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The first cohomology group of trivial extensions of special biserial algebras

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Science china mathematics 2004年第4期47卷 578-592页

作者： XU Yungedepartment of mathematics & Computer Sciences, hubei university, wuhan 430062. china 1. department of mathematics & Computer Sciences Hubei University 430062 Wuhan China 2. Institute of mathematics Chinese Academy of Sciences 100080 Beijing China

Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A × DA in terms of the combinatorics of the quiver and relations is determined.

关键词： Hochschild (co)homology, trivial extension, special biserial algebra.

Comparison of fractal measures

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Science china mathematics 2005年第11期48卷 1545-1553页

作者： QU Yanhui,WEN Shengyou & WEN Zhiying department of mathematics,Tsinghua university,Beijing 100084,china department of mathematics,hubei university, wuhan 430062. china 1. department of mathematics Tsinghua University 100084 Beijing China 2. department of mathematics Hubei University 430062 Wuhan China

In this paper, the relationship between the s-dimensional Hausdorff measures and the g-measures in Rd is discussed, where g is a gauge function which is equivalent to ts and 0 < s≤d. It shows that if s=d, then Hg = c1Hd, Cg = c2Cd and Pg = c3Pd on Rd, where constants c1, c2 and c3 are determined by where Wg, Cg and Pg are the g-Hausdorff, g-central Hausdorff and g-packing measures on Rd respectively. In the case 0

关键词： gauge function Hausdorff measure central Hausdorff measure packing measure.

Hochschild cohomology of special biserial algebras

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Science china mathematics 2007年第8期50卷 1117-1128页

作者： Yun-ge XU Faculty of mathematics & Computer Science,hubei university,wuhan 430062.china Faculty of mathematics & Computer Science Hubei University Wuhan 430062 China

Based on a four-term exact sequence,the formulae on the dimensions of the first and the second Hochschild cohomology groups of special biserial algebras with normed bases are obtained in terms of combinatorics.

关键词： special biserial algebra Hochschild cohomology medal 16E40 16G10

LARGE DEVIATIONS FOR STATIONARY Φ-MIXING SEQUENCES IN τ-TOPOLOGY

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Chinese Annals of mathematics,Series B 1996年第2期17卷 149-158页

作者： Hu YIJUN department of mathematics, wuhan university, wuhan 430072, china. department of mathematics Wuhan University Wuhan 430072 China

The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.

关键词： Large deviation Empirical measure Stationary sequence Φ-mixing τ-topology

NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

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Journal of Computational mathematics 2002年第6期20卷 583-590页

作者： Cheng-jian Zhang(department of mathematics, Huazhong university of Science and Technology, wuhan 430074, hubei, P. R. china) department of mathematics Huazhong University of Science and Technology Wuhan 430074

Presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDE). Discussion on the numerical analogous results of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDE; Review of the related concepts and results on RK methods; Information on the asymptotic stability and global stability of the induced NRK method.

关键词： nonlinear stability neutral delay differential equations natural Runge-Kutta methods

Large deviation principles for stationary NA sequences

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Chinese Science Bulletin 1998年第7期43卷 536-540页

作者： HU Yijun department of mathematics, wuhan university, wuhan 430072, china department of mathematics Wuhan University Wuhan China

Under general conditions, the large deviation principles for partial sums of stationary NA sequences are proved.

关键词： NA sequence stationary sequence partial sums large deviation principle.

ON A SUBCLASS OF CLOSE TO CONVEX FUNCTIONS

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Acta Mathematica Scientia 2010年第5期30卷 1449-1456页

作者：彭志刚 Faculty of mathematics and Computer Science Hubei University

Let C＇（α,β） be the class of functions f（z） =analytic in D ={z：｜z｜〈 1}, satisfying for some convex function g（z） with g（O） = g＇（O） - 1 =- 0 and for allz in D the condition zf＇（z）-1/g（z）/zf＇（z）/g（z）＋1-2α）｜〈β for some α β （0 ≤ α〈1,0 〈 β 〈 1）. A sharp coefficient estimate, distortion theorems and radius of convexity are determined for the class C＇（α ,β ）. The results extend the work of C. Selvaraj.

关键词： starlike convex close to convex radius of convexity

STUDY ON THE MISCIBILITY OF DYNAMICALLY VULCANIZED EPDM/PP BLEND BY POSITRON ANNIHILATION SPECTROSCOPY

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Chinese Journal of Polymer Science 2000年第2期18卷 123-128页

作者： Tao Jiang Xue-liang Jiang Shi-yuan Cheng Yi-qun Dai Shao-jie Wang Bo Wang Faculty of Chemistry & Material, hubei university, wuhan 430062. china department of Physics, wuhan university, wuhan 430072, china hubei Univ Fac Chem & Mat Wuhan 430062 Peoples R China wuhan Univ Dept Phys Wuhan 430072 Peoples R China

Positron annihilation spectroscopy (PAS) was utilized to investigate the relationship between the free-volume hole properties and miscibility of dynamically vulcanized EPDM/PP blend. The results showed that the noncrystalline region of PP and EPDM in the blend was partially miscible and the miscibility of the blend became worse when the weight percent of EPDM was <50%. This was also demonstrated by DMTA and mechanical properties of the blends with various compositions.

关键词： EPDM PP dynamic vulcanization miscibility PAS

THE EXTREME POINTS OF SEVERAL CLASSES OFANALYTIC FUNCTIONS

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Acta Mathematica Scientia 1999年第4期19卷 457-462页

作者：彭志刚 hubei Univ Coll Math & Comp Sci Wuhan 430062 Peoples R China

Let P-n(c(1),c(2),...,c(n-1)) = {p(z) : p(z) is analytic in \z\ 0 and p(z) = 1 + c(1)z + c(2)z(2) +...+ c(n-1)z(n-1) + d(n)z(n) +..., where c(1),c(2),...,c(n-1) are fixed complex constants}. Let P-R,P-n(b(1),b(2),...,b(n-1)) = {p(z) : p(z) is analytic in \z\ 0 and p(z) = 1 + b(1)z + b(2)z(2) +...+ b(n-1)z(n-1) + d(n)z(n) +..., where b(1),b(2),...,b(n-1) are fixed real constants and the coefficients of p(z) are real}. Let T-n(l(1),l(2),...,l(n-1)) = {f(z) : f(z) is analytic in \z\ < 1 and f(z) = z + l(1)z(2) + l(2)z(3) +...+ l(n-1)z(n) + d(n)z(n+1) +...; where l(1),l(2),...,l(n-1) are fixed real constants and the coefficients of f(z) are real}. It is understood that P-n(c(1),c(2),...,c(n-1)), P-R,P-n(b(1),b(2),...,b(n-1)) and T-n(l(1),l(2),...,l(n-1)) are not empty when the constants c(k)(k = 1,...,n-1), b(k)(k = 1,2,...,n-1) and l(k)(k = 1,...,n-1) satisfy certain conditions. This paper obtaines the extreme points of P-n(c(1),...,c(n-1)), P-R,P-n(b(1),...,b(n-1)) and T-n(l(1),...,l(n-1)).

关键词： Blaschke product extreme point