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Science China mathematics 2004年第5期47卷 659-674页

作者： SHI Peihu & WANG Mingxindepartment of mathematics, Southeast university, Nanjing 210018, China department of mathematics, Xuzhou normal university, Xuzhou 221116, China 1. department of mathematics Southeast University 210018 Nanjing China 2. department of mathematics Xuzhou Normal University 221116 Xuzhou China

This paper is devoted to study the classification of self-similar solutions to the quasilinear parabolic equations with nonlinear gradient termsu t = Δ(u m) - uq∣Δu∣ p withm ≥ 1,p,q > 0 andp +q >m. Form = 1, it is shown that the very singular self-similar solution exists if and only ifnq + (n +1)p 2, and in case of existence, such solution is unique. Form > 1, it is shown that very singular self-similar solutions exist if and only if 1 2 andnq + (n + 1)p 2 +mn, and such solutions have compact support if they exist. Moreover, the interface relation is obtained.

关键词： quasilinear parabolic equations, self-similar solutions, very singular solution, classification.

Some new results on planar harmonic mappings

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Science China mathematics 2010年第3期53卷 597-604页

作者： CHEN HuaiHui department of mathematics, Nanjing normal university, Nanjing 210097, China 1. department of mathematics Nanjing Normal University Nanjing 210097 China

This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings.

关键词： harmonic mapping Landau theorem Bloch constant Schwarz-Pick lemma quasi-regularity

Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems

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Science China mathematics 2006年第12期49卷 1864-1866页

作者： CHEN Jing & BAI Yuzhen department of mathematics, Nanjing university, Nanjing 210093, China department of mathematics, Qufu normal university, Qufu 273165, China 1. department of mathematics Nanjing University Nanjing 210093 China 2. department of mathematics Qufu Normal University Qufu 273165 China

Mane conjectured that every minimal measure in the generic Lagrangian systems is uniquely ergodic. In this paper, we will show that the answer to the Mane's conjecture is negative by analyzing the structure of the sup... 详细信息

关键词： minimal probability measure,uniquely ergodic,Mather theory,Lagrangian systems.

Joint density of hitting time and point to an ellipse for Brownian motion

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Chinese Science Bulletin 1997年第24期42卷 2054-2058页

作者： YIN Chuancun ZHAO Xuelei department of mathematics, Qufu normal university, Qufu 273165, China 2. Institute of mathematics, Shantou university, Shantou 515063, China department of mathematics Qufu Normal University Qufu 273165 China

IT is well known that the distribution of hitting time, hitting point, last exiting time, and lastexiting point for Brownian motion to balls has been extensively studied. A similar investi-gation of rectangles or cubes has also been well done. However, analogous questions for Brow-nian motion to ellipsoid are rarely concerned. Bai and Cai obtained the distribution of

关键词： Brownian motion hitting time hitting point ellipse.

Differential operators and automorphism schemes

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Science China mathematics 2010年第9期53卷 2363-2380页

作者： LI KeZheng department of mathematics,Capital normal university,Beijing 10004.,China 1. department of mathematics Capital Normal University Beijing 100048 China

The ring of global differential operators of a variety is in closed and deep relation with its automorphism *** relation can be applied to the study of homogeneous schemes,giving some criteria of homogeneity,a general... 详细信息

关键词： differential operator deformative automorphism automorphism scheme homogeneous scheme abelian variety

The maximal super-singular integral operators on product spaces

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Science China mathematics 2011年第12期54卷 2615-2626页

作者： WANG Hui1 & CHEN JieCheng2,3, 1department of mathematics, Xidian university, Xi’an 710071, China 2department of mathematics, Zhejiang normal university, Jinhua 321004. China 3department of mathematics, Zhejiang university, Hangzhou 310027, China 1. department of mathematics Xidian University Xi’an 710071 China2. Department of Mathematics Zhejiang Normal University Jinhua 321004 China3. Department of Mathematics Zhejiang University Hangzhou 310027 China

We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2〉0｜∫｜u｜〉ε1,｜v｜〉ε2 b1（｜u｜）b2（｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2 ∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.

关键词： super-singular integral maximal operator product spaces

On SS-quasinormal subgroups and the structure of finite groups

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Science China mathematics 2011年第3期54卷 449-456页

作者： WEI XianBiao1,2 & GUO XiuYun2, 1department of mathematics and Physics, anhui Institute of Architecture and Industry, Hefei 230022, China 2department of mathematics, Shanghai university, Shanghai 2004.4. China 1. department of mathematics and Physics Anhui Institute of Architecture and Industry Hefei 230022 China2. Department of Mathematics Shanghai University Shanghai 200444 China

A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpotent if there is a subgroup D of P with 1 2|D| whenever p = 2 and |D| = 2 is SS-quasinormal in G, where p is the smallest prime dividing the order of G and P is a Sylow p-subgroup of G.

关键词： S-quasinormal subgroups SS-quasinormal subgroups p-nilpotent groups supersolvable groups

Bergman kernel function on Hua construction of the fourth type

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Progress in Natural Science:Materials International 2007年第8期17卷 893-899页

作者： Yin Weiping~(**) Lin Ping (department of mathematics,Capital normal university,Beijing 100037,China) [a]department of mathematics Capital Normal University Beijing China

This paper introduces the Hua construction and presents the holomorphic automorphism group of the Hua construction of the fourth *** the Bergman kernel function,under the condition of holomorphie automorphism and the standard complete or- thonormal system of the semi-Reinhardt domain,the infinite series form of the Bergman kernel function is *** applying the prop- erties of polynomial andΓfunctions,various identification relations of the aforementioned form are developed and the explicit formula of the Bergman kernel function for the Hua construction of the fourth type is obtained,which suggest that many of the previously-reported results are only the special cases of our findings.

关键词： Hua construction Bergman kernel function holomorphic automorphism group

ON THE APPROXIMATELY SIMILARITY OF OPERATORS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 465-472页

作者： WEI GUOQIANG (department of mathematics, East China normal university, Shanghai 200062, China.) E China normal Univ Dept Math Shanghai 200062 Peoples R China

The author shows that a rank-preserving *-isorporphism between separable C*-algebras with unity is approximately equivalent to the identity representation. Some applications are made for approximately similarity of n-... 详细信息

关键词： C*-algebra Rank-preserving *-isomorphism Approximately equevalent,Approximately similar n-tuples of operators