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Waring−Goldbach problem for one prime power and four prime cubes under Riemann Hypothesis: 《Frontiers of Mathematics in China》2023年第2期139-146,共8页Xiaoming PAN Liqun HU; the National Natural Science Foundation of China(Grant No.11761048);the Natural Science Foundation of Jiangxi Province for Distinguished Young Scholars(Grant No.20212ACB211007);Natural Science Foundation of Jiangxi Province(Grant No.20224BAB201001).; Let k≥1 be an integer.Assume that RH holds.In this paper we prove that a suitable asymptotic formula for the average number of representations of integers n=p^(k)_(1)+p^(3)_(2)+p^(3)_(3)+p^(3)_(4)+p^(3)_(5),where p_(...; 关键词：Hardy−Littlewood method Waring−Goldbach problem Riemann Hypothesis short intervals

Rational design of stratified material with spatially separated catalytic sites as an efficient overall water-splitting photocatalyst被引量：1: 《Chinese Journal of Catalysis》2021年第6期1040-1050,共11页Yi-Lei Li Xiao-Jing Wang Ying-Juan Hao Jun Zhao Ying Liu Hui-Ying Mu Fa-Tang Li; 国家自然科学基金(21776059);河北省杰出青年自然科学基金(B2015208010).; The development of metal sulfide catalysts with remarkable activity toward efficient overall photocatalytic water splitting remains challenging owing to the dominant charge recombination and deficient catalytic active...; 关键词：Stratified material Hollow cubes Overall water splitting Anion/cation exchange Spatially separated site

Decomposition of the Sum of Cubes, the Sum Raised to the Power of Four and Codeviance: 《Applied Mathematics》2020年第10期1013-1020,共8页Fabio Manca Claudia Marin; The purpose of this paper is to achieve decomposition formulas of sums regarding deviation cubes, the sum of deviation raised to the power of four and codeviance, because they allow to evaluate the contribution of dif...; 关键词：Decomposition Formulas Deviation Cubes Codeviance Decomposition

Matchings extend to Hamiltonian cycles in hyper cubes with faulty edges被引量：2: 《Frontiers of Mathematics in China》2019年第6期1117-1132,共16页Xie-Bin CHEN; The work was supported by the National Natural Science Foundation of China(Grant No.11401290).; We consider the problem of existence of a Hamiltonian cycle containing a matching and avoiding some edges in an n-cubc Qn,and obtain the following results.Let n≥3,MСE(Qn),and FСE(Qn)\M with 1≤|F|≤2n-4-|M|.If M is...; 关键词：HYPERCUBE Hamiltonian cycle fault tolerance matching interconnection network

Slim exceptional set for sums of two squares, two cubes, and two biquadrates of primes: 《Frontiers of Mathematics in China》2019年第5期1017-1035,共19页Rui ZHANG; The author would like to express the most sincere gratitude to Prof.Zhixin Liu for his valuable advice and constant encouragement;This work was supported by the National Natural Science Foundation of China(Grant No.11871367).; We prove that,with at most O(N17/192+ε)exceptions,all even positive integers up to N are expressible in the form P1^2+P2^2+P3^3+P5^4+P6^4,where Pi,P2,……,P6 are prime numbers.This gives large improvement of a recent...; 关键词：Waring-Goldbach problem circle method exceptional set

Synergistic effects of CuO and Au nanodomains on Cu_2O cubes for improving photocatalytic activity and stability被引量：5: 《Chinese Journal of Catalysis》2019年第1期105-113,共9页Denghui Jiang Yuegang Zhang Xinheng Li; supported by National Natural Science Foundation of China(21573263,21872157,51402346);National Key Research and Development Program of China from Ministry of Science and Technology of China(2016YFE0105700);Jiangsu Provincial Fundamental Research Foundation of China(BK20151236);Henan provincial co-operation and open foundation(60);China Postdoctoral Science Foundation(2018M632984)~~; Cu2O is a promising photocatalyst,but it suffers from poor photocatalytic activity and stability,especially for Cu2O cubes.Herein,we report the deposition of CuO and Au nanodomains on Cu2O cubes to form dual surface h...; 关键词：Cuprous oxide Photocatalytic activity STABILITY Sequential surface engineering Charge transfer

On the Waring-Goldbach Problem for Six Cubes and Two Biquadrates: 《Chinese Annals of Mathematics,Series B》2018年第6期1033-1046,共14页Sanying SHI Li LIU; supported by the National Natural Science Foundation of China(No.11201107);the China Scholarship Council; Let Pr denote an almost prime with at most r prime factors, counted according to multiplicity. In the present paper, it is proved that for any sufficiently large even integer n, the equation n=x^3＋p1^3＋p2^3＋p3^3＋p...; 关键词：Waring-Goldbach problem Hardy-Littlewood method Sieve theory

Fabrication of zinc-based coordination polymer nano-cubes and post-modification through copper decoration被引量：1: 《Nano Research》2018年第11期5890-5901,共12页Ngoc Minh Tran Hien Duy Mai Hyojong Yoo

On the Addition of Two Cubes of Units and Nonunits mod pα: 《Journal of Mathematical Research with Applications》2017年第3期274-280,共7页Cuifang SUN Zhi CHENG; Supported by the Research Culture Fundation of Anhui Normal University(Grant No.2014xmpy11);the National Natural Science Foundation of China(Grant No.11471017); Let p ≡ 2（mod 3） be an odd prime and α be a positive integer. In this paper,for any integer c, we obtain a formula for the number of solutions of the cubic congruence x^3＋ y^3≡ c（mod p~α） with x, y units, non...; 关键词：residue classes cubes of units exponential sum

Strictly Ergodic Models Under Face and Parallelepiped Group Actions: 《Communications in Mathematics and Statistics》2017年第1期93-122,共30页Wen Huang Song Shao Xiangdong Ye; NNSF for Distinguished Young Schooler(11225105);all authors aresupported by NNSF of China(11371339,11431012,11571335)and by the Fundamental Research Fundsfor the Central Universities.; The Jewett-Krieger theorem states that each ergodic system has a strictlyergodic topological model.In this article,we show that for an ergodic system onemay require more properties on its strictly ergodic model.For ex...; 关键词：Ergodic averages Model CUBES Face transformations

CUBES