulae,two four-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3ψ_3-series,and two five-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3φ_3-series,which contain many known results as their special cases,such as non-terminating q-Saalschütz summation formula,Bilateral _6ψ_6 series summation formula of Bailey,non-terminating Watson transformation formula and some transformations of _3φ_2-series etc.

通过对Cauchy方法的推广，我们得到修正的Cauchy方法，采用这个方法分别得到两个双边的_3ψ_3和_4ψ_4基本超几何级数的求和公式、单边_3φ_~(2-)级数和双边_3ψ_(3~-)级数的两个四项求和变换公式和两个五项求和变换公式，它们包括许多已有的结果为特例，如非终止的q-Saalschütz求和公式、Bailey的very-well-poised双边级数_6ψ_6求和公式、非终止的Watson变换公式和一些关于单边_3φ_(2~-)级数的变换公式等。

Arad and Blau proved that an abelian table algebra can be viewed as a group algebra of some abelian group G. Chapter 3 of this paper gives the structural theorem of abelian table algebras by defining a group structure in table basis. Furthermore, the structure of elementary abelian table algebras is discussed using the number of composition series of table algebras.

Arad和Blau证明了abel表代数等价于某个有限生成abel群G的群代数，受此启发本文第3节通过定义表基的一个群结构给出了abel表代数的结构定理，并从合成列数目的角度对初等abel表代数进行了细致刻画。

In chapter three,we have derived a generalized dual London equation for the Abelian "electric" field A_μfrom the effective dual Abelian-Higgs model.The approximative result and the numerical simulation result as well as their figs were shown via solving the dual Abelian-Higgs model with different methods.Hereby the vortex solution of the chromo-electric field and the vortex energy density were also discussed.Finally,we have studied the dual Abelian-Higgs model with additional vacuum constant,and have unpuzzled the vacuum constant corresponding to the bag model.When the quark sources is introduced, the vacuum constant in the MIT bag model is proportional to the quartic of the monopole mass.

利用不同方法求解该方程，给出了该方程的近似结果和数值模拟结果，并分别对两种情形画出图像作了比较，据此还讨论了色电场的涡旋解及能量密度，最后讨论了含有附加真空常数的对偶阿贝尔-黑格斯模型并对应口袋模型给出了附加真空常数的物理解释，引入夸克源之后还预言麻省口袋模型中的真空常数正比于单极质量的四次方。

Firstly,by the analysis of influencing factors of settlement of loessal foundation, results indicated that among the three settlement methods such as the layer-wise summation method based on chord modulus, the layer-wise summation method based on modulus of compressibility and the layer-wise summation method based on modulus of deformation and so on, the layer-wise summation method based on chord modulus is superior to the other two methods and is very close to the actual measurement settlement of building according to the grey incidence analysis on influencing factors of settlement.

本文采用灰色系统理论中的关联分析法对黄土地基变形进行了因素关联分析，并取得一些成果。通过分析影响黄土压缩变形的因素，对于沉降变形因素的关联分析，在对影响变形的诸因素进行分析的基础上，最终证明选择了四种因素作为确定弦线模量表依据的正确性，证明了据此建立的以弦线模量为基础的变形定量分析的表达式是可行的。从关联分析以及弦线模量法的简便、直观、便于推广应用的特点来看，弦线模量法计算沉降是值得大力推广的。

The main content of this thesis is to find and prove some summation and transformation formulae of basic hypergeometric series by the modified Cauchy method,operator method and inversion techniques,which include many well-known results as special cases,for example,q-Saalschiitz summation formula,Baileys _6ψ_6 summation formula,non-terminating Watson transformation formula and Rogers-Ramanujan identities etc.

本文的主要内容是利用修正的Cauchy方法、算子方法和组合反演技巧来发现和证明一些基本超几何级数求和公式和变换公式，其中包含一些著名的公式，如q-Saalschüz求和公式、Bailey的_6ψ_6求和公式和非终止的Watson变换公式等作为其特殊情况。

Summation of infinite series is part of the process of learning more difficult to grasp the progression part, this article summarizes the common summation of several infinite series method, as has the use of progression and the definition of sum, the use of itemized points or one differential sum, the use of split-phase elimination method of summation methods, and problem-solving steps in detail.

无穷级数的求和部分是学生学习级数过程中较难掌握的部分，本文归纳了常见的几种无穷级数的求和方法，像有利用级数和的定义求和、利用逐项积分或逐项微分法求和、利用裂项相消法求和等方法，并提出了详细的解题步骤。

Using the main result, we also obtain a simple criterion to check if a given C(superscript *)-algebra A is Abelian, that is, A is Abelian if and only for any two positive elements a, b∈A, there is a'∈A such that ab=ba'.

利用文中的主要结论，还得到了判断C-代数A是交换一个简单条件，即A是交换的当且仅当对A中的任何两个正元a，b存在a'∈A使得ab=ba'。

Using the main result, we also obtain a simple criterion to check if a given mathrm C^*-algebra A is Abelian, that is, A is Abelian if and only for any two positive elements a, bin A, there is a'in A such that ab=ba'.

利用文中的主要结论，还得到了判断 mathrm C^*-代数 A 是交换一个简单条件，即 A 是交换的当且仅当对 A 中的任何两个正元 a， b 存在 a'in A 使得 ab=ba'。

Group is an important concept in Modem Algebra. Viewed from a different angle it may be divided into two different categories: finite group and infinite group; and Abelian group and non-Abelian group.

群是《近世代数》的一个重要概念，从不同的角度出发，群可以分为有限群和无限群两大类，又可以分为交换群和非交换群两大类。

Let G be a finite Abelian group ,an ideal in the grouping Zpr is called an Abelian code over Zpr.

设G为有限阿贝尔群，群环Zpr中的理想称为Zpr上的阿贝尔码。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。