硕士生导师

硕士生导师

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个人信息
  • 姓名：刘华宁
  • 部门：计算数学系
  • 职称：教授
  • 荣誉：全国百篇优秀博士论文提名获得者，陕西省杰出青年基金，陕西省青年科技新星，西北大学“优秀青年学术骨干支持计划”，博士生导师，学术学位硕士生导师
  • 电子邮件：hnliu@nwu.edu.cn
  • 研究方向：数论及其应用

 

个人简介

 

 

    刘华宁，男，1997年9月考入西北大学数学系计算数学专业，2001年本科毕业后进入数学系基础数学专业攻读硕士研究生。2004年硕士研究生毕业后留校任教，同时考取数学系基础数学专业博士研究生，2007年7月毕业并获得博士学位。2007年7月至2011年7月在山东大学数学学院从事博士后研究。2009年5月晋升为副教授。2012年1月至2013年1月在英国剑桥大学纯粹数学与数理统计系从事博士后研究。2013年5月晋升为教授。

 

项目、成果、论文、奖励

 

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  • 1.主要课题

     

    2024.1-2026.12: 主持陕西省杰出青年基金项目，编号2024JC-JCQN-04

    2021.1-2024.12: 主持国家自然科学基金面上项目，编号12071368

    2016.1-2019.12: 主持国家自然科学基金面上项目，编号11571277
    2014.5.1-2016.4.30: 主持陕西省青年科技新星项目，编号2014KJXX-61
    2014.5.1-2016.4.30: 主持陕西省自然科学基金，编号2014JM1007
    2010.1-2012.12: 主持国家自然科学基金青年科学基金，编号10901128
    2007.1-2008.12: 主持陕西省自然科学基金，编号2006A04
    2009.1-2010.12: 主持中国博士后科学基金特别资助，编号200801410
    2008.1-2009.12: 主持中国博士后科学基金面上项目，编号20070421084
    2008.1-2009.12: 主持山东省博士后创新项目，编号200702036

     

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    2.主要成果    

     

    科研方面主要研究具有密码学意义的伪随机数列与子集。以下是部分论著目录。

    A. 著作目录
    1. 刘华宁. 数论中的伪随机二进制数列. 北京: 科学出版社, 2008年5月.

    B. SCI论文目录
    1．张文鹏, 刘华宁. A note on the Cochrane sum and its hybrid mean value formula. Journal of Mathematical Analysis and Applications, 2003, 288(2): 646-659. (SCI，IDS Number: 752PG)
    2. 张文鹏, 刘华宁. On the general Gauss sums and their fourth power mean. Osaka Journal of Mathematics, 2005, 42(1): 189-199. (SCI，IDS Number: 920EI)
    3. 刘华宁, 张文鹏. On the hybrid mean value of Gauss sums and generalized Bernoulli numbers. Proceedings of the Japan Academy Series A- Mathematical Sciences, 2004, 80(6): 113-115. (SCI，IDS Number: 845WL)
    4. 刘华宁, 张文鹏. On certain Hardy sums and their $2m$-th power mean. Osaka Journal of Mathematics, 2004, 41(4): 745-758. (SCI，IDS Number: 895ET)
    5. 刘华宁, 张文鹏. On the even power mean of a sum analogous to Dedekind sums. Acta Mathematica Hungarica, 2005, 106(1-2): 67-81. (SCI，IDS Number: 909GW)
    6. 刘华宁, 张文鹏. On the squarefree and squarefull numbers. Journal of Mathematics of Kyoto University, 2005, 45(2): 247-255. (SCI，IDS Number: 979KL)
    7. 刘华宁, 张文鹏. On a problem of D. H. Lehmer. Acta Mathematica Sinica English Series, 2006, 22(1): 61--68. (SCI，IDS Number: 994EY)
    8. 刘华宁, 张文鹏. On the mean value of $L(m,\chi )L(n,\overline \chi )$ at positive integers $m,n\ge 1$. Acta Arithmetica, 2006, 122(1): 51-56. (SCI，IDS Number: 087NE)
    9. 刘华宁, 张小蹦. On the mean value of $\frac{L^{'}}{L} (1,\chi)$. Journal of Mathematical Analysis and Applications, 2006, 320(2): 562-577. (SCI，IDS Number: 049FW)
    10. 刘华宁, 张文鹏. Hybrid mean value on the difference between a quadratic residue and its inverse modulo $p$. Publicationes Mathematicae Debrecen, 2006, 69(1-2): 227-243. (SCI，IDS Number: 056VO)
    11. 刘华宁. New pseudorandom sequences constructed using multiplicative inverses. Acta Arithmetica, 2006, 125(1): 11-19. (SCI，IDS Number: 163FD)
    12. 刘华宁, 张文鹏. General Kloosterman sums and the difference between an integer and its inverse modulo $q$.  Acta Mathematica Sinica English Series, 2007, 23(1): 77-82. (SCI，IDS Number: 107FZ)
    13. 刘华宁, 张文鹏. Hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums. Journal of the Korean Mathematical Society, 2007,44(1): 11-24.  (SCI，IDS Number: 123QL)
    14. 刘华宁, 张文鹏. Generalized Cochrane sums and Cochrane-Hardy sums, Journal of Number Theory, 2007, 122(2): 415-428. (SCI，IDS Number: 138HG)
    15. 刘华宁. A note on local randomness in polynomial random number and random function generators. Applied Mathematics and Computation, 2007, 186(2): 1360-1366. (SCI，IDS Number: 163MK; EI, Accession Number: 071410523951)
    16. 刘华宁, 张文鹏. Mean value on the difference between a quadratic residue and its inverse modulo $p$.  Acta Mathematica Sinica English Series, 2007, 23(5): 915-924. (SCI，IDS Number: 157VX)
    17. 刘华宁. New pseudorandom sequences constructed by quadratic residues and Lehmer numbers. Proceedings of the American Mathematical Society, 2007, 135(5): 1309-1318. (SCI，IDS Number: 139PV)
    18. 刘华宁. Some generalizations of Knopp's identity. Bulletin of the Brazilian Mathematical Society, 2007, 38(2): 179-188. (SCI，IDS Number: 187NY)
    19. 刘华宁. A note on the upper bound estimate of high-dimensional Cochrane sum. Journal of Number Theory, 2007, 125(1): 7-13. (SCI，IDS Number: 181AG)
    20. 刘华宁, 张文鹏.  Hybrid mean value results for a generalization on a problem of D.H. Lehmer and Hyper-Kloosterman sums. Osaka Journal of Mathematics, 2007, 44(3): 615-637. (SCI，IDS Number: 230UK)
    21. 刘华宁. On the mean values of the homogeneous Dedekind sums and Cochrane sums in short intervals. Journal of the Korean Mathematical Society, 2007, 44(6): 1243-1254. (SCI，IDS Number: 228LG)
    22. 刘华宁, 张文鹏.  Hybrid mean value for a generalization of a problem of D. H. Lehmer. Acta Arithmetica, 2007, 130(1): 1-17. (SCI，IDS Number: 277OW)
    23. 刘华宁. A family of pseudorandom binary sequences constructed by the multiplicative inverse. Acta Arithmetica, 2007, 130(2): 167-180. (SCI，IDS Number: 277OY)
    24. 刘华宁. Mean value of mixed exponential sums. Proceedings of the American Mathematical Society, 2008, 136(4): 1193-1203. (SCI，IDS Number: 250OT)
    25. 刘华宁, 张文鹏. Hybrid mean value on the difference between an integer and its inverse modulo $q$. Arkiv for Matematik, 2008, 46(2): 337-347. (SCI，IDS Number: 339CF)
    26. 刘华宁, 杨存典. On a problem of D. H. Lehmer and pseudorandom binary sequences. Bulletin of the Brazilian Mathematical Society, 2008, 39(3): 387-399. (SCI，IDS Number: 352HL)
    27. 刘华宁. On the mean values of Dedekind sums and Hardy sums. Journal of the Korean Mathematical Society, 2009, 46(1): 187-213. (SCI，IDS Number: 391UY)
    28. 刘华宁, 翟文广. A note on the pseudorandomness of the Liouville function. Acta Arithmetica, 2009, 136(2): 101-121. (SCI，IDS Number: 514HR)
    29. 刘华宁, 张文鹏. Some applications of certain character sums. Rocky Mountain Journal of Mathematics, 2009, 39(2): 573-589. (SCI，IDS Number: 496GI)
    30. 刘华宁. A large family of pseudorandom binary lattices. Proceedings of the American Mathematical Society, 2009, 137(3): 793-803. (SCI，IDS Number: 375ZV)
    31. 刘华宁, 展涛, 王小云. On the correlation of pseudorandom binary sequences with composite moduli. Publicationes Mathematicae Debrecen, 2009, 74(1-2): 195-214. (SCI, IDS Number: 404MO)
    32. 刘华宁, 展涛, 王小云. Large families of elliptic curve pseudorandom binary sequences. Acta Arithmetica, 2009,140(2): 135-144. (SCI, IDS Number: 554EG)
    33. 刘华宁. A note on Lehmer $k$-tuples. International Journal of Number Theory, 2009, 5(7): 1169-1178. (SCI, IDS Number: 523SI)
    34．刘华宁. Mean value of some exponential sums and applications to Kloosterman sums. Journal of Mathematical Analysis and Applications, 2010,361(1):205-223. (SCI, IDS Number: 536SK)
    35. 张小蹦, 刘华宁. Inversion of $L$-functions, general Kloosterman sums weighted by incomplete character sums. Journal of the Korean Mathematical Society，2010, 47(5): 947-965. (SCI, IDS Number: 646HQ)
    36. 刘华宁. Gowers uniformity norm and pseudorandom measures of the pseudorandom binary sequences. International Journal of Number Theory, 2011, 7(5): 1279-1302. (SCI, IDS Number: 816PE)
    37. 刘华宁, 王小云. On the correlation of pseudorandom binary sequences using additive characters. Publicationes Mathematicae Debrecen, 2011, 79(1-2): 145-170. (SCI, IDS Number: 816CQ)
    38. 刘华宁, 翟文广. The equation $n_1n_2=n_3n_4$, the gcd-sum function and the mean values of certain character sums. Acta Arithmetica, 2012, 152(2): 137-157. (SCI, IDS Number: 927BM)
    39. 高静, 刘华宁. Dirichlet characters, Gauss sums and inverse $Z$ transform. Abstract and Applied Analysis, vol. 2012, Article ID 821949, 9 pages, 2012. (SCI, IDS Number: 922UH)
    40. 刘华宁, 高静. Large families of pseudorandom binary sequences constructed by using the Legendre symbol. Acta Arithmetica, 2012, 154(1): 103-108. (SCI, IDS Number: 998XM)
    41. 刘华宁, 高静. On the Gauss sums and generalized Bernoulli numbers. Ukrainian Mathematical Journal, 2012, 64(6): 971-978. (SCI, IDS Number: 050OV)
    42. 刘华宁, 高静. Generalized Knopp identities for homogeneous Hardy sums and Cochrane-hardy sums. Czechoslovak Mathematical Journal, 2012, 62(4): 1147-1159. (SCI, IDS Number: 068KA)
    43. 高静, 刘华宁. On the mean value of character sums in short intervals. Journal of Computational Analysis and Applications, 2013, 15(1): 65-72. (SCI, IDS Number: 100KL)
    44. 杜永光, 刘华宁. On the mean value of the mixed exponential sums with Dirichlet characters and general Gauss sum. Czechoslovak Mathematical Journal, 2013, 63(2): 461-473. (SCI, IDS Number: 182RQ)
    45．刘华宁, 张婷. On the distribution of square-full numbers in arithmetic progressions. Archiv der Mathematik, 2013, 101(1): 53-64. (SCI, IDS Number: 185JL)
    46. 刘华宁. Large families of pseudorandom binary sequences and lattices by using the multiplicative inverse. Acta Arithmetica, 2013, 159(2): 123-131. (SCI, IDS Number: 213SY)
    47. 刘华宁, 高静. A note on certain modular constructions of pseudorandom binary sequences with composite moduli. Periodica Mathematica Hungarica,  2013, 67(2): 175-185. (SCI, IDS Number: 238LN)
    48. 徐哲峰, 刘华宁. On the mean values of certain character sums. Abstract and Applied Analysis, vol. 2013, Article ID 326597, 19 pages, 2013. (SCI, IDS Number: 266MW)
    49. 刘华宁. A family of elliptic curve pseudorandom binary sequences. Designs, Codes and Cryptography, 2014, 73(1): 251-265. (SCI, IDS Number: AK8CZ)
    50. 高静, 刘华宁. Dirichlet characters, Gauss sums and arithmetic Fourier transforms. Applied Mathematics-A Journal of Chinese Universities, 2014, 29(3): 307-316. (SCI, IDS Number: AP6RS)
    51. 刘华宁, 高静. A note on large families of pseudorandom binary sequences and lattices. Journal of Information Science and Engineering, 2014, 30(5): 1635-1654. (SCI, IDS Number: AP8KV)
    52. 刘华宁. Large family of pseudorandom subsets of the set of the integers not exceeding $N$. International Journal of Number Theory, 2014, 10(5): 1121-1141. (SCI, IDS Number: AO0PM)
    53. 刘华宁, 宋尔萍. A note on pseudorandom subsets formed by generalized cyclotomic classes. Publicationes Mathematicae Debrecen, 2014, 85(3-4): 257-271. (SCI, IDS Number: AZ0CE)
    54. 刘华宁. On the mean values of Dirichlet $L$-functions. Journal of Number Theory, 2015, 147: 172-183. (SCI, IDS Number: AT8PF)
    55. 刘华宁, 董慧. On the distribution of consecutive square-free primitive roots modulo $p$. Czechoslovak Mathematical Journal, 2015，65(2): 555-564. (SCI, IDS Number: CL2YV)
    56. 张华, 刘华宁. Pseudorandom subsets with composite moduli. Bulletin of the Belgian Mathematical Society – Simon Stevin, 2015, 22(3): 353-375. (SCI, IDS Number: CU0QH)
    57. 刘华宁, 张敏. A large family of Boolean functions. Acta Arithmetica, 2016, 172(3): 251-262. (SCI, IDS Number: DC7BK)
    58. 刘华宁, 祁玉婵. On multi-dimensional pseudorandom subsets. Journal of Number Theory, 2017, 181: 73-88. (SCI, IDS Number: FG3FG)
    59. 刘华宁, 高波. A large family of pseudorandom sequences of $k$ symbols with length $pq$. Acta Arithmetica, 2017, 181.1: 1-26 (SCI, IDS Number: FN6NJ)
    60. 曹艳梅, 刘华宁. Large families of subsets arising from Woods problem and their pseudorandomness. Acta Mathematica Hungarica, 2018, 156(1): 204-219. (SCI, IDS Number: GU3LH)

    61.刘华宁, 张国佗. Pseudo-random subsets constructed by using Fermat quotients. Publicationes Mathematicae Debrecen, 2019, 94(1-2): 55-74. (SCI, IDS Number: HJ8LQ)

  • 62.刘华宁. Large families of pseudorandom binary lattices by using the multiplicative inverse modulo $p$. International Journal of Number Theory, 2019, 15(3): 527-546. (SCI, IDS Number: HP9AU)

  • 63. 陈晓林, 刘华宁. Autocorrelation values of generalized cyclotomic sequences with period $p^{n+1}$. Mathematics, 2019, 7, 950 (SCI, IDS Number: JP6WY)

  • 64. 刘华宁, Christian Mauduit. On the correlation measures of subsets. Annals of Combinatorics，2020, 24(2): 311-336. (SCI, IDS Number: LY0GP)

  • 65. 刘华宁, 陈晓林. Autocorrelation values of quaternary cyclotomic sequence of length $2p^m$. International Journal of Wavelets, Multiresolution and Information Processing，2020, 18(6): 2050047 (23 pages) (SCI, IDS Number: PG7SU)

  • 66. 刘华宁, 刘茜. On the properties of generalized cyclotomic binary sequences of period $2p^m$. Designs, Codes and Cryptography, 2021, 89: 1691-1712. (SCI, IDS Number: SS2XK)

  • 67. 刘华宁, Christian Mauduit. On the distribution of the truncated sum-of-digits function of polynomial sequences in residue classes. Acta Mathematica Hungarica, 2021, 164(2): 360-376. (SCI, IDS Number: SR1XI)

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    C. 一级会报与核心
    1. 高静, 刘华宁. 广义Möbius变换和算术Fourier变换. 应用数学学报, 2004, 27(3):530-535.
    2. 刘华宁. 关于 Möbius 反转公式的一个推广. 系统科学与数学, 2004, 24(1): 51-55.
    3. 刘华宁, 张文鹏. 关于广义 Kloosterman 和的高次均值的一个注记. 数学年刊, 2005, 26(2): 233-240.
    4. 刘华宁, 张文鹏. Lehmer 问题的两个推广. 数学学报, 2006, 49(1): 95-104.
    5. 刘华宁, 张文鹏. 广义Dedekind和与Hardy和. 数学学报, 2006, 49(5): 999-1008.
    6. 刘华宁. 广义 k 次 Gauss 和及其四次均值. 数学研究与评论, 2006, 26(3): 591-597.
    7. 刘华宁. On a problem of D. H. Lehmer and Hyper-Kloosterman sums. 数学进展, 2007, 36(2): 245-252.
    8. 刘华宁. 一些新数列的偏差与伪随机性. 数学年刊, 2007, 28(3): 319-328.
    9. 刘华宁,高静. 由椭圆曲线生成的 $\mathbb{Z}_p$ 中的伪随机子集. 数学学报, 2009, 52(2): 209-216.
    10. 张小蹦, 刘华宁.Mean value of higher order generalized Bernoulli numbers, Gauss sums and general Kloosterman sums. 数学进展, 2011, 40(3): 373-383.
    11. 刘华宁,高静. 合数模上的伪随机二进制数列. 数学学报, 2012, 55(5):869-880.
    12. 刘华宁. 一类伪随机二进制数列的碰撞与雪崩效应. 数学学报, 2013, 56(6): 907-914.
    13. 张小蹦, 刘华宁. Mean value of generalized Bernoulli numbers, general Kloosterman sums and character sums. 数学进展, 2013, 42(5): 665-675.
    14. 刘华宁, 李万梅. On the fourth power mean of generalized three-term exponential sums. Journal of Mathematical Research with Applications, 2017, 37(2): 169-182.
    15. 刘华宁, 张珍珍. 关于短区间的并集中 Woods 问题的一个推广. 中国科学: 数学, 2017, 47(4): 467-478.
    16. 刘华宁, 高波. 大族长度为 $pq$ 的伪随机 $k$ 元序列. 数学学报,2017, 60(3): 401-414.
    17. 刘华宁, 高波. 基于 Ding-Helleseth 广义割圆类构造的伪随机 $k$ 元序列, 信息网络安全，2017，(1): 8-15.
    18. 刘华宁, 李万梅. 关于三项指数和的四次均值. 数学进展,2017, 46(4): 529-547.
    19. 刘华宁. On the mean values of the general Kloosterman sums. 数学进展，2017，46(5): 682-700.
    20. 刘华宁, 陈晓林. 基于伪随机子集生成的布尔函数. 数学杂志, 2018, 28(1): 167-176.
    21. 王晓瑛，岳霞霞，刘华宁. 关于合数模上 Hardy 和的均值. 数学杂志,  2018, 28(1): 155-166.

  • 22. 刘华宁, 陈晓林. 一类新的广义割圆序列的线性复杂度及其自相关值. 数学学报, 2019, 62(2): 233-246.

  • 23. 刘华宁, 祁玉婵. 子集的 Gowers 范数与伪随机测度. 数学进展，2019, 48(4): 399-418.

  • 24. 陈智雄、刘华宁、杨阳. 基于 RSA 模数的一类新型广义割圆序列的迹表示. 电子学报，2019，47(7): 1512-1517.

  • 25. 陈晓林、陈智雄、刘华宁. A family of pseudorandom binary sequences derived from generalized cyclotomic classes modulo $p^{m+1}q^{n+1}$. International Journal of Network Security,2020，22(4): 610-620.(EI).

  • 26. 刘华宁, 李柯瑶. 基于有限域中的二次特征生成的伪随机二进制格点. 数学学报, 2021，64(1): 145-150.

  • 27. 刘华宁, 高樊. 基于有限域中的迹函数生成的伪随机二元格点. 数学进展，2021, 50(5): 689-698.

 

 

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    3.获奖情况        

     

    2004年：获得“陕西省青年突击手”称号
    2005年：获得中国数学会第七届钟家庆数学奖
    2006年：获得“陕西省青年突击手”称号
    2008年：成果“算术函数性质研究”获得陕西高等学校科学技术奖二等奖，本人为第二完成人
    2009年：获得全国百篇优秀博士论文提名以及陕西省优秀博士学位论文
    2010年：成果“基于数论方法的伪随机二进制数列研究” 获得陕西高等学校科学技术奖一等奖以及陕西省科学技术奖三等奖，本人排名第一
    2012年：获得第十三届霍英东教育基金会青年教师奖
    2012年：成果“算术函数性质研究”获得陕西省科学技术奖二等奖，本人排名第二
    2013年：获得“陕西省青年科技新星”称号

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