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Congruence Subgroups of Hecke Groups

Acta Mathematica Sinica,English Series 2009年第6期25卷 931-944页

作者： Bo CHEN ping zhi yuan School of Science Chongqing Jiaotong University Chongqing 400074 P. R. China School of Mathematics South China Normal University Guangzhou 510631 P. R. China

Hecke groups are an important tool in subgroups of Hecke groups play an important rule investigating functional equations, and congruence in research of the solutions of the Dirichlet series. When q, m are two primes, congruence subgroups and the principal congruence subgroups of level m of the Hecke group H（√q） have been investigated in many papers. In this paper, we generalize these results to the case where q is a positive integer with q ≥ 5, √q ￠ Z and m is a power of an odd prime.

关键词： Hecke group principal congruence subgroup congruence subgroup

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On the Terai-Jésmanowicz Conjecture

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Acta Mathematica Sinica,English Series 2008年第12期24卷 2061-2064页

作者： Jian Ye XIA ping zhi yuan Department of Basic Science Guangdong University of Finance Guangzhou 510521 P. R. China School of Mathematics South China Normal University Guangzhou 510631 P. R. China

In this paper, we prove that if a, b and c are pairwise coprime positive integers such that a^2＋b^2=c^r,a〉b,a≡3 （mod4）,b≡2 （mod4） and c-1 is not a square, thena a^x＋b^y=c^z has only the positive integer solution （x, y, z） = （2, 2, r）. Let m and r be positive integers with 2｜m and 2 r, define the integers Ur, Vr by （m ＋√-1）^r=Vr＋Ur√-1. If a = ｜Ur｜,b=｜Vr｜,c = m^2＋1 with m ≡ 2 （mod 4）,a ≡ 3 （mod 4）, and if r 〈 m/√1.5log3（m^2＋1）-1, then a^x ＋ b^y = c^z has only the positive integer solution （x,y, z） = （2, 2, r）. The argument here is elementary.

关键词： exponential diophantine equations Terai-Jesmanowicz conjecture Lucas sequences

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Expression of interleukin-22/STAT3 signaling pathway in ulcerative colitis and related carcinogenesis

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World Journal of Gastroenterology 2013年第17期19卷 2638-2649页

作者： Lian-Zhen Yu Hai-Yang Wang Shu-ping Yang zhi-ping yuan Fang-yuan Xu Chao Sun Rui-Hua Shi Department of Gastroenterology First Affiliated Hospital of Nanjing Medical University Department of Internal Medicine Affiliated Mingde Hospital of Nanjing Medical University

AIM:To investigate the expression of interleukin (IL)-22 and its related proteins in biopsy specimens from patients with ulcerative colitis (UC) and UC-related carcinogenesis. METHODS:Biopsy specimens were obtained from patients with inactive (n = 10), mild-to-moderately active (n = 30), severely active (n = 34), initial (n = 30), and chronic UC (n = 44), as well as UC patients with dysplasia (n = 10). Specimens from patients without colonic abnormalities (n = 20) served as controls. Chronic colitis in experimental mice was induced by 2.5% dextran sodium sulfate. The expression levels of IL-22, IL-23, IL-22R1 and phosphorylated STAT3 (p- STAT3) were determined by immunohistochemistry. Bcl-2, cyclin D1 and survivin expression was detected by Western blotting. RESULTS:Patients with active UC had significantly more IL-22, IL-23, IL-22R1 and p-STAT3-positive cells than the patients with inactive UC and normal controls. Furthermore, IL-22 and related proteins were closely related to the severity of the colitis. The expression of IL-22 and IL-22R1 in the tissue of initial UC was stronger than in that of chronic UC, whereas the expression of p-STAT3 was significantly increased in chronic UC tissues. In dysplasia tissues, the expression level of IL-22 and related proteins was higher compared with controls. Mouse colitis model showed that expression of IL-22, IL-22R1 and IL-23 was increased with time, p-STAT3 and the downstream gene were also remarkably ***:IL-22/STAT3 signaling pathway may be related to UC and UC-induced carcinogenesis and IL-22 can be used as a biomarker in judging the severity of UC.

关键词： Ulcerative colitis Ulcerative colitis-related carcinogenesis Interleukin-22 Interleukin-22R1 STAT3

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