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Hua's Theorem on prime Squares in Short Intervals

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Acta Mathematica Sinica,English Series 2000年第4期16卷 669-690页

作者： Jianya Liu Tao Zhan Department of Mathematics. Shandong University. Jinan 250100. P. R. China Department of Mathematics Shandong University Jinan 250100 P. R. China

It is proved that every large integer N≡5（mod24）can be written as N=p12+…+p52 with each prime pj satisfying |pJ-（N/5|）1/2≤N11/23.This gives a short interval version of Hua’s theorem on the quadratic Waring-Gol... 详细信息

关键词： Waring-Goldbach problem Hua’s theorem prime Circle method

On a Class of prime Entire Functions

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Acta Mathematica Sinica,English Series 2009年第10期25卷 1647-1652页

作者： Kuldeep Singh CHARAK Ilpo LAINE Department of Mathematics University of Jammu Department of Physics and Mathematics University of Joensuu

In this note it is proved that entire functions of the form Fa（z）=H（z）-aα（z）where H andα are entire functions, with α having at least one zero, H＇ and α＇having no common zeros and T（r, α） = S（r, H）, are prime in entire sense for most values of a. The class of these functions is seen to contain examples of both periodic and non-periodic prime entire functions found by Noda, Qiao, Urabe and by Singh and Charak. Another result due to Singh and Charak will be improved as well.

关键词： meromorphic function prime right-primeness value distribution

On prime Spectrum of Maximal Subgroups in Finite Groups

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Algebra Colloquium 2018年第4期25卷 579-584页

作者： Chi Zhang Wenbin Guo Natalia V.Maslova Danila O.Revin Department of Mathematics University of Science and Technology of ChinaHefei 230026China Krasovskii Institute of Mathematics and Mechanics UB RAS and Ural Federal University Yekaterinburg 620990Russia Sobolev Institute of Mathematics SB RAS and Novosibirsk State University Novosibirsk 630090Russia

For a positive integer n,we denote byπ(n)the set of all prime divisors of *** a finite group G,the setπ(G):=π(|G|)is called the prime spectrum of *** M 详细信息

For a positive integer n,we denote byπ(n)the set of all prime divisors of *** a finite group G,the setπ(G):=π(|G|)is called the prime spectrum of *** M

关键词： finite group finite simple group prime spectrum maximal subgroup

On a Diophantine Inequality Involving prime Numbers (Ⅲ)

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Acta Mathematica Sinica,English Series 1999年第3期15卷 387-394页

作者： Yingchun Cai Department of Mathematics, Shanghai University, Shanghai 201800, P. R. China Department of Mathematics Shanghai University Shanghai P. R. China

Let 10 such that for each real number N>N（c） the inequality |p1c+p2c+p3c-N|-（1/c）（11/10-c）logc1 N is solvable in prime numbers p1, p2, p3, where c1 is some absolute positive constant.

关键词： prime Inequality Exponential sum

On Certain Identities with Automorphisms on Lie Ideals in prime and Semiprime Rings

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Algebra Colloquium 2019年第1期26卷 93-104页

作者： Vincenzo De Filippis Nadeem ur Rehman Department of Engineering University of Messina 98166 Messina Italy Department of Mathematics Aligarh Muslim University Aligarh India

Let R be a prime ring of characteristic different from 2, Z(R) its center, L a Lie ideal of R, and m, n, s, t≥> 1 fixed integers with t ≤ m + n + s. Suppose that a is a non-trivial automorphism of R and let φ(x,y)=[x,y]^t -[x,y]^m[α([x,y]),[x,y]^n[x,y]^s. Thus,(a)if φ(u, v)= 0 for any u,v∈L, then L■Z(R);(b) if φ(u,v)∈ Z(R) for any u,v∈L, then either L■Z(R) or R satisfies S4, the standard identity of degree 4. We also extend the results to semiprime rings.

关键词： auto morphism (semi-) prime ring Lie ideal

The distribution of the zeros of L-functions and the least prime in some arithmetic progression

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Science China Mathematics 2000年第9期43卷 937-944页

作者：蒙在照 Department of Mathematics and Institute of Mathematics Peking University Beijing 100871 China

This paper gives some new estimations to the distribution of the zeros of L-functions and proves that the least prime in an arithmetic progression with a prime differenceq is ?q 4.5.

关键词： distribution of zeros least prime Laplace transform.

Explore the dominant factor in prime editing via a view of DNA processing

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Synthetic and Systems Biotechnology 2023年第3期8卷 371-377页

作者： Zhimeng Xu Dacheng Ma Houzhen Su Xiaodong Jia Yinqing Li Yinying Lu Zhen Xie MOE Key Laboratory of Bioinformatics and Bioinformatics Division Center for Synthetic and System BiologyDepartment of AutomationBeijing National Research Center for Information Science and TechnologyTsinghua UniversityBeijing100084China Research Center for Biological Computation Zhejiang LaboratoryHangzhou311100China Comprehensive Liver Cancer Centre The Fifth Medical Center of PLA General HospitalBeijingChina School of Pharmaceutical Sciences IDG/McGovern Institute for Brain ResearchTsinghua UniversityBeijingChina

prime editing is a revolutionary gene-editing method that is capable of introducing insertions,deletions and base substitutions into the ***,the editing efficiency of prime Editor(PE)is limited by the DNA repair ***,we show that overexpression of the flap structure-specific endonuclease 1(FEN1)and the DNA ligase 1(LIG1)increases the efficiency of prime editing,which is similar to the dominant negative mutL homolog 1(MLH1dn).In addition,MLH1 is still the dominant factor over FEN1 and LIG1 in prime *** results help to further understand the relationship of proteins involved in prime editing and envisage future directions for the development of PE.

关键词： process. prime directions

On Sums of a prime and Four prime Squares in Short Intervals

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Acta Mathematica Sinica,English Series 2008年第8期24卷 1291-1302页

作者： Guang Shi LU Xian Meng MENG Department of Mathematics Shandong University Ji'nan 250100 P. R. China Department of Statistics and Mathematics Shandong Finance Institute Ji'nan 250014 P. R. China

In this paper, we prove that each sufficiently large integer N ≠1（mod 3） can be written as N=p＋p1^2＋p2^2＋p3^2＋p4^2, with｜p-N/5｜≤U,｜pj-√N/5｜≤U,j=1,2,3,4,where U=N^2/20＋c and p,pj are primes.

关键词： exponential sums over primes circle method prime

Sums of five almost equal prime squares II

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Science China Mathematics 1998年第7期41卷 710-722页

作者：刘建亚展涛 1. Department of Mathematics Shandong University 250100 Jinan China

It is proved that every large integerN≡5 (mod 24) can be written as $N = p_1^2 + ... + p_5^2 $ with each primep j satisfying $|p_j - \sqrt {N/5} | \leqslant N^{\frac{{12}}{{25}} + E} $ , which gives a short interval ... 详细信息

关键词： prime circle method zero density estimate large sieve.