教师个人简历

姓    名:

袁平之

英文名:

Pingzhi Yuan

性 别:

出生年月:

1966年6月

籍 贯:

湖南隆回

政治面貌:

盟员

学 位:

博士

职 称:

教授,基础数学专业博士生导师

研究领域:

数论及应用.近期主要关心的问题是:Thue equations,Zero-sum Problems,Transcendence of series and Permutation polynomials.

联系方式:

yuanpz@scnu.edu.cn

工作经历



学习与访问:

1981.9-1985.7湖南师范大学数学系获得学士学位。

1985.9--1988.7四川大学数学系获得硕士学位, 导师:柯召院士和孙琦教授。

1991.9-1992.7 四川大学数学系访问

1994.9--1997.7四川大学数学系获得理学博士学位,导师:孙琦教授。

1997.10--1999.11解放军信息工程大学密码学博士后流动站从事研究工作。

2000.9-2001.1广东外语外贸大学出国英语培训。

2002.5--2002.10荷兰Leiden大学数学研究所访问,合作教授著名数论专家Robert Tijdeman。期间应著名数论专家Yann Bugeaud教授邀请访问Strasbourg大学,应著名数论专家Yuri Bilu教授邀请访问Bordeaux大学。

2006.3--2006.5 香港科技大学计算机系访问,合作者著名密码学专家丁存生教授。 近年来多次访问香港科技大学丁存生教授。

2011.3.1-3.8应邀访问日本程溪大学,参加国际会议“Diophantine analysis and related fields 2011”国际会议,并做一小时特邀报告

2011.6-2011.7 访问奥地利Graz大学数学学院,合作者著名组合数论专家Alfred Geroldinger教授

2014.1.17应著名数学家Liqun Qi教授邀请参加在香港理工大学主办的“The workshop on Structure Tensors”并作一小时学术报告。

2014.7-2014.8访问加拿大Brock大学,合作者著名环论专家Yuanlin Li教授。

2016.1.4-1.8将参加在Graz大学举办的国际会议"Combinatorial and Additive NumberTheory"并被邀请做一小时特邀报告

来访(国外学者):万大庆教授、丁存生教授、向青教授、李元林教授Alfred Geroldinger教授(一个月)Alain Togbe教授(一个月)Takafumi Miyazaki博士(二周)Ravindranathan Thangadurai教授(二周)。

工作:

1988.7--2003.3中南大学数学院, 讲师、副教授、教授(1999年聘2000年评)、博士生指导教师(2001年)。

2003.3--2009.1中山大学数学与计算科学学院, 教授博士生指导教师。

2009.1-- 华南师范大学数学科学学院, 教授博士生指导教师.

获奖:

2016广东省特支计划领军人才

科研项目:

  1. 国家自然科学基金项目,11671153不可分极小零和序列的结构与Davenport 常数2017/01-2020/12在研,主持。

  2. 国家自然科学基金项目,11271142,非唯一分解理论与Thue型方程,2013/01-2016/12已结题,主持。

  3. 安全项目,2014/01-2015/12,已结题,参加。

  4. 广东省自然科学基金项目,S2012010009942,非唯一分解理论与零和问题,2012/10-2014/10已结题,主持。

  5. 国家自然科学基金项目,10971072Thue型方程,零和问题与逆零和问题,2010/01-2012/12 已结题,主持。

  6. 国家自然科学基金项目,10571180,丢番图分行与超越数,2006/01-2007/12 已结题,主持。

  7. 广东省自然科学基金项目,S2012010009942,非唯一分解理论与零和问题,2012/10-2014/10已结题,主持。

  8. 广东省自然科学基金项目,10152606101000000,丢番图分析与级数的超越性,2008/10-2010/10已结题,主持。

  9. 广东省自然科学基金项目,04009801,三项不定方程与ABC猜测, 2004/09-2006/09已结题,主持。

  10. 广东省科技计划项目,2004B10101004,数学与信息新技术,2004/09-2006/09,已结题,参加。

教学情况:

1. 本科教学: 高等数学、 线性代数、积分变换、高等代数、近世代数、常微分方程、拓扑学、离散数学、初等数论。

2、研究生公共课: 《矩阵论》、《交换代数》、《代数学》和《离散数学》。

3、研究生专业课:《数论基础》、《代数数论》、《应用密码学》、《有限域》、《椭圆曲线与模型式》、《丢番图分析》等。


科研成果

学术贡献:

1、柯召方法与丢番图逼近:进一步发展了柯召方法的应用范围,并应用于解决了与二元四次方程有关的问题和猜测。如MR2545931(2011d:11068) Yuan,Pingzhi; Li,YuanSquares in Lehmer sequences and the Diophantineequation Acta Arith.139(2009),no.3, 275–302.我们用精细的柯召方法的技巧完全解决了关于不定方程S. Akhtari, A. Togbé and P. G. Walsh猜测,他们一度认为这一猜测在近十年不可能被解决。MR2124046(2005j:11024) Yuan,Pingzhi; Hu,YongzhongOn the Diophantine equation J. Number Theory111(2005),no.1, 144–153解决了关于不定方程的一个猜测。Sun, Qi;Yuan,Ping ZhiA note on the Diophantine equation Sun, Qi;Yuan,Ping ZhiA note on the Diophantine equation (Chinese) Sichuan Daxue Xuebao34(1997),no.3, 265–268完全解决了这一方程的求解问题。论文Cohn,J. H. E.The Diophantineequation . Acta Arith. 78 (1997), no. 4, 401–403的结论完全相同。 Cohn论文被SCI引用36次。

在丢番图逼近理论方面,我们拓广了Thue性方程的应用范围,我们可以有效地处理满足一定条件的二个参变数的不定方程。 J. Number Theory的审稿评价为The author, Ibelieve, the first to use Liouville’s inequality as itapplied to imaginary quadratic fields. 在日本报告会后,苏联科学院院士著名超越数论专家Yu.V.Nesterenko对我们关于不定方程的工作MR2679095(2011g:11064) Yuan,PingZhi; Zhang,ZhongFengOn the Diophantine equation Sci. China Math.53(2010),no.8, 2143–2158给出了不错的评价。论文MR1612564(99b:11079) Yuan,PingzhiRational and algebraic approximations ofalgebraic numbers and their application.Sci. China Ser. A40(1997),no.10, 1045–1051.完全解决了关于方程的求解问题 论文J. H. Chen and P. M.Voutier, A complete solution of the Diophantine equation  and arelated family of quartic Thue equations, J. Number Theory 62 (1997),71–99结论完全相同。ChenVoutier论文被SCI引用33次。

2关于联立丢番图方程的一系列结论(Acta Arith.2002, Proc. AMS 132(2004), 1561-1566, Acta Arith. 115.2(2004), 119-131 )。Bennett在Mathematical Review的评价为This sharpening derives from a combination of lower bounds forlinear forms in logarithms of algebraic numbers with elementary arithmeticinformation about binary recurrence sequences, applied in a clever way.利用代数数的对数线性型的估计和二阶递归序列的性质,得到了这一许多学者关心的问题的最好结果。Proc AMS2004的审稿评价为a  nice little paper, Acta Arith 2004 一文的审稿评价为The final result are not far off best possible. This is a solidpiece of work. J. Number Theory 112(2005),20-25审稿评价为Animportant step forward, the argument is elegant and requires some instrinsicargumentation。论文:On the Diophantine Equation ,完全求出了为奇数时方程的全部解。关于此方程,Makowski、 Schinzel、 Nesterenko、 Shorey、 Bugeaud和乐茂华都有很好的工作。此文在J.Number Theory 的Top25下载统计连续9个月排在前25位(1、11和22)。

3、关于组合数论的Index猜想:论文Yuan,PingzhiOn the index of minimal zero-sum sequences overfinite cyclic groups. J. Combin. Theory Ser. A 114 (2007), no. 8, 1545–1551.解决了高维东教授关于Index的一个著名猜想,由此推动了相关的学科的研究。论文被SCI引用26次,它引18次。最近我们在此方面有取得了长足进展。

4、关于广义EGZ猜测: Yuan, Pingzhi; Zeng, Xiangneng Davenport constant with weights. European J. Combin. 31 (2010), no. 3, 677–680.SCI它引8次(共引9次)和Zeng,Xiangneng; Yuan, Pingzhi Weighted Davenport's constant and the weighted EGZ theorem.Discrete Math. 311 (2011), no. 17, 1940–1947SCI它引4次)用精巧的组合方法和数学归纳法极大地推广了高维东教授著名的EGZ定理。这一结论及相关的证明组成了著作Grynkiewicz,David J.Structural additive theory. Developments in Mathematics, 30.Springer, Cham, 2013.xii+426 pp. ISBN: 978-3-319-00415-0; 978-3-319-00416-7的整整一章。这一方面最早的进展和最后的结论都是我和我的学生曾祥能给出的,这完整地解决了EGZ定理的推广问题。

5、有限域上置换多项式:候向东教授(FFA副主编)的综述论文Hou,Xiang-dongPermutation polynomials over finite fields—asurvey of recent advances.Finite Fields Appl.32(2015),82–119引用了我的论文有7篇,这在国内是最多的。之后我们在FFA又发表论文两篇。候的综述论文中,采用了我们最先引用的交换图表,应用这一新技术,许多新的置换多项式可以构造出来。论文Yuan,Pingzhi; Ding, Cunsheng Permutation polynomials over finite fields from a powerful lemma.Finite Fields Appl. 17 (2011), no. 6, 560–574。推广了许多已有的关于置换多项式的结论。特别,我们首次用交换图表来描述置换多项式的结论,这对许多已有的结论有了很好的注解,同时也提供了判别置换多项式的一个系统的新方法。论文被SCI引用17次,它引11次。

6、张量的本原指数:我们解决了著名图论专家邵嘉誉教授提出的关于张量的本原指数的猜测,并对本原指数集进行了系统的研究。论文Yuan,Pingzhi; He, Zilong; You, Lihua A conjecture on the primitive degree of tensors. Linear Algebra Appl. 450 (2014), 175–185.解决了著名学者邵嘉誉教授提的一个猜测。

7、级数的无理性:论文Tijdeman, R.; Yuan, Pingzhi On the rationality of Cantor and Ahmes series. Indag. Math. (N.S.) 13 (2002), no. 3, 407–418.首次得到了一类级数的无理性,被SCI引用12次,它引12次,是这一方面它引很多的无理性的论文。



科研论文

1、ON THE CONGRUENCE 2~(n-k)≡1(mod n),Chinese Science Bulletin,1988/13。关于同余式  2~(n-k)≡1(mod n),科学通报, 1988/05。
 2、(和曾庆宗)可用计算机实现的两个武术数学模型,成都体育学院学报,1989/02。
 3、关于同余式a~(n-k)≡1(modn),四川大学学报(自然科学版),1988/04。
 4、关于丢番图方程X~2+4P~m-1=4P~n,铁道科学与工程学报,1989/03。
 5、On the Diophantine Equations ax~n-1/ax-1=y~2 and ax~n+1/ax+1= y~2, 数学进展, 1989/03.
 6、Sun, Qi; Yuan, Ping Zhi On the Diophantine equations $(ax\sp n-1)/(ax-1)=y\sp 2$ and $(ax\sp n+1)/(ax+1)=y\sp 2$. (Chinese) Sichuan Daxue Xuebao 26 (1989), Special Issue, 20--24.
 7、关于幂数问题的一个Golomb猜想, 数学研究与评论,1989/03.
 8、有关幂数的几个问题, 四川大学学报(自然科学版),1989/03.
 9、A.Rotkiewiez问题的推广, 铁道科学与工程学报,1991/01.
 10、本原大素因子和Selfridge问题, 铁道科学与工程学报,1992/03.
 11、关于三角形的一个猜想的解答, 中学数学,1993/11.
 12、关于矩阵迹的Bellman问题, 铁道科学与工程学报, 1993/01.
 13、余新河数学题的一个结果, 铁道科学与工程学报, 1993/04.
 14、Pillai猜想的一点注记, 湖南理工学院学报(自然科学版), 1993/02.
  15、Yuan, Ping Zhi On a special Diophantine equation $a{x\choose n}=by\sp r+c$. Publ. Math. Debrecen 44 (1994), no. 1-2, 137--143.
 16、Graham猜测的一点注记, 益阳师专学报,1994/06.
 17、关于四项指数不定方程ap_1~(x_1)…P_r~(x_r)+bq_1~(y_1)…q_s~(y_s)=c+d(p_1…p_r)~z(q_1…q_s)~w, 岳阳师范学院学报(自然科学版),1994/Z1.
 18、Pell方程的一个新性质和应用, 长沙铁道学院学报, 1994/03.
 19、陈新明,袁平之,常系数非齐次线性微分方程求特解的递推公式, 长沙铁道学院学报,1994/02.
 20、Diophantus方程x~2-Dy~2=-1的可解性,长沙铁道学院学报, 1994/01.
 21、(with Sun Qi, Han Qing) A question about Aurifeuillian factorizations, Chinese Science Bulletin, 1995/20. 关于Aurifeuillian分解的一个问题, 科学通报, 1995/10.
 22、关于丢番图方程x~2=4p~m+4p~n+1, 岳阳师范学院学报(自然科学版), 1995/01.
 23、S.Chowla的一个猜想的几点注记, 长沙铁道学院学报, 1995/01.
 24、关于自然数乘法分拆数的一个猜想, 湖南教育学院学报, 1996/05.
 25、关于丢番图方程的一个注记, 数学学报, 1996/02.
 26、关于Pell方程的一个猜想, 数学年刊A辑(中文版), 1996/03.
 27、Sun, Qi; Yuan, Ping-Zhi On the number of solutions of diagonal equations over a finite field. Finite Fields Appl. 2 (1996), no. 1, 35--41.
 28、 $D$-invariants and the solvability of $kx\sp 2-ly\sp 2=1,2$. Japan. J. Math. (N.S.) 22 (1996), no. 2, 355--361.
 29、Sun, Qi; Yuan, Ping-Zhi,On the Diophantine Equation x~4- Dy~2= 1, 数学进展, 1996/01.  30、Rational and algebraic approximations of algebraic numbers and their application, Science in China,Ser.A, 1997/10. 代数数的有理和代数逼近及应用, 中国科学A辑,1997/09.
 31、关于素数幂的一条表示定理, 益阳师专学报, 1997/06.
 32、 Scott的一个猜想及相关问题, 淮北煤师院学报(自然科学版),1997/01.
 33、(with Sun Qi)关于不定方程x~4-Dy~2=1的一个注记, 四川大学学报(自然科学版),1997/03.
 34、CM域、单位与不定方程, 四川大学学报(自然科学版),1997/02.
 35、也谈实二次域类数的可除性, 数学学报, 1998/03.
 36、关于方程xy+yz+zx=n的正整数解, 数学年刊A辑(中文版), 1998/06.
 37、直径为4的整树, 系统科学与数学,1998/02.
 38、关于方程x~2-D=p~n的解数(英文), 四川大学学报(自然科学版), 1998/03.
 39、关于丢番图方程x~2+b~y=c~z, 四川大学学报(自然科学版), 1998/01.
 40、Yuan, Pingzhi; Wang, Jiabao On the Diophantine equation $x\sp 2+b\sp y=c\sp z$. Acta Arith. 84 (1998), no. 2, 145--147.
 41、F-L序列的表示, 长沙铁道学院学报, 1998/04.
 42、(with Chen Xuesheng)Eisenstein判别法的推广, 长沙铁道学院学报,1998/03.
 43、关于丢番图方程ax~2+by~2=cP~n, 数学年刊A辑(中文版), 1999/02.
 44、(with Xiao Guoneng)关于一类数论函数方程的解, 长沙铁道学院学报,1999/01.
 45、几个未解决的不定方程问题, 数学研究与评论, 2000/04.
 46、方程xy+yz+zx=n的正整数解, 数学学报, 2000/03.
 47、广义Lucas序列与不定方程(Ⅰ) 数学学报, 2000/01.
 48、Sun, Qi; Ren, Debin; Hong, Shaofang; Yuan, Pingzhi; Han, Qing A new class of Aurifeuillian factorizations of $M\sp n±1$. Sci. Math. 2 (1999), no. 3, 353--360 。
 49、(with Lin Jun) 二次方程ax~4+bx~2y~2 +dy~4=cz~2 的可解性(英文), 四川大学学报(自然科学版), 2000/04。
 50、广义Lucas序列的重复度与相关的不定方程的解数, 高校应用数学学报A辑(中文版), 2000/03.
 51、(with Luo Jiagui)关于一类高次不定方程的解, 数学研究与评论, 2001/01.
 52、Ren, Debin; Sun, Qi; Yuan, Pingzhi Number of zeros of diagonal polynomials over finite fields. Dedicated to Professor Chao Ko on the occasion of his 90th birthday. Finite Fields Appl. 7 (2001), no. 1, 197--204.
 53、(with Luo Jiagui)关于不定方程x~2-Dy~4=1, 四川大学学报(自然科学版),2001/03
 54、(with Xiao Guoneng, Liu Weijun, Li Maosheng)一类密码体制的完全保密性,长沙铁道学院学报,2001/03.
 55、(with Wang Jiabao, Li Maosheng)矩阵特征值内插定理的拓广, 长沙铁道学院学报, 2001/02.
 56、Tijdeman, R.; Yuan, Pingzhi On the rationality of Cantor and Ahmes series. Indag. Math. (N.S.) 13 (2002), no. 3, 407--418.  
 57、A note on the divisibility of the generalized Lucas sequences. Fibonacci Quart. 40 (2002), no. 2, 153--156.
 58、  On the number of solutions of simultaneous Pell equations. Acta Arith. 101 (2002), no. 3, 215--221.
 59、 On algebraic approximations of certain algebraic numbers. J. Number Theory 102 (2003), no. 1, 1--10.
 60、Lehmer序列中的平方数, 数学学报, 2003/05.
 61、(with Jiang Zhengtao)和整树相关的一个联立不定方程, 长沙铁道学院学报, 2003/01.
 62、 A conjecture on Euler numbers. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 9, 180--181.
 63、Integers not of the form $c(2\sp a+2\sp b)+p\sp \alpha$. Acta Arith. 115 (2004), no. 1, 23--28.
 64、 Simultaneous Pell equations. Acta Arith. 115 (2004), no. 2, 119--131.
 65、 On the number of solutions of $x\sp 2-4m(m+1)y\sp 2=y\sp 2-bz\sp 2=1$. Proc. Amer. Math. Soc. 132 (2004), no. 6, 1561--1566。
 66、(with Hu Yongzhong)指数丢番图方程a~x+b~y=c~z, 数学学报, 2005/06.
 67、关于丢番图方程Dx~2+1=ca~n(英文), 黑龙江大学自然科学学报, 2005/02.
 68、(with Luo Jagui)Lehmer序列中的平方数与平方类, 数学学报, 2005/04.
 69、YuanPingzhi, Yahui, Hu A note on power residue difference sets. J. Algebra 291 (2005), no. 1, 269--273.
 70、 On the Diophantine equation $\frac{x\sp 3-1}{x-1}=\frac{y\sp n-1}{y-1}$. J. Number Theory 112 (2005), no. 1, 20--25.
 71、Yuan, Ping Zhi; Chen, Hai Bo Two inequalities for convex functions. Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 1, 193--196.
 72、Yuan, Pingzhi; Hu, Yongzhong On the Diophantine equation $x\sp 2+D\sp m=p\sp n$. J. Number Theory 111 (2005), no. 1, 144--153.
 73、Yuan, Pingzhi On the Diophantine equation $ax\sp 2+by\sp 2=ck\sp n$. Indag. Math. (N.S.) 16 (2005), no. 2, 301--320.
 74、Chen, Xuesheng; Yuan, Pingzhi A note on Kneser's theorem. JP J. Algebra Number Theory Appl. 6 (2006), no. 1, 77--83.
 75、(with Chen Xuesheng)Kemperman结构定理之推广, 数学学报, 2006/06.(with Luo Jiagui) Lucas序列中的平方类, 数学进展, 2006/02.
 76、(with Chen Bo)Hecke群的同余子群, 中山大学学报(自然科学版), 2007/06.
 77、Yuan, Pingzhi On the index of minimal zero-sum sequences over finite cyclic groups. J. Combin. Theory Ser. A 114 (2007), no. 8, 1545--1551.
 78、Li, Zhigang; Xia, Jianye; Yuan, Pingzhi On some special forms of simultaneous Pell equations. Acta Arith. 128 (2007), no. 1, 55--67.
 79、Hu, Yahui; Yuan, Pingzhi; Liu, Weijun The $k$-exponents of primitive, nearly reducible matrices. Ars Combin. 83 (2007), 47--63.
 80、Luo, Jiagui; Yuan, Pingzhi Square-classes in Lehmer sequences having odd parameters and their applications. Acta Arith. 127 (2007), no. 1, 49--62.
 81、Hu, Yahui; Yuan, Pingzhi; Chen, Xuesheng The generalized exponent sets of primitive, minimally strong digraphs. I. Ars Combin. 82 (2007), 97--124.
 82、(with Li Zhigang)一类不定方程组的解的个数, 数学学报, 2007/06.
 83、(with Jiang Zhentao)对分圆子群中元素表示的几个结果的改进, 通信学报, 2007/01
 84、Xia, Jian Ye; Yuan, Ping Zhi On the Terai-Jésmanowicz conjecture. Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 12, 2061--2064.
 85、Chen, Bo; Yuan, Pingzhi Normal congruence subgroups of Hecke groups. Algebra Colloq. 15 (2008), no. 4, 707--720.
 86、Saltzman, Peter W.; Yuan, Pingzhi On sums of consecutive integral roots. Amer. Math. Monthly 115 (2008), no. 3, 254--261.
 87、Zhuang, Jujuan; Yuan, Pingzhi Minimal zero-sum sequences in finite cyclic groups. Taiwanese J. Math. 13 (2009), no. 3, 1007--1015.
 88、Chen, Bo; Yuan, Ping Zhi Congruence subgroups of Hecke groups. Acta Math. Sin. (Engl. Ser.) 25 (2009), no. 6, 931--944.
 89、Ding, CunSheng; Xiang, Qing; Yuan, Jin; Yuan, PingZhi Explicit classes of permutation polynomials of $\Bbb F\sb {3\sp {3m}}$. Sci. China Ser. A 52 (2009), no. 4, 639--647.
 90、Yuan, Pingzhi Subsequence sums of a zero-sumfree sequence. European J. Combin. 30 (2009), no. 2, 439--446.
 91、Pingzhi Yuan and Xiangneng Zeng, A new result on Davenport constant, Journal of Number Theory, 129(2009), 3026-3028.

 92、Michael Stoll, P.G. Walsh and Pingzhi Yuan,  On the Diophantine equation  , Acta Arith. 139(2009), 57-63.
 93、Pingzhi Yuan and Li Yuan,  Squares in Lehmer sequences and the Diophantine equation  , Acta Arith. 139(2009),275-302.
 94、Pingzhi Yuan, Subsequence sums of a zero-sum-free sequences, Electronic Journal of Combinatorics,16(2009),#97.
 95、Subsequence Sums of Zero-sum-free Sequences, the electronic journal of combinatorics 16 (2009), #R97.
 96、 (with Zeng Xiangneng) A new result on Davenport constant, Journal of Number Theory 129 (2009) 3026–3028.
 97、Yuan, Pingzhi; Li, Yuan On the Diophantine equation $y^2=px(Ax^2-2)$. JP J. Algebra Number Theory Appl. 14 (2009), no. 2, 185--190.
 98、Hu, Yong Zhong; Yuan, Ping Zhi The Diophantine equation system $a^2+b^2=c^3$ and $a^x+b^y=c^z$. (Chinese) Acta Math. Sinica (Chin. Ser.) 52 (2009), no. 5, 1027--1032.

 99、(with Hu, Yong Zhong)Jeśmanowícz's conjecture concerning Pythagorean numbers. (Chinese) Acta Math. Sinica (Chin. Ser.) 53 (2010), no. 2, 297—300
 100、(with Zhang Zhongfeng) Squares in $\prod^n_{k=1}(ak^2+bk+c)$. (Chinese) Acta Math. Sinica (Chin. Ser.) 53 (2010), no. 1, 199—204
  101、 (with Li, Zhi Gang)The Diophantine equations $(a-1)x^2+(91a+9)=4a^n$. (Chinese) Acta Math. Sinica (Chin. Ser.) 53 (2010), no. 1, 37--44.
 102、(with Hu Yongzhong) On the Diophantine equation $ax^2+(3a+1)^m=(4a+1)^n$. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 53(101) (2010), no. 1, 51--59.
 103、Luo, Jiagui; Yuan, Pingzhi A generalization of the question of Sierpiński on geometric progressions. J. Integer Seq. 13 (2010), no. 3, Article 10.3.4, 14 pp.
 104、 Yuan, Pingzhi; Luo, Jiagui Three triangular numbers contained in geometric progression. Funct. Approx. Comment. Math. 42 (2010), , part 1, 59--65
  105、 Yuan, Pingzhi More explicit classes of permutation polynomials of $\Bbb F_{3^{3m}}$. Finite Fields Appl. 16 (2010), no. 2, 88--95.
 106、Yuan, Pingzhi; Zeng, Xiangneng Davenport constant with weights. European J. Combin. 31 (2010), no. 3, 677--680.
 107、Xia, Xingwu; Yuan, Pingzhi Indexes of unsplittable minimal zero-sum sequences of length $\Bbb I(C_n)-1$. Discrete Math. 310 (2010), no. 5, 1127--1133.
 108、 袁平之, 张中峰, On the Diophantine equation  Science ChinaMath53 (2010),2143-2158.  SCI
 109、 Pingzhi Yuan, Jiagui Luo, On the Diophantine equation  . Acta Arith. 144 (2010), no. 1, 69–95.SCI
 110、 Guan, Huan Huan; Zeng, Xiang Neng; Yuan, Ping Zhi Description of the invariant  of zero-sum-free sequence. (Chinese)中山大学学报 49 (2010), no. 3, 1–4. EI
 111、 袁平之,张中峰,丢番图方程$ax^4-by^2=1$, 数学学报,3(2010),443-454。
 112、YuanlinLi, C. Plyley, Pingzhi Yuan, X. Zeng, Minimal zero sum sequences of length four over finite cyclic groups, J. Number Theory, 130(2010)2033-2048.SCI
 113、袁平之,曾祥能,On zero-sum free subsets of length 7, the electronic journal of combinatorics,17(2010)#104. SCI
 114、 (with B. He, A. Togbe) On the Diophantine equation $X^2 - (p^{2m} + 1)Y^6 = -p^{2m}. Functiones et Approximatio Commentarii Mathematici Volume 43, Number 1 (2010), 31-44.

 115、Zeng,Xiangneng ; Yuan, Pingzhi ,Two conjectures on an addition theorem. Acta Arith. 148 (2011), no. 4, 395–411.
 116、Yuan, Pingzhi ; Hu,Yongzhong On the Diophantine equation x2 −kxy +y2 +lx = 0, l 2 {1, 2, 4}. Comput. Math. Appl. 61 (2011), no. 3, 573–577.

 117、Zeng,Xiangneng ; Yuan, Pingzhi,Weighted Davenport’s constant and the weighted EGZ theorem.Discrete Math. 311 (2011), no. 17, 1940–1947.

118、 Guan, Huanhuan ; Yuan, Pingzhi ;Zeng,Xiangneng,Normal sequences over finite abelian groups. J. Combin. Theory Ser. A 118 (2011), no. 4, 1519–1524.

119、 Luo, Jiagui; Togb´e, Alain; Yuan, Pingzhi On some equations related to Ma’s conjecture. Integers 11 (2011), A27, 11 pp.

120、 Jiagui Luo and Pingzhi Yuan, On the Diophantine equation  , Acta Math. Hungar., 133 (4) (2011), 342–358.
 121、  A. Togbé and P. Yuan, On a variant of a Diophantine equation of Cassels, 46(2) (2011), 325-331.

 122、 Guixin Deng and Pingzhi Yuan, Symmetric Digraphs from Powers Modulo n, Open Journal of Discrete Mathematics, 2011, 1, 103-107.

 123、 Pingzhi Yuan and Cunsheng Ding, Permutation polynomials over finite fields from a powerful Lemma, Finite Fields and Their Applications 17 (2011) 560–574

 124、 Pingzhi Yuan and Xiangneng Zeng, A note on linear permutation polynomials, Finite Fields and Their Applications, 17(2011), 488-491.
  125、  Guixin Deng and Pingzhi Yuan, Isomorphic Digraphs from powers moduluo p, Czechoslovak Mathematical Journal, 136(61)(2011),771-779.
 126、 Pingzhi Yuan and Yuan Li, The Transcendence of Alternating Series of Rational Functions, Int. J. of Diophantine Approximation and Number Theory, Vol. 1, No.1, June 2011, 5-21
 127.  Deng, Guixin; Yuan, PingzhiOn the symmetric digraphs from powers modulon .Discrete Math.312 (2012), no. 4, 720–728.

  128.Zhang, Zhongfeng; Yuan, PingzhiOn the Diophantine equation.Int. J. Number Theory8 (2012), no. 3, 813–821.

  129. Yuan, Pingzhi; Zhang, ZhongfengOn the Diophantine equation .Publ. Math. Debrecen80 (2012), no. 3-4, 327–331.
  130.Feng, Li; Yuan, Ping ZhiA class of quadratic Diophantine equations. (Chinese) J. South China Normal Univ. Natur. Sci. Ed.44 (2012), no. 2, 46–47.

131.Zhang, Zhongfeng; Luo, Jiagui; Yuan, PingzhiOn the Diophantine equation .Colloq. Math.128 (2012), no. 2, 277–285.
132.Geroldinger, Alfred; Yuan, PingzhiThe set of distances in Krull monoids.Bull. Lond. Math. Soc.44 (2012), no. 6, 1203–1208.

133.  Deng, Guixin; Yuan, PingzhiOn a combinatorial conjecture of Tu and Deng.Integers12 (2012), Paper No. A48, 9 pp.

134.Geroldinger, Alfred; Yuan, PingzhiThe monotone catenary degree of Krull monoids.Results Math.63 (2013), no. 3-4, 999–1031.

135.Feng, Li; Yuan, Pingzhi; Hu, YongzhongOn the Diophantine equation  .Integers13 (2013), Paper No. A8, 8 pp.

136.Zhang, Zhong Feng; Luo, Jia Gui; Yuan, Ping ZhiThe Diophantine equation . (Chinese) Chinese Ann. Math. Ser. A34 (2013), no. 3, 279–284.

137.Zhang, Zhongfeng; Yuan, PingzhiA note on a conjecture of Erdős, Graham, and Spencer.Integers13 (2013), Paper No. A76, 6 pp.

138. Guan, Huan Huan; Yuan, Ping ZhiStructure of unsplittable atoms over C 2 C 2n . (Chinese) Acta Sci. Natur. Univ. Sunyatseni52 (2013), no. 5, 78–81.

139.Yuan, PingzhiAn upper bound for the number of odd multiperfect numbers.Bull. Aust. Math. Soc.89 (2014), no. 1, 1–4.

140.Yuan, Pingzhi; Zhang, ZhongfengAddition to `An upper bound for the number of odd multiperfect numbers' [MR3162998].Bull. Aust. Math. Soc.89 (2014), no. 1, 5–7.

141.Yuan, Pingzhi; Ding, CunshengFurther results on permutation polynomials over finite fields.Finite Fields Appl.27 (2014), 88–103.

142. Deng, Guixin; Yuan, PingzhiOn the structure of G(H,k) .Algebra Colloq.21 (2014), no. 2, 317–330.

143.Yuan, Pingzhi; He, Zilong; You, LihuaA conjecture on the primitive degree of tensors.Linear Algebra Appl.450 (2014), 175–185.

144.Miyazaki, Takafumi; Yuan, Pingzhi; Wu, DanyaoGeneralizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples II.J. Number Theory141 (2014), 184–201.

145.Luo, JiaGui; Yuan, PingZhiOn the solutions of a system of two Diophantine equations.Sci. China Math.57 (2014), no. 7, 1401–1418

146.Yuan, Pingzhi; Ding, CunshengPermutation polynomials of the form over  .Finite Fields Appl.29 (2014), 106–117.

147. Yuan, Pingzhi; You, LihuaOn the similarity of tensors.Linear Algebra Appl.458 (2014), 534–541.

148. Yuan, Pingzhi; You, LihuaSome remarks on and B 0 tensors.Linear Algebra Appl.459 (2014), 511–521

149. Yuan, PingzhiSubsequence sums of zero-sum free sequences II.Ars Combin.116 (2014), 433–444.

150. Guan, Huan Huan; Yuan, Ping ZhiStructure of zero-sum free sequences over . (Chinese) Chinese Ann. Math. Ser. A 35 (2014), no. 2, 211-214; translation in Chinese J. Contemp. Math.35 (2014), no. 2, 181–192

151.Yuan, Pingzhi; He, Zilong; Zhou, JunyiOn the sum of reciprocal generalized Fibonacci numbers.Abstr. Appl. Anal.2014, Art. ID 402540, 4 pp

152.Li, Yuanlin; Parmenter, M. M.; Yuan, PingzhiOn clean group rings.J. Algebra Appl.14 (2015), no. 1, 1550004, 11 pp.

153.He, Zilong; Yuan, Pingzhi; You, LihuaOn the exponent set of nonnegative primitive tensors.Linear Algebra Appl.465 (2015), 376–390.

154.Ding, Cunsheng; Qu, Longjiang; Wang, Qiang; Yuan, Jin; Yuan, PingzhiPermutation trinomials over finite fields with even characteristic.SIAM J. Discrete Math.29 (2015), no. 1, 79–92.

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155Zeng,Xiangneng; Li, Yuanlin;Yuan, PingzhiOn a conjecture of Lemke and Kleitman. Acta Arith.168 (2015), no. 3,289–299.

156Yuan, Pingzhi;He, Zilong;You, LihuaFurther results and some open problems on the primitive degree of nonnegativetensors. LinearAlgebra Appl.480 (2015), 72–92.

157Yuan, Pingzhi;Zheng, YanbinPermutation polynomials from piecewise functions. Finite FieldsAppl.35 (2015), 215–230.

158Gao, Weidong;Li, Yuanlin;Yuan, Pingzhi;Zhuang,Jujuan On the structure of long zero-sum free sequences and n  n-zero-sum free sequences over finite cyclic groups. Arch. Math.(Basel)105 (2015), no. 4,361–370.

159Zheng, Yanbin;Yuan, Pingzhi;Pei, DingyiPiecewise constructions of inverses of some permutation polynomials. Finite FieldsAppl.36 (2015), 151–169.

160Guan,Huanhuan; Yuan, Pingzhi;Zeng,Xiangneng A generalization of Graham's conjecture. Electron. J.Combin.22 (2015), no. 4,Paper 4.7, 22 pp.

161Geroldinger,Alfred; Grynkiewicz,David J.; Yuan, PingzhiOn products of k  katoms II. Mosc. J.Comb. Number Theory5 (2015), no. 3,3–59.

162Chen,Yong-Gao; Fang, Jin-Hui;Yuan, Pingzhi;Zheng,Yueping On multiplicative functions with f(p+q+n 0 )=f(p)+f(q)+f(n 0 ) f(p+q+n_0)=f(p)+f(q)+f(n_0). J. NumberTheory165 (2016), 270–289.

163Yuan, Pingzhi;Li, YuanlinLong unsplittable zero-sum sequences over a finite cyclic group. Int. J.Number Theory12 (2016), no. 4,979–993.

164Liu, Yang;Lu, Ziqun;Yuan, PingzhiOn p  p-Brauer characters and p  p-regular conjugacy classes. Comm. Algebra44 (2016), no. 6,2443–2454.

165Miyazaki, T.;Togbé, A.;Yuan, P.On the Diophantine equationa x +b y =(a+2) z   a^x+b^y=(a + 2)^z. Acta Math.Hungar.149 (2016), no. 1,1–9.

166Huang, Hongdi;Li, Yuanlin;Yuan, PingzhiOn  \ast-clean group rings II. Comm. Algebra44 (2016), no. 7,3171–3181.

167Zheng, Yanbin;Yuan, Pingzhi;Pei, DingyiLarge classes of permutation polynomials over F q 2   \Bbb{F}_{q^2}. Des. CodesCryptogr.81 (2016), no. 3,505–521.

168Zeng,Xiangneng; Yuan, Pingzhi;Li, YuanlinOn the structure of long unsplittable minimal zero-sum sequences. Acta Arith.176 (2016), no. 2,131–159.

169You, Lihua;Shu, Yujie;Yuan, PingzhiSharp upper and lower bounds for the spectral radius of a nonnegativeirreducible matrix and its applications. LinearMultilinear Algebra65 (2017), no. 1,113–128.

170

Wu, Danyao;Yuan, Pingzhi;Ding,Cunsheng; Ma, YuzhenPermutation trinomials over F 2 m    \Bbb F_{2^m}. Finite FieldsAppl.46 (2017), 38–56.