N指示d维广义Wiener过程象集内点存在性

令Ｗ＾￣（ｔ）：ＩＲ＋＾Ｎ→ＩＲ＾ｄ是Ｎ指标ｄ维广义Ｗｉｅｎｅｒ过程，对任意紧集Ｅ＝ＩＲ＋＾Ｎ／（０），如果ｄｉｍＥ〉βｄ／２，那么，Ｗ＾￣（Ｅ）几乎处处存在内点，Ｂｒｏｗｎｉａｎ Ｓｈｅｅｔ为特例。     

一类具周期系数的Riccati型方程的周期解

给出Ｒｉｃｃａｔｉ型方程ｘ＾&;#183;＝Ａ（ｔ）ｘ＾２ｍ＋Ｂ（ｔ）ｘ＾２ｋ－１＋Ｃ（ｔ）（Ａ（ｔ），Ｂ（ｔ），Ｃ（ｔ）是周期为Ｔ的连续函数，ｍ，ｋ∈Ｎ且ｍ≥ｋ）无周期解及存在周期解的充分条件。     

利用尺度函数寻求常微分方程的近似解

论的结论是：设ｍ－１阶线性常微分方程的一般形式为ｄ＾ｍ－１ｕｄｘ＾ｍ－１＋ａ１（ｘ）ｄ＾ｍ－２ｕｄｘ＾ｍ－２＋…＋ａｍ－２（ｘ）ｄｕｄｘ＋ａｍ－１（ｘ）ｕ＝ｆ（ｘ）那么,当限定ｘ∈「０,１」时,它的近似解为ｕＮ（ｘ）＝∑２＾Ｎ－１ｋ＝－ｍ＋１ｃ＾ＮｋＮｍ（２＾Ｎｘ－ｋ）其中,ｍ≥２,Ｎｍ是ｍ阶样条函数。ｃ＾Ｎｋ是待定常数,它由ｍ－１个定解条件和导出等式产生的２＾Ｎ个条件决定。     

某类有界拟凸域双全纯不变量的极限

Ｅ＝Ｅ（ｍ，ｎ，ｋ）＝｛（ｚ，ω）∈Ｃ＾ｎ＋ｍ：│ｚ│＾２＋│ω│＾２ｋ〈１，ｚ∈Ｃ＾ｎ，ω∈Ｃ＾ｍ，ｋ〉０｝是Ｃ＾ｍ＋ｍ中的一类有界拟凸域。该文证明了在δＥ的强拟凸点上，当ｍ〉１时，ｌｉｍ（ｚ，ω）→δＥＪＥ（（ｚ，ω））＝π＾ｎ＋ｍ（ｎ＋ｍ＋１）＾ｎ／（ｎ＋ｍ）！．ｍ＝１时，ｌｉｎ（ｚ，ω）→δＥＪＥ（ｚ，ω））＝π＾ｎ＋１（ｎ＝）＾ｎ＋１／（ｎ＋１）！，在δＥ的弱拟凸点上，上述极限不存在。     

关于分圆域及其最大实子域的类数的上界

设ｍ是适合ｍ≠２（ｍｏｄ４）的正整数，ζｍ是ｍ次本原单位根，又设△ｋ，ｈｍ分别是分圆域Ｋ＝Ｑ（ζｍ）的判别式和类数，本文证明了：当ψ（ｍ）≥２２０时，ｈｍ〈４２３ｗｍＱｍ√△ｋ／（１９．４７）其中ψ（ｍ）是ｍ的Ｅｕｌｅｒ函数ｗｍ是Ｋ中单位根的人数，当ｍ是素数方幂时，Ｑｍ＝１否则Ｑｍ＝２由此可推知：当奇素数Ｐ≥２２３时，ｈｐ〈３６ｐ＾７．５（ｐ／２１．６）＾（ｐ－２）／２     

n次多项式系统不变直线条数的两个估计

该文将ｎ次多项式系统简称为Ｅｎ系统。该文证明了Ｅｎ系统当ｎ≥３时可存在Ｒｎ＝２ｎ＋１＋（－１）＾ｎ２条方向各异的不变直线及当ｎ≥２时至多存在ｎ组平行的不变直线；本文举例说明，当ｎ≥２时，Ｅｎ系统可以存在Ｓｎ＝２ｎ＋３＋（－１）＾ｎ＋１２条不变直线。提出了二个估计：（１）当ｎ≥２时，Ｅｎ系统至多存在Ｓｎ条不变直线，证明了ｎ＝２，３，４时这一估计是对的；（２）当ｎ≥３３时，Ｅｎ系统至多存在Ｒｎ条方向各     

一维m次多项式实映射的窗口分析

本文利用作者提出的代数分析法［１］首次严格地给出了一维ｍ次多项式实映射的周期Ｎ轨道窗口个数ＭＮ（ｍ）的显式计算公式，并严格地证明了在反对称映射中存在的对称周期２Ｎ轨道的轨道数目ｒ２Ｎ（ｍ）等于通过周期倍分叉产生的周期２Ｎ轨道的轨道β２Ｎ（ｍ）等结论。     

N指标d维广义Wiener过程象集代数和性质

令Ｗ↑￣（ｔ）：Ｒ＋＾Ｎ→Ｒ＾ｄ是Ｎ指标ｄ维广义Ｗｉｅｎｅｒ过程，对任意紧集Ｅ，Ｆ∩→Ｒ＋＾Ｎ／｛０｝，本文研究了代数和Ｗ↑￣（Ｅ）－Ｗ↑￣（Ｆ）的Ｈａｕｓｄｏｒｆｆ维数及内点存在性，此结果包含并推广了Ｂｒｏｗｎｉａｎ Ｓｈｅｅｔ的结果。     

REGULARITY AND EXPLICIT REPRESENTATION OF（0，1，…，m－2，m） INTERPOLATION ON THE ZEROS OF（1－x~2）P_（n－2）~（α，β）（x）

ＲＥＧＵＬＡＲＩＴＹＡＮＤＥＸＰＬＩＣＩＴＲＥＰＲＥＳＥＮＴＡＴＩＯＮＯＦ（０，１，…，ｍ－２，ｍ）ＩＮＴＥＲＰＯＬＡＴＩＯＮＯＮＴＨＥＺＥＲＯＳＯＦ（１－ｘ~２）Ｐ_（ｎ－２）~（α，β）（ｘ）ＳＨＩＹＩＮＧＧＵＡＮＧ（史应光）（ＣｏｍｐｕｔｉｎｇＣ?..     

关于HSOLSSOM（2^nu^1）的谱

本文讨论型为２＾ｎｕ＾１的有对称正交侣的带洞自正交拉丁方（ＨＳＯＬＳＳＯＭ（２＾ｎｕ＾１））的谱。证明当ｎ≤９时,ＨＳＯＬＳＳＯＭ（２＾ｎｕ＾１）存在的充分必要条件是ｕ为偶数且ｎ≥３ｕ／２＋１;当ｎ≥２６３时,若ｕ为偶数且ｎ≥２（ｕ－２）,则ＨＳＯＬＳＳＯＭ（２＾ｎｕ＾１）存在。     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.