一类实奇芽等价的充要条件

给定一自反的Ｂａｎａｃｈ空间Ｘ．在ｃ^∞函数芽环∈（Ｘ）中,任何在原点Ｏ∈Ｘ的实奇芽ｆ,若其二阶Ｆｒｅｃｈｅｔ导数ｆ″（０）＝Ｔ是一个Ｆｒｅｄｈｏｌｍ算子,则它同构于形如：1/2+g(v)的一个芽．如果代替ｇ以一个与之同构的芽ｇ_１,显然得到一个与原来的芽同构的芽．然而,其逆是否真呢？本文将证明其逆命题亦真     

C-等价充要条件的一个应用

在C^∞函数芽的奇点理论和突变论中,很多基本问题涉及到n个变元的函数芽环E_n中有限余维理想任一补空间一组基的计算。例如J.N.Maffler对有限余维的函数芽的universal deformation证明了下述基本定理:f的一个P——参数的deformation是universal,当且仅当它的初速度F_i(i=1,2,…,p)使得: J(f)+R{F₁,F₂,…,F_p}=E_{n相似文献}   

多元Szász—Mirkjan算子的一致逼近

本文研究了多元Szása—Mirakjan算子在C_2B(T)中的逼近性质,利用K—泛函,建立了等价的逼近定理.主要结果如下 定理设f∈C_2B(T),0a) ;(ii)‖S_n,m(f)-f‖_∞ =0(n^-a);(iii)a)‖f(x+tφ(x),y)-2f(x,y)+f(x-tφ(x),y)‖_∞ =0(t<     

关于P.Turán问题24,Ⅱ

在本文中我们得到了一个比[1]中更好的P.Turán问题24的答案:若Hermite—Fejér插值过程对于任何f∈C[-1,1]都一致收敛,则定义于同一组节点上的Lagrange插值过程对于每个f∈{f:E_n(f)=o(n^-(23)/(18)}都一致收敛,这里E_n(f)为f∈C[-1,1]的用次数≤n的代数多项式逼近的偏差.     

加权BMO函数空间上的Hardy－Littlewood极大算子

本文给出了Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ极大函数和加权ＢＭＯ的有界性证明：即若f∈ＢＭＯ_w,w∈A_∞,且(?)Mf(x)<∞, 则M(f)(x) ∈BMO_w, 且‖Mf‖_w^*≤c‖f‖_w^*.     

映射的横截性定理

Hirsch conjectured: M、N、A are differential manifolds, g∈C^∞(A,N), then the set T = {f∈C^∞(M,N)|f∈g} is dense in C∞(M,N)and open if g is proper.In this paper, we prove the transversality theorem of map in the Jet bundle.Theorem 1 Let M, N. A be differential manifolds, g∈C^∞(A,J^τ(M、N)), then the set T{f∈C^∞(M,N)|f^τf∈g } is residual in C^∞(M,N) and open if g is proper.Theorem 1 contains Thom's transversal ity theorem as a special case. We can obtain Hirsch's conjecture by using theorem 1.     

球面上等收敛算子的有界性

设Rⁿ 是n-维欧氏空间n≥3.用Ω_n表示Rⁿ 上的单位球面,对于函数f∈L（Ω_n）,E_N^δ（f）表示其Fourier-Laplace级数的δ阶Cesaro平均所决定的等收敛算子,其中,λ:=（n-2）/2,δ是熟知的临界指标.对于0<δ≤λ,令p₀:=(2λ)/（λ+δ）,本文主要证明了如下结果:     

关于算子方程f(A)=A解的唯一性

设H是复Hilbert空间,又设f(z)=(?)(B_nZⁿ),z∈Δ={z:|z|<1},其中{B_n}是H上一列两两交换的正常算子,满足条件:级数按范数收敛,‖f(z)‖<1在Δ上处处成立,且1∈σ(B₁)又记X={A∈F(H):σ(A)?Δ且A与每个B_n交换}。本文证明了,若有T∈X使得f(T)=T,则T是X中满足所论方程的唯一元素。此外,T必须是正常算子。     

Banach空间中φ-半压缩型映象不动点的迭代逼近

设X为实一致光滑Banach空间,K为X的非空凸子集满足K+K?K.设T：K→K为有界φ-半压缩映象.设{v_n｝_n=0^∞,｛v_n｝_n=0^∞为K中的序列,{α_n｝_n=0^∞,{β_n｝_n=0^∞为[0,1]中的实数列满足(?)若｛Ty_{n相似文献}   

广义态空间中Krein-Milman定理的算子类似

讨论在C^*-凸理论下C^*-代数A的广义态空间S_Cⁿ(A)中的Krein-Milman型问题.证明了S_Cⁿ(A)的任意一个BW-紧的C^*-凸子集K都具有一个C^*-端点,而且K是其C^*-端点的C^*-凸包.     

关于Morse引理的推广

Morse Lemma是奇点理论中一个极为重要的结论。[1]的作者称其文中的定理1和定理2是Morse Lemma的推广。为此我们愿就[1]中的几个问题与[1]的作者商榷。     

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     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.