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The Number of Solutions of Certain Equations over Finite Fields

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Wuhan University Journal of Natural Sciences 2022年第1期27卷 49-52页

作者： hu shuangnian LIU Jianghan QIN Zhentao School of Mathematics and Statistics Nanyang Institute of TechnologyNanyang 473004HenanChina College of Computer and Information Science Southwest UniversityChongqing 400715China School of Mathmatics and Computer Panzhihua UniversityPanzhihua 617000SichuanChina

Let s be a positive integer,p be an odd prime,q=p^(s),and let F_(q)be a finite field of q *** N_(q)be the number of solutions of the following equations:(x_(1)^(m_(1))+x_(2)^(m_(2))+…+x_(n)^(m_(n)))^(k)=x_(1)x_(2)…x_(n)x^(k_(n+1))_(n+1)…x^(k_(t))_(t)over the finite field F_(q),with n≥2,t>n,k,and k_(j)(n+1≤j≤t),m_(i)(1≤i≤n)are positive *** this paper,we find formulas for N_(q)when there is a positive integer l such that dD|(p^(l)+1),where D=1 cm[d_(1),…,d_(n)],d=gcd(n∑i=1M/m_(i)-kM,(q-1)/D),M=1 cm[m_(1),…,m_(n)],d_(j)=gcd(m_(j),q-1),1≤j≤*** we determine N_(q)explicitly under certain *** extends Markoff-hurwitz-type equations over finite field.

关键词： finite field rational point diagonal equation Markoff-hurwitz-type equations

Note on the Number of Solutions of Cubic Diagonal Equations over Finite Fields

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Wuhan University Journal of Natural Sciences 2023年第5期28卷 369-372页

作者： hu shuangnian WANG Shihan LI Yanyan NIU Yujun School of Mathematics and Physics Nanyang Institute of TechnologyNanyang 473004HenanChina Faculty of Science and Technology Beijing Normal University-Hong Kong Baptist University United International CollegeZhuhai 519087GuangdongChina School of Information Engineering Nanyang Institute of TechnologyNanyang 473004HenanChina

Let Fqbe the finite field,q=p^(k),with p being a prime and k being a positive *** F_(q)^(*)be the multiplicative group of Fq,that is F_(q)^(*)=F_(q){0}.In this paper,by using the Jacobi sums and an analog of Hasse-Davenport theorem,an explicit formula for the number of solutions of cubic diagonal equation x_(1)^(3)+x_(2)^(3)+…+x_(n)^(3)=c over Fqis given,where c∈F_(q)^(*)and p≡1(mod 3).This extends earlier results.

关键词： finite field rational point diagonal equations Jacobi sums

Further Results on Generalized LCM Matrices

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Wuhan University Journal of Natural Sciences 2017年第1期22卷 1-4页

作者： hu shuangnian LIAN Dongyan DIAO Tianbo LIU Jing School of Mathematics and Statistics Nanyang Institute of Technology School of Mathematics and Statistics Zhengzhou University

Let S={x_1,x_2,...,x_n } be a set of n distinct positive integers and f be an arithmetic ***（f[S]）（resp.（ f[S]））,we denote the n＊n matrix whose i,j entry is Σ[x_i,x_j]｜l l∈S f（l）（resp.Σx∈Sf（x）-Σ x_i,｜l l∈S f（l）-Σ x_j,｜l l∈S f（l）＋Σ[x_i,x_j]｜l l∈S f（l））.In this paper,we first investigate the structures of the matrices （ f[S]） and（ f[S]）,then we give the formulae for the determinants of these *** extend the results obtained by Bege in ***,we give two examples to demonstrate the validity of our main results.

关键词： least common multiple (LCM) matrix arithmeticfunction determinant

Research on a Class of Equations overFinite Fields

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Wuhan University Journal of Natural Sciences 2018年第6期23卷 493-497页

作者： hu shuangnian DIAO Tianbo NIU Yujun WU Honge School of Mathematics and Statistics Nanyang Institute of Technology

Let Fq stand for the finite field of odd characteristic p with q elements（q=pn,n∈N）and Fq＊ denote the set of all the nonzero elements of *** this paper,by using the augmented degree matrix and the result given by Cao,we obtain a formula for the number of rational points of the following equation over Fq：f（x 1,x 2,...,x n）=（a1 x1 x2d＋a2 x2 x3d...＋a（n-1）x（n-1）xnd＋an xn x1d）λ-bx1（d1）x2d2...xn（dn）,with ai,b∈Fq＊,n≥2,λ〉0 being positive integers,and d,di being nonnegative integers for 1≤i *** technique can be applied to the polynomials of the form h1λ=h2 with λ being positive integer and h1,h2∈Fq[x 1,x 2,...,x n].It extends the results of the Markoff-hurwitz-type equations.

关键词： finite field rational point degree matrix

有限域上广义Markoff-hurwitz-type方程的有理点个数（英文）

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浙江大学学报（理学版） 2017年第5期44卷 516-519,537页

作者：胡双年李艳艳南阳理工学院数学与统计学院河南南阳473004 郑州大学数学与统计学院河南郑州450001 南阳理工学院电子与电气工程学院河南南阳473004

设N_q表示有限域F_q上广义Markoff-hurwitz-type方程的有理点个数(a_1x_1^(m_1)+a_2x_2^(m_2)+…+a_nx_n^(m_n))~k=cx_1^(k_1)x_2^(k_2)…x_t^(k_t),其中n≥2,m_i,k,k_j和t≥n是正整数,a_i,c属于F_q~*,其中1≤i≤n,1≤j≤t.最近有研究推广了Carlitz的结果,给出了上述方程当k=k_1=…=k_t=1时的有理点个数.当未定元的指数满足一定条件时,本文给出了上述广义方程的有理点个数,推广了已有结论.

关键词：有限域有理点 Markoff-hurwitz-type方程

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伪双曲方程一个非协调混合元方法超收敛分析

信阳师范学院学报（自然科学版） 2018年第1期31卷 21-26页

作者：马戈胡双年南阳理工学院数学与统计学院河南南阳473004

基于非协调EQrot1元和零阶R-T元针对伪双曲方程,建立了一个自然满足B-B条件的非协调低阶混合元逼近格式.借助单元插值算子的特殊性质、导数转移技巧和插值后处理技术,在半离散格式下给出了原始变量在H1-模和中间变量在L2-模意义下的O(h2... 详细信息

基于非协调EQrot1元和零阶R-T元针对伪双曲方程,建立了一个自然满足B-B条件的非协调低阶混合元逼近格式.借助单元插值算子的特殊性质、导数转移技巧和插值后处理技术,在半离散格式下给出了原始变量在H1-模和中间变量在L2-模意义下的O(h2)阶超逼近性与整体超收敛结果.同时,对于一个二阶全离散格式得到了原始变量H1-模的O(h2+τ2)超逼近性和中间变量L2-模的O(h+τ2)最优误差估计.

关键词：伪双曲方程非协调混合有限元半离散和全离散超逼近和超收敛

Overcoming adaptive resistance in AML by synergistically targeting FOXO3A-GNG7-mTOR axis with FOXO3A inhibitor Gardenoside and rapamycin

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Genes & Diseases 2024年第1期11卷 397-412页

作者： Zhe Chen Qian Guo Shichen huang Lei Li Feng Wu Zhilong Liu Zhigang Li Tao Chen Guanbin Song shuangnian Xu Jieping Chen Yu Hou Department of Hematology Southwest HospitalThird Military Medical University(Army Medical University)Chongqing 400038China Institute of Life Sciences Chongqing Medical UniversityChongqing 400016China Key Laboratory of Biorheological Science and Technology Ministry of EducationCollege of BioengineeringChongqing UniversityChongqing 400044China Chongqing Foreign Language School Chongqing 400039China

Therapeutic targeting FOxO3A(a forkhead transcription factor)represents a prom-ising strategy to suppress acute myeloid leukemia(AML).However,the effective inhibitors that target FOXO3A are lacking and the adaptive response signaling weakens the cytotoxic effect of FOxO3A depletion on AML ***,we show that FOxO3A deficiency induces a compensa-tory response involved in the reactive activation of mTOR that leads to signaling rebound and adaptive *** metabolism acts downstream of mTOR to provoke activa-tion of JNK/c-JUN via reactive oxygen species(ROS).At the molecular level,FOXO3A directly binds to the promoter of G protein gamma subunit 7(GNG7)and preserves its expression,while GNG7 interacts with mTOR and restricts phosphorylated activation of ***,combinatorial inhibition of FOXO3A and mTOR show a synergistic cytotoxic effect on AML cells and prolongs survival in a mouse model of *** a structure-based virtual screening,we report one potent small-molecule FOxO3A inhibitor(Gardenoside)that exhibits a strong effect of anti-FOXO3A DNA *** synergizes with rapamycin to substantially reduce tumor burden and extend survival in AML patient-derived xenograft *** results demonstrate that mTOR can mediate adaptive resistance to FOxO3A inhibition and validate a combinatorial approach for treating AML.

关键词： AML Combinatorial inhibition FOXO3A GNG7 mTOR

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基于天空区域改进的暗通道先验算法研究

实验技术与管理 2019年第9期36卷 120-123页

作者：吴宏锷胡双年南阳理工学院数学与统计学院

针对天空区域不满足暗通道先验理论从而导致求解的透射率不够准确、去雾后颜色失真的问题,提出一种基于天空区域改进的暗通道先验算法。首先利用像素的分布规律排除白色物体的干扰,解出准确的大气光,再利用暗通道先验理论估计出图像的... 详细信息

针对天空区域不满足暗通道先验理论从而导致求解的透射率不够准确、去雾后颜色失真的问题,提出一种基于天空区域改进的暗通道先验算法。首先利用像素的分布规律排除白色物体的干扰,解出准确的大气光,再利用暗通道先验理论估计出图像的透射率,然后利用图像的原始信息对透射率进行修正、优化,得到较为准确的透射率图,最后求解得到清晰图像。通过样本实验,说明该算法在细节强度、图像平均梯度和峰值信噪比方面有较好的效果,能作为图像去雾的一种有效辅助手段。

关键词：图像去雾暗通道先验天空区域

定点脉冲信号作用下Duffing-Rayleigh系统的混沌预测

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合肥工业大学学报（自然科学版） 2020年第12期43卷 1718-1722页

作者：牛玉俊乔俊峰胡双年南阳理工学院数理学院河南南阳473004

文章采用摄动法研究了定点脉冲系统的Melnikov方法,得到了定点脉冲系统出现Smale马蹄意义下混沌的必要条件,为定点脉冲系统的混沌研究提供了一种解析工具;利用定点脉冲信号作用下Duffing-Rayleigh系统的混沌预测检验了Melnikov函数的有... 详细信息

文章采用摄动法研究了定点脉冲系统的Melnikov方法,得到了定点脉冲系统出现Smale马蹄意义下混沌的必要条件,为定点脉冲系统的混沌研究提供了一种解析工具;利用定点脉冲信号作用下Duffing-Rayleigh系统的混沌预测检验了Melnikov函数的有效性,并通过数值模拟验证了理论结果的正确性。

关键词：脉冲系统 Melnikov方法摄动法 Duffing-Rayleigh系统混沌预测