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ON PJATECKII-SAPIRO PRIME NUMBER THEOREM

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Chinese Annals of Mathematics,Series B 1994年第1期15卷 9-22页

作者： jia chaohua ACAD SINICA INST MATHBEIJING 100080PEOPLES R CHINA

It is proved that, for 1 < c < e, there are infinitely many primes of the form [n'l.

关键词： Pjateckii-Sapiro theorem Prime number Sieve method.

STATE DERIVATIVE-FREE VARIABLE STRUCTURE MODEL REFERENCE ADAPTIVE CONTROL OF LINEAR PARABOLIC SYSTEMS

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Journal of Systems Science & Complexity 2013年第6期26卷 957-967页

作者： jia chaohua SHAO Zhi-Chao School of Mathematics and Systems Science Beihang University Department of Applied Mathematics School of StatisticsUniversity of International Business and Economics

The problem of constructing a model dimensional parabolic system is considered in this reference adaptive control law for an uncertain 1- article. The controller designed here involves only the plant state but no its derivatives. A priori bounds on the plant＇s uncertain parameters are used to propose switching laws which serve as an adaptive mechanism. The exponential decay to zero of the state error with any prescribed rate is guaranteed by choosing a controller parameter correspondingly. Numerical studies are also presented to illustrate the applicability of the control law.

关键词： Distributed parameter systems model reference adaptive control parabolicsystems.

Kloosterman sums with multiplicative coefficients

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Science China Mathematics 2016年第4期59卷 653-660页

作者： GONG Ke jia chaohua Department of Mathematics Henan University Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of Sciences

Let f(n)be a multiplicative function satisfying |f(n)|≤1,q(≤N^2)be a positive integer and a be an integer with(a,q)= *** this paper,we shall prove that ∑n≤N(n,q)=1f(n)e(an/q)■(1/2)(τ(q)/q)N loglog(6N)+ q^(1/4+ε/2)N^(2/1)(log(6N))^(1/2)+N/(1/2)(loglog(6N)),where n is the multiplicative inverse of n such that nn ≡ 1(mod q),e(x)= exp(2πix),and τ(·)is the divisor function.

关键词： Kloosterman sum multiplicative function finite version of Vinogradov's inequality

Three Primes Theorem in a Short Interval(Ⅶ)

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Acta Mathematica Sinica,English Series 1994年第4期10卷 369-387页

作者： jia chaohua Institute of Mathematics Academia Sinica Beijing China

In this paper,we shall prove that for a sufficiently large odd number N,the equation N=p1+p2+p3,N/3-N（7/12）+ε

关键词：三尸 Math exp

The Greatest Prime Factor of the Integers in a Short Interval (Ⅳ)

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Acta Mathematica Sinica,English Series 1996年第4期12卷 433-445页

作者： jia chaohua Institute of Mathematics Academia Sinica Beijing, 100080 China Institute of Mathematics Academia Sinica Beijing China

Let P（x） denote the greatest prime factor of ∏x1/2n. In this paper, we shall prove that P（x）>x0.728holds true for sufficiently large x.

关键词： Math In The Greatest Prime Factor of the Integers in a Short Interval

On the Decay Property of Solutions of Viscous Burgers Equation with Boundary Feedback

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Journal of Partial Differential Equations 2010年第2期23卷 194-202页

作者： jia chaohua School of Mathematics and System Science Beihang University LMIB of the Ministry of Education Beijing 100191 China.

In this article, we will investigate the viscous Burgers equation with boundary feedback. The existence of the solution is proved by constructing a convergence sequence inductively. Moreover, the decay property of the... 详细信息

关键词： Burgers equation nonlocal boundary maximum principle.

On the inverse problem relative to dynamics of the ω function

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Science China Mathematics 2009年第5期52卷 849-856页

作者： jia chaohua Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Let P be the set of prime numbers and P (n) denote the largest prime factor of integer n > 1. Write C3 = {p1p2p3 : pi ∈ P (i = 1, 2, 3), pi = pj (i = j)}, B3 = {p1p2p3 : pi ∈ P (i = 1, 2, 3), p1 = p2 or p1 = p3 or p2 = p3, but not p1 = p2 = p3}. For n = p1p2p3 ∈ C3 ∪ B3, we define the w function by ω(n) = P (p1 + p2)P (p1 + p3)P (p2 + p3). If there is m ∈ S - C3 ∪ B3 such that ω(m) = n, then we call m S-parent of n. We shall prove that there are infinitely many elements of C3 which have enough C3-parents and that there are infinitely many elements of B3 which have enough C3-parents. We shall also prove that there are infinitely many elements of B3 which have enough B3-parents.

关键词： dynamics prime number ω function

THE GREATEST PRIME FACTOR OF THE INTEGERS IN A SHORT INTERVAL(Ⅰ)

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Chinese Science Bulletin 1987年第7期32卷 500-501页

作者：贾朝华 Department of Mathematics Peking University

Let P（x, y） denote the greatest prime factor of multiply from xx15/26 and P(x,x1/2)>x5/8（see J. London Math. Soc., 1（1969）, 303—306 and J. Indian Math. Soc., 34（1970）, 39—48）. In 1981, Graham improved the ex... 详细信息

关键词： exponent Graham multiply Indian London greatest Vaughan letter Heath

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分布阻尼下非线性梁光滑解的存在性

数学物理学报（A辑） 2011年第2期31卷 273-288页

作者：贾超华冯德兴北京航空航天大学数学与系统科学学院北京100191 “数学、信息与行为”教育部重点实验室北京100191 中国科学院数学与系统科学研究院系统所北京100190

该文研究一个描述梁振动的非线性模型,主要研究该模型在分布阻尼下局部光滑解的存在性,首先应用发展方程理论证明相关线性系统存在光滑解,然后由一系列能量估计结合不动点定理证明所考察的非线性系统局部光滑解的存在性.

关键词：非线性梁分布阻尼发展方程.