Water quality sensor networks are promising tools for the exploration of oceans.Some key areas need to be monitored effectively.Water quality sensors are deployed randomly or uniformly,however,and understanding how to...Water quality sensor networks are promising tools for the exploration of oceans.Some key areas need to be monitored effectively.Water quality sensors are deployed randomly or uniformly,however,and understanding how to deploy sensor nodes reasonably and realize effective monitoring of key areas on the basis of monitoring the whole area is an urgent problem to be solved.Additionally,energy is limited in water quality sensor networks.When moving sensor nodes,we should extend the life cycle of the sensor networks as much as possible.In this study,sensor nodes in non-key monitored areas are moved to key areas.First,we used the concentric circle method to determine the mobile sensor nodes and the target locations.Then,we determined the relationship between the mobile sensor nodes and the target locations according to the energy matrix.Finally,we calculated the shortest moving path according to the Floyd algorithm,which realizes the redeployment of the key monitored area.The simulation results showed that,compared with the method of direct movement,the proposed method can effectively reduce the energy consumption and save the network adjustment time based on the effective coverage of key areas.展开更多
Abstract [ Objective ] This study aimed to screen a marine-derived cellulase producing filamentous fungus and to investigate the yielding conditions and celluase activity. [ Method] A total of 25 marine-derived filame...Abstract [ Objective ] This study aimed to screen a marine-derived cellulase producing filamentous fungus and to investigate the yielding conditions and celluase activity. [ Method] A total of 25 marine-derived filamentous fungus were screened out of from Bohai Bay, and one producing cellulase was obtained through Congo red transparent circle method and cellulase activity assay. After that, optimum conditions were examined for cellulase producing and catalyzing. [ Result] CMC-Na could induce ZDTJ097-1-(7 ) strain to produce filter paper cellulase, CMC cellulase and 13-glucosidase. The optimum conditions for ZDTJ097-1-(7) to produce en- zymes were 0.5% CMC-Na, 0. 2% NH4NO3 , pH 6.0 at 25 ℃. [ Conclusion] This study provided reference for furfller development and utilization of cellulase produ-cing fungus ZDTJ097-1-(7).展开更多
In 1923, Hardy and Littlewood[1] conjectured that each integer n can be written asp+m12+ m22 = n,and Linnik[2,3] proved that this conjecture is true. But if these mi with i = 1,2 are restricted to primes Pi, the corre...In 1923, Hardy and Littlewood[1] conjectured that each integer n can be written asp+m12+ m22 = n,and Linnik[2,3] proved that this conjecture is true. But if these mi with i = 1,2 are restricted to primes Pi, the corresponding result is out of reach at present. We consider the following Diophantine equation展开更多
Let k be a positive integer.Denote by D_(1/k)the least integer d such that for every set A of nonnegative integers with the lower density 1/k,the set(k+1)A contains an infinite arithmetic progression with difference a...Let k be a positive integer.Denote by D_(1/k)the least integer d such that for every set A of nonnegative integers with the lower density 1/k,the set(k+1)A contains an infinite arithmetic progression with difference at most d,where(k+1)A is the set of all sums of k+1 elements(not necessarily distinct)of A.Chen and Li(2019)conjectured that D_(1/k)=k~2+o(k~2).The purpose of this paper is to confirm the above conjecture.We also prove that D_(1/k)is a prime for all sufficiently large integers k.展开更多
We investigate the distribution of rational points on singular cubic surfaces,whose coordinates have few prime factors.The key tools used are universal torors,the circle method and results on linear equations in primes.
It is proved that with at most O(N^(11/12+ε)) exceptions, all positiveintegers n ≤ N satisfying some necessary congruence conditions are the sum of three squares ofprimes. This improves substantially the previous re...It is proved that with at most O(N^(11/12+ε)) exceptions, all positiveintegers n ≤ N satisfying some necessary congruence conditions are the sum of three squares ofprimes. This improves substantially the previous results in this direction.展开更多
In this paper, we give an explicit numerical upper bound for the moduli of arithmetic progressions, in which the ternary Goldbach problem is solvable. Our result implies a quantitative upper bound for the Linnik const...In this paper, we give an explicit numerical upper bound for the moduli of arithmetic progressions, in which the ternary Goldbach problem is solvable. Our result implies a quantitative upper bound for the Linnik constant.展开更多
It is proved that every large integer N≡5(mod24)can be written as N=p<sub>1</sub><sup>2</sup>+…+p<sub>5</sub><sup>2</sup> with each prime p<sub>j</sub> s...It is proved that every large integer N≡5(mod24)can be written as N=p<sub>1</sub><sup>2</sup>+…+p<sub>5</sub><sup>2</sup> with each prime p<sub>j</sub> satisfying |p<sub>J</sub>-(N/5|)<sup>1/2</sup>≤N<sup>11/23</sup>.This gives a short interval version of Hua’s theorem on the quadratic Waring-Goldbach problem展开更多
We investigate the exceptional set of real numbers not close to some value of a given binary linear form at prime arguments. Let λ1 and λ2 be positive real numbers such that λ1/λ2 is irrational and algebraic. For ...We investigate the exceptional set of real numbers not close to some value of a given binary linear form at prime arguments. Let λ1 and λ2 be positive real numbers such that λ1/λ2 is irrational and algebraic. For any (C, c) well-spaced sequence v and δ 〉 0, let E(v, X,δ ) denote the number of ν∈v with v ≤ X for which the inequality |λ1P1 + λ2P2 - v| 〈 v-δ has no solution in primes P1,P2. It is shown that for any ε 〉 0, we have E(V, X, δ) 〈〈 max(X3/5+2δ+ε, X1/3+4/3δ+ε).展开更多
In this paper we study the distribution of primes in quadratic progressions on average. Our result improves a previous result of Baier and Zhao in some aspects.
For the normalized Fourier coefficients of Maass cusp forms λ(n) and the normalized Fourier coefficients of holomorphic cusp forms a(n), we give the bound of
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.
In this paper we sharpen Hua's result by proving that each sufficiently large integer N congruent to 5 modulo 24 can be written as N=p1^2+p2^2+p3^2+p4^2+p5^2,with │pj-√N/5│≤U=N^1/2-1/28+ε,where pj are primes.
We prove that each sufficiently large odd integer N can be written as sum of the form N = p1^3 +p2^3 +... +p9^3 with [pj - (N/9)^1/31 ≤ N^(1/3)-θ, where pj, j = 1,2,...,9, are primes and θ = (1/51) -ε.
For arbitrary c00, if A is a subset of the primes less than x with cardinality δx(logx)-1, δ≥(logx)-c0, then there exists a positive constant c such that the cardinality of A+A is larger than cδx(loglogx)-1.
In this paper, we extend a classical result of Hua to arithmetic progressionswith large moduli. The result implies the Linnik Theorem on the least prime in an arithmeticprogression.
In this paper we prove that, with at most O(N^5/12+ε) exceptions, all positive odd integers n ≤ N with n ≡ 0 or 1(mod 3) can be written as a sum of a prime and two squares of primes.
Let G(k) denote the smallest number s such that every sufficiently large natural number is the sum of, at most, s k-th powers of natural numbers. In this paper, we give new bounds for G(12), G(13) and G(19).
基金This research was funded by the National Natural Science Foundation of China(Grant No.61802010)National Social Science Fund of China(Grant No.19BGL184)+1 种基金Beijing Excellent Talent Training Support Project for Young Top-Notch Team(Grant No.2018000026833TD01)and Hundred-Thousand-Ten Thousand Talents Project of Beijing(Grant No.2020A28).
文摘Water quality sensor networks are promising tools for the exploration of oceans.Some key areas need to be monitored effectively.Water quality sensors are deployed randomly or uniformly,however,and understanding how to deploy sensor nodes reasonably and realize effective monitoring of key areas on the basis of monitoring the whole area is an urgent problem to be solved.Additionally,energy is limited in water quality sensor networks.When moving sensor nodes,we should extend the life cycle of the sensor networks as much as possible.In this study,sensor nodes in non-key monitored areas are moved to key areas.First,we used the concentric circle method to determine the mobile sensor nodes and the target locations.Then,we determined the relationship between the mobile sensor nodes and the target locations according to the energy matrix.Finally,we calculated the shortest moving path according to the Floyd algorithm,which realizes the redeployment of the key monitored area.The simulation results showed that,compared with the method of direct movement,the proposed method can effectively reduce the energy consumption and save the network adjustment time based on the effective coverage of key areas.
基金Supported by the National Natural Science Foundation of China(30971904)
文摘Abstract [ Objective ] This study aimed to screen a marine-derived cellulase producing filamentous fungus and to investigate the yielding conditions and celluase activity. [ Method] A total of 25 marine-derived filamentous fungus were screened out of from Bohai Bay, and one producing cellulase was obtained through Congo red transparent circle method and cellulase activity assay. After that, optimum conditions were examined for cellulase producing and catalyzing. [ Result] CMC-Na could induce ZDTJ097-1-(7 ) strain to produce filter paper cellulase, CMC cellulase and 13-glucosidase. The optimum conditions for ZDTJ097-1-(7) to produce en- zymes were 0.5% CMC-Na, 0. 2% NH4NO3 , pH 6.0 at 25 ℃. [ Conclusion] This study provided reference for furfller development and utilization of cellulase produ-cing fungus ZDTJ097-1-(7).
文摘In 1923, Hardy and Littlewood[1] conjectured that each integer n can be written asp+m12+ m22 = n,and Linnik[2,3] proved that this conjecture is true. But if these mi with i = 1,2 are restricted to primes Pi, the corresponding result is out of reach at present. We consider the following Diophantine equation
基金supported by National Natural Science Foundation of China(Grant Nos.12171243 and 11922113)the National Key Research and Development Program of China(Grant No.2021YFA1000700)。
文摘Let k be a positive integer.Denote by D_(1/k)the least integer d such that for every set A of nonnegative integers with the lower density 1/k,the set(k+1)A contains an infinite arithmetic progression with difference at most d,where(k+1)A is the set of all sums of k+1 elements(not necessarily distinct)of A.Chen and Li(2019)conjectured that D_(1/k)=k~2+o(k~2).The purpose of this paper is to confirm the above conjecture.We also prove that D_(1/k)is a prime for all sufficiently large integers k.
文摘We investigate the distribution of rational points on singular cubic surfaces,whose coordinates have few prime factors.The key tools used are universal torors,the circle method and results on linear equations in primes.
基金Supported by The National Science Foundation(Grants #10125101 and #10131010)by a Ministry of Education Major Grant Program in Sciences and Technology
文摘It is proved that with at most O(N^(11/12+ε)) exceptions, all positiveintegers n ≤ N satisfying some necessary congruence conditions are the sum of three squares ofprimes. This improves substantially the previous results in this direction.
基金supported by the National Natural Science Foundation of China(Grant Nos.10125101&10531060)a Major Grant Program in Science and Technology by the Ministry of EducationTianyuan Mathematics Foundation(Grant No.10526028).
基金Project supported partially by NNSF of China NSF of Henan Province
文摘In this paper, we give an explicit numerical upper bound for the moduli of arithmetic progressions, in which the ternary Goldbach problem is solvable. Our result implies a quantitative upper bound for the Linnik constant.
基金Supported by MCSEC and the National Natural Science Foundation (Grant No. 19701019) Supported by MCSFC and the National Natural Science Foundation
文摘It is proved that every large integer N≡5(mod24)can be written as N=p<sub>1</sub><sup>2</sup>+…+p<sub>5</sub><sup>2</sup> with each prime p<sub>j</sub> satisfying |p<sub>J</sub>-(N/5|)<sup>1/2</sup>≤N<sup>11/23</sup>.This gives a short interval version of Hua’s theorem on the quadratic Waring-Goldbach problem
文摘We investigate the exceptional set of real numbers not close to some value of a given binary linear form at prime arguments. Let λ1 and λ2 be positive real numbers such that λ1/λ2 is irrational and algebraic. For any (C, c) well-spaced sequence v and δ 〉 0, let E(v, X,δ ) denote the number of ν∈v with v ≤ X for which the inequality |λ1P1 + λ2P2 - v| 〈 v-δ has no solution in primes P1,P2. It is shown that for any ε 〉 0, we have E(V, X, δ) 〈〈 max(X3/5+2δ+ε, X1/3+4/3δ+ε).
基金Supported by National Natural Science Foundation of China (Grant No. 10701048), Shandong Province Natural Science Foundation (Crant No. ZR2009AM007), and IIFSDU
文摘In this paper we study the distribution of primes in quadratic progressions on average. Our result improves a previous result of Baier and Zhao in some aspects.
基金Acknowledgements This work was supported in part by the Natural Science Foundation of Jiangxi Province (Nos. 2012ZBAB211001, 20132BAB2010031).
文摘For the normalized Fourier coefficients of Maass cusp forms λ(n) and the normalized Fourier coefficients of holomorphic cusp forms a(n), we give the bound of
基金the National Natural Science Foundation of China (Grant No.10701048)
文摘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.
基金Supported by Tianyuan Mathematics Foundation(Grant No.10526028)the NSF of China(Grant Nos.10301018,10571107)
文摘In this paper we sharpen Hua's result by proving that each sufficiently large integer N congruent to 5 modulo 24 can be written as N=p1^2+p2^2+p3^2+p4^2+p5^2,with │pj-√N/5│≤U=N^1/2-1/28+ε,where pj are primes.
文摘We prove that each sufficiently large odd integer N can be written as sum of the form N = p1^3 +p2^3 +... +p9^3 with [pj - (N/9)^1/31 ≤ N^(1/3)-θ, where pj, j = 1,2,...,9, are primes and θ = (1/51) -ε.
基金Supported by National Natural Science Foundation of China (Grant No.11271249)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20120073110059)
文摘For arbitrary c00, if A is a subset of the primes less than x with cardinality δx(logx)-1, δ≥(logx)-c0, then there exists a positive constant c such that the cardinality of A+A is larger than cδx(loglogx)-1.
基金Project supported by National Natural Science Foundation(No.10171027,60373039)of ChinaResearch Foundation(No.XK01071)of Henan University
文摘In this paper, we extend a classical result of Hua to arithmetic progressionswith large moduli. The result implies the Linnik Theorem on the least prime in an arithmeticprogression.
基金Project supported by National Natural Science Foundation(No. 90304009)Foundation of Qufu Normal University for Ph.D.
文摘In this paper we prove that, with at most O(N^5/12+ε) exceptions, all positive odd integers n ≤ N with n ≡ 0 or 1(mod 3) can be written as a sum of a prime and two squares of primes.
文摘Let G(k) denote the smallest number s such that every sufficiently large natural number is the sum of, at most, s k-th powers of natural numbers. In this paper, we give new bounds for G(12), G(13) and G(19).