关于Briot－Bouquet微分从属

本文主要研究如下的Ｂｒｉｏｔ－Ｂｏｕｑｕｅｔ微分从属　其中ｐ在｜ｚ｜＜１内解析，β．γ、ａ、ｂ为适当的实数．并由此解决了Ｓ．Ｓ．Ｍｉｌｌｅｒ和Ｐ．Ｔ·Ｍｏｃａｎｕ提出的一个问题．     

关于Briot—Bouquet微分从属

本文主要研究如下的Ｂｒｉｏｔ－Ｂｏｕｑｕｅｔ微分从属Ｐ（Ｚ）＋ＺＰ＇（Ｚ）／βＰ（Ｚ）＋γ＜１＋ａｚ／１＋ｂｚ，ｐ（０）＝１其中ｐ在｜ｚ｜Ｄ＜１内解析，β、γ、ａ、ｂ为适当的实数，并由此解决了Ｓ．Ｓ．Ｍｉｌｌｅｒ和Ｐ．Ｔ．Ｍｏｃａｎｕ提出的一。     

关于多项式型Hammerstein积分方程的唯一正解

关于多项式型Ｈａｍｍｅｒｓｔｅｉｎ积分方程的唯一正解赵增勤（曲阜师范大学数学系，山东曲阜２７３１６５）１９９１年２月２８日收到，１９９１年１０月５日收到修改压缩稿．一、引言文［１，２］研究了Ｈａｍｍｅｒｓｔｅｉｎ型积分方程的解与固有值．本文讨论多项式...     

关于弱半可微映象方程的几个问题

关于弱半可微映象方程的几个问题１）杨书郎（厦门大学系统科学系，３６１００５）１）本文部分内容的摘要已刊登在《科学通报》１９９０年第１７期上．１９９１年１月２３日收到．一、引言在带锥的（Ｂ）空间单值映象的研究中，适当意义的可微性概念已逐步被引入，并作为...     

Hiriart—Urruty问题与Clarke广义梯度的若干性质

Ｈｉｒｉａｒｔ—Ｕｒｒｕｔｙ问题与Ｃｌａｒｋｅ广义梯度的若干性质刘晓华（湖南财经学院信息系，长沙４１００７９）１９８８年５月２６日收到，１９９２年４月２９日收到第一次修改稿，１９９３年４月２３日收到第二次修改稿．一、引言Ｈｉｒｉａｒｔ－Ｕｒｒｕｔｙ等...     

成败型寿命试验──GLM和E-M算法

成败型寿命试验──ＧＬＭ和Ｅ－Ｍ算法王学仁云南省应用数学研究所石磊（云南大学统计系，昆明６５００９１）１９９０年１０月１５日收到．１９９２年８月２４日收到修改稿．一、引言在可靠性分析中，成败型寿命试验是经常碰到的问题．某些产品随着时间的推移，其可靠程...     

带梯度项的半线性椭圆与抛物型方程解的死核问题

带梯度项的半线性椭圆与抛物型方程解的死核问题程尚斌（兰州大学数学系，兰州７３００００）兰州大学科研基金资助课题．１９９１年３月１１日收到，１９９１年１１月２３日收到修改压缩稿．一、引言１９８４年，人们发现对一定类型的半线性椭圆与抛物型方程，它们具非零...     

半无穷向量最优化问题的最优性条件

半无穷向量最优化问题的最优性条件李泽民（重庆建筑大学，６３００４５）１９９０年８月２７日收到．１９９３年３月１日收到修改、压缩稿．无穷维空间中的向量极值问题已引起了不少学者的兴趣［２－４］．本文研究半无穷向量极值问题的最优性条件，得出了一系列有意义的...     

实轴上Freud-Fourier级数的平均收敛性

实轴上Ｆｒｅｕｄ－Ｆｏｕｒｉｅｒ级数的平均收敛性闵国华，肖资阳（南京理工大学应用数学系，南京２１００１４）１９９１年２月４日收到１９９２年２月１０日收到修改压缩稿．一、引言记Ｈｅｒｍｉｔｅ权函数，Ｓｎ（ｘ）为ｆ（ｘ）的Ｈｅｒｍｉｔｅ级数的前１项和．关...     

论多目标分式规划

论多目标分式规划徐增堃（浙江师范大学数学系，金华３２１００４）基金项目：浙江省教委自然科学基金资助课题．１９９０年１０月２９日收到，１９９１年１０月５日收到第一次修改稿．１９９２年９月７日收到第二次修改稿，１９９３年２月１３日收到第三次修改、压缩稿．...     

关于有界全纯函数在边界附近的某些性质

<正> 在[1]中 H.G.Eggleston 曾经证明了如下一个很有用的定理.设 f(z)是区域 D 内的有界全纯函数并 z_0为 D 的某一界点,z_0可为∞,但 D 至少人含有一有限还点为其界点.让 L 是一弧而以 z_0为其一端点且其他各点全属 D 内.若     

一类正则函数的性质

设函数 f( z) =z+a2 z2 +…在单位圆盘 D={z |z|<1 }中正则 ,我们记这种函数的全体为 N,设β>0 ,令Sβ=f ( z) f ( z)∈ N且 (β-1 ) zf′( z)f ( z) -1 +1 +zf″( z)f ( z) 1 +4 z+z21 -z2 .本文给出了 Sβ 中函数的一些性质     

A fully invariant ideal of alternative algebras

Let ϕ be an associative commutative ring with 1, containing 1/6, and A be an alternative ϕ-algebra. Let D be an associator ideal of A and H a fully invariant ideal of A, generated by all elements of the form h(y, z, t, x, x)=[{[y, z], t, x}-, x]+[{[y, x], z, x}-, t], where [x, y]=xy−yx, {x, y, z}-=[[x, y], z]−[[x, z], y]+2[x,[y, z]]. Here we consider an ideal Q=H∩D and prove that Q⁴=0 in the algebra A. If A is unmixed, then HD=0, DH=0, and Q²=0 in particular. If A is a finitely generated unmixed algebra, then the ideal H lies in its associative center and Q=0. It follows that any finitely generated purely alternative algebra satisfies the identity h(y,z,t,x,x)=0. We also show that a fully invariant ideal H₀ of the unmixed algebra A, generated by all elements of the form h(x, z, t, x, x), lies in its associative center and H₀∩D=0. Consequently, every purely alternative algebra satisfies the identity h(x,z,t,x,x)=0. Translated fromAlgebra i Logika, Vol. 36, No. 3, pp. 323–340, May–June, 1997.     

單葉函數的係數與開始多項式

<正> 以fk(z)表單位圓內的K次對稱單葉全純函數,亦即fk(z)=z+a_I~((k))z~(k+1)+a_2~((k))z~(2k+1)+…,|z|<1.以S_k表此種函數之全體.特別,書S以代S_1.     

The Chebyshev Spectral Method for Burgers-Like Equations

The Chebyshev polynomials have good approximation properties which are not affected by boundary values. They have higher resolution near the boundary than in the interior and are suitable for problems in which the solution changes rapidly near the boundary. Also, they can be calculated by FFT. Thus they are used mostly for initial-boundary value problems for P.D.E.'s (see [1, 3-4, 6, 8-11]). Maday and Quarterom discussed the convergence of Legendre and Chebyshev spectral approximations to the steady Burgers equation. In this paper we consider Burgers-like equations.$$\begin{cases}∂_iu+F(u)_x-vu_{zx}=0, & -1≤x≤1, 0＜t≤T \\ u (-1,t) =u (1,t) =0, & 0≤t≤T & (0.1)\\ u (x,0) =u_0(x), & -1≤x≤1\end{cases}$$ where $F\in C(R)$ and there exists a positive function $A\in C(R)$ and a constant $p＞1$ such that $$|F(z+y)-F(z)|\leq A(z)(|y|+|y|^p).$$ We develop a Chebyshev spectral scheme and a pseudospectral scheme for solving (0.1) and establish their generalized stability and convergence.     

ON THE GENERALIZED POLYNOMIALS OF L. V. KANTOROVITCH AND THEIR ASYMPTOTIC BEHAVIORS

In this article we generahze the polynomials of Kantorovitch \({P_n}(f)\) . Let \({B_n}\) be a sequence of linear operators from C[a,b] into \({H_n}\), if \[f(t) \in L[a,b],F(u) = \int_a^u {f(t)dt} ,{A_n}(f(t),x) = \frac{d}{{dx}}{B_{n + 1}}(F(u),x)\], here \({B_n}\)satisfy\[\begin{array}{l} (a):{B_n}(1,x) \equiv 1,{B_n}(u,x) \equiv x;\(b):for{\kern 1pt} {\kern 1pt} g(u) \in C[a,b]{\kern 1pt} {\kern 1pt} we{\kern 1pt} {\kern 1pt} have{\kern 1pt} {\kern 1pt} {B_n}(g(u),b) = g(b). \end{array}\]. we call such \({A_n}(f)\) generalized polynomials of Kantorovitch (denoted by \({A_n}(f) \in K\) ). Let \[\begin{array}{l} {\varepsilon _n}({W^2};x)\mathop = \limits^{def} \mathop {\sup }\limits_{f \in {W^2}} \left| {{A_n}(f(t),x) - f(x) - f'(x)({A_n}(t,x) - x)} \right|,\{\varepsilon _n}{({W^2}{L^p})_{{L^p}}}\mathop = \limits^{def} \mathop {\sup }\limits_{f \in {W^2}{L^p}} {\left\| {{A_n}(f(t),x) - f(x) - f'(x)({A_n}(t,x) - x)} \right\|_p}. \end{array}\] We have proved the following results: Let An he a sequence of linear continuous operators of type \[C[a,b] \Rightarrow C[a,b],{D_n}(x,z)\mathop = \limits^{def} {A_n}(\left| {t - z} \right|,x) - \left| {x - z} \right| - ({A_n}(t,x) - x)Sgn(x - z),{A_n}(1,x) = 1\] then (1):\({\varepsilon _n}({W^2};x) = \frac{1}{2}\int_a^b {\left| {{D_n}(x,z)} \right|} dz\), (2): Moreover, if \({A_n}\) be a sequence of linear positive operators, then for \(\left[ {\begin{array}{*{20}{c}} {a \le x \le b}\{a \le z \le b} \end{array}} \right]\) ,we have \({D_n}(x,z) \ge 0\), and \({\varepsilon _n}({W^2};x) = \frac{1}{2}{A_n}({(t - x)^2},x)\). Let \({A_n}(f) \in K\) be a sequence of linear positive operators,\[{R_n}{(z)_L} = \frac{1}{2}\int_a^b {\left| {{D_n}(x,z)} \right|} dx\],then \[{R_n}{(z)_L} = \frac{1}{2}\left[ {{B_{n + 1}}({u^2},z) - {z^2}} \right]\] and \[{\varepsilon _n}{({W^2}L)_L}{\rm{ = }}\frac{1}{2}\left\| {{B_{n + 1}}({u^2},z) - {z^2}} \right\|\]. Let \[{g_n} = \frac{1}{2}\mathop {\max }\limits_{a \le x \le b} {A_n}({(t - x)^2},x),{h_n} = \frac{1}{2}\mathop {\max }\limits_{a \le z \le b} \left[ {{B_{n + 1}}({u^2},z) - {z^2}} \right],\] then \[{\varepsilon _n}{({W^2}{L^p})_{{L^p}}} \le {g_n}^{1 - \frac{1}{p}}{h_n}^{\frac{1}{p}}(1 < p < \infty ).\]     

THE SECTIONS OF ODD UNIVALENT FUNCTIONS

Let $\[{S_k}\]$ be the class of functions $\[f(z) = z + \sum\limits_{m = 1}^\infty {b_{mk + 1}^{(k)}{z^{mk + 1}}} \]$ which are regular and univalent in $\[\left| z \right| < 1\]$ and denote $\[S_n^{(k)}(z) = z + \sum\limits_{m = 1}^\infty {b_{mk + 1}^{(k)}{z^{mk + 1}}} \]$. The authors prove that the functions $\[S_n^{(2)}(z)\]$ are starlike in $\[\left| z \right| < \frac{1}{{\sqrt 3 }}\]$.     

多复变数Einstein空间中的Schwarz引理

<正> 本文主要的目的是来证明定理1.设■域是 n 个复变数■=(z~1,…,z~n)空间中的简单域且为Einstein空间(不失一般性,不妨假设其 Ricci 曲率为-1),其Bergman度量为     

Heisenberg群上的带状小波及函数空间的正交分解

令P＝NAM是SU（n＋1,1）的极小抛物子群,它可以看作是Heisenberg群Hn上的仿射自同构群.根据［1］中的可允许条件,我们给出了Hn上的带状小波.利用小波变换,我们得到了L2（Un＋1,dμl（z,t,ρ））的另一个正交直和分解.进一步还给出了L2（P,dμl（z,t,ρ,u））的正交分解.     

一族特殊的星像函數

<正> 設函數w=f(z)在單位圓|z|<1中是正則的.f(0)=0,f′(0)=1.假如f(z)是單葉的,那末w=f(z)映照|z|<1於w平面上的單葉的像D_f.記這種單葉函數的全體為S.若D_f以原點w=0為星形中心,就稱f(z)是|z|<1中的星