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    On Theory of A Class of Dual Algorithms in Nonlinear Optimization
    非线性优化中的一对偶算法的理论研究
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    Research on the Theory and the Application of Basic Spline Class Curves & Surfaces
    B样条曲线曲面理论及其应用研究
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    The Research of a Class of Generalized Set-Valued Variational Inclusion Problems
    一广义集值变分包含问题的研究
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    On the Research of Parameter Estimation for a Class of β-ARCH Model
    关于一β-ARCH模型参数估计的研究
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    A Class of Nonlinear Diffusion Equations in Perforated Domains
    有孔区域上的一非线性扩散方程
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  课堂
    The Preliminary Study of the Design of Class Instruction—a Design and Practice for the Typical Example Lesson of the Mean-Theorem
    课堂教学设计初探——“微分中值定理”课例教学设计与实践
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    A quantitative analysis of the class instruction system based on symmetric combined system
    基于对称组合系统的课堂教学系统定量分析
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    How to Improve the Class Efficiency of Mathematics Teaching
    数学教学如何提高课堂教学效率
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    The Application of Models of Comprehensive Evalutions of Fuzzy Mathematics in the Assesment of Class Teaching
    模糊综合评判模型在考评课堂教学中的应用
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    Thinking on the Reform of Teaching Method in Economic Mathematics——Application of Enlightened Teaching in the Class of Economic Mathematics
    对经济数学教学方法改革的思考——启发式教学在经济数学课堂上的运用
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  类的
    On the Degree of Approximation of Functions Belonging to the Lip α Class
    关于Lipα函数类的逼近阶
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    On the Polynomial Representation of (0,l)-Matrix Class
    论(0,1)-矩阵类的多项式表示
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    The Structure of the Class P Under the Polynomial Equivalence Relation
    在多项式等价关系下P类的结构
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    Two Method for Proving a Problem is in p Class
    证明问题属于P类的两个方法
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    ON BEHAVIORS OF NEIGHBOURHOODS OF C(A, B) CLASS
    关于C(A,B)类的邻域性质
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  “class”译为未确定词的双语例句
    Broyden's Class of Modified Quasi-Newton Methods and Their Applications
    修正Broyden族拟牛顿算法及其应用
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    On the four-dimensional Einstein spaces of class one
    关于一阶四维爱因斯坦空间
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    On functions of the class H_δ
    函数族H_δ中的函数
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    On the theorems of existence solutions for a class of non-linear integral equations
    关于一类型非线性积分方程解的存在定理(Ⅱ)
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    Fourier Series for the Class of BMO Functions
    BMO函数的富里埃级数
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  class
In this paper, we prove the degenerations of Schubert varieties in a minusculeG/P, as well as the class of Kempf varieties in the flag varietySL(n)/B, to (normal) toric varieties.
      
The aim of this paper is to discuss a construction of a class of linear isomorphisms σ:S(g)→U(g) which commute with the adjoint representation.
      
An important class consists of those that we calln-coset groups; they arise as orbit spaces of groupsG modulo a group of automorphisms withn elements.
      
A theorem of Richardson states that the algebra of regular functions ofG is a free module over the subalgebra of regular class functions.
      
We then go on to identify the group up to commensurability class.
      
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Let f(z)=z+sum from n=2 to ∞ a_nz~n be regular and schlicht in the unit circle. M. Schiffer proved that the function w=f(z) in the class of such functions, which renders |a_κ| the maximum, maps |z|<1 onto the whole W-plane with a finite number of analytic cuts. For the cases k=4 and k=5 Schaeffer-Spencer [3] and Golusin [5] proved respectively that there is only one cut for the extremal domain. The principal object of the present paper is to show that the same thing holds true for the cases k=6 and k=7....

Let f(z)=z+sum from n=2 to ∞ a_nz~n be regular and schlicht in the unit circle. M. Schiffer proved that the function w=f(z) in the class of such functions, which renders |a_κ| the maximum, maps |z|<1 onto the whole W-plane with a finite number of analytic cuts. For the cases k=4 and k=5 Schaeffer-Spencer [3] and Golusin [5] proved respectively that there is only one cut for the extremal domain. The principal object of the present paper is to show that the same thing holds true for the cases k=6 and k=7. Our proof depends upon the following lemmas: Lemma A. If{f(z)~2}_6=0; then |a_2|<1.63; and if {f(z)~2}_7=0; then |a_2|<1.77; Where {g(z)}_n denotes g~((n))(0). Lemma B. If |a_6|≥6 and {f(z)~2}6=0, than |a_2|>1.95, If |a_7|≥7 and {f(z)~2}_7=0, then |a_2|>1.85. Using merely the method of variation, without appealing to L(?)wner's method as done by M. Fekete and G. Szeg [6], we can prove the known theorem that (?)|a_3-αa_2~2|=1+2 exp(-2α/(1-α))(0≤α<1) with the "uniqueness" of the extremal function. For the functions f(z) satisfying the pair of conditions R(a_3)>0 and R(a_2)<0, we can pnove that the greatest value of R(a_2+a_3)is 1.03…,and that the correspondiong extremal function is of real coefficients.

S表示單位圆|z|<1上單葉且正則的函數 f(z)=z+α_2z~2+α_3z~3+… (1.1)的全體所成之族。設S′是S的一個子族,S′中任一函數满足條件 R(α_3)>0,R(α_2)<0。對於S′中的函數,本文證明R(α_2+α_3)之最大值是可以達到的,其值是1.03…。達到此值的極值函數的一切係數都是實數,極值函數只有一個。舍勾和飛克得[6]謝缶和斯賓塞爾[3]以及沙拉烏洛夫先後用樓五納的參數表示法和變分法,求出 |a_3-αa_2~2|(0≤α<1)的值,並指出達到此值的極值函數的一切係數都是實數,而且極值函數只有一個。本篇僅用變分法来建立他們的定理。惜缶[4]指出使|a_n|達到最大值的函數(1.1),其映象區域的境界是一組伸展到無窮遠處的解析若當曲綫。謝缶和斯賓塞爾[3],戈魯辛[5]分別證明對於|a_4|和|a_5|的極值區域,其境界綫只有一根。本篇對於|a_6|和|a_7|證明同樣的事實。證明是靠着如下的引理:

For a class of nonlocal potentials, the S matrix element is proved to be analytic in the right half λ planeexcept at the poles.

本文对一类非定域位势证明了散射矩阵元在λ的右半平面的奇点都是极点。

The purpose of this paper is to present an alternating direction method involving a general parameter as an iterative technique for a more general class of self-adjoint ellip- tic difference equations in P rpace variables. In theorem 1, the conuergence of this itera- tion scheme is established for 4 certain range of this iteration parameter. In theorem 2. it is proved that. if aij=4ji = 0 (i ≠ j). the number of iterations reqiured in order to reduce an initial error by a preassigned factor it given...

The purpose of this paper is to present an alternating direction method involving a general parameter as an iterative technique for a more general class of self-adjoint ellip- tic difference equations in P rpace variables. In theorem 1, the conuergence of this itera- tion scheme is established for 4 certain range of this iteration parameter. In theorem 2. it is proved that. if aij=4ji = 0 (i ≠ j). the number of iterations reqiured in order to reduce an initial error by a preassigned factor it given by 0 (ln ), so that the total number of numerical operationsis 0 (h-pln ), for any arbitrary value of this iteration parameter within the convergence range. Finally we consider the greater-accuracy diffefe- nce equation approximation to the Laplacian operaior equation, for the case p=2,3. wheh this alternating direction iteration technique it adopted. the number of iterations required is again guien by 0 (ln ).

用差分法求解自共轭椭园型方程的第一边值问题时,使用交替方向法[1][2]具有很大的优越 性。本文对当空间维数力P时的这一类议程提出带某个实参数的交替方向格式,求出收敛的参数区 间,指出当aij=aji = 0(i≠j)时,对于收敛区域的任何参数,为使逐次近似达到指定的准确度所必 须实行的迭代数力0(ln  )。其次对2和3维的情况,考虑用高准确度的差分方程逼近Laplace算 子的微分方程时的线性方程组,建立了交替方向迭代格式,证明对所迭取的参数序列,为使误差缩 小一个因子 10-Q所必须突行的迭代数N仍为 0(ln )。特别孚P=2时,N≤-1.2Q logsin   ; 当P=3时,N≤-16.81 Qlogsin2  。由于此时比通常的差分方程的截断误差来得小,可以 期望,随着步长相应的放大,总的计算量不一定会增加。

 
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