Energy-Efficient Deployment of Water Quality Sensor Networks

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.

Screening of Cellulase Producing Fungus ZDTJ097-1-(7) from Bohai Bay and Its Yielding Conditions

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）.

On Sums of a Prime, and a Square of Prime, and a κ-power of Prime

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

On infinite arithmetic progressions in sumsets

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.

On the saturation number for singular cubic surfaces

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.

The Exceptional Set in Hua's Theorem for Three Squares of 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 results in this direction.

The Ternary Goldbach Problem with Primes in Arithmetic Progressions

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.

Hua's Theorem on Prime Squares in Short Intervals

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-Goldbach problem

Values of binary linear forms at prime arguments

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）.

Prime in Quadratic Progressions on Average

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.

Quadratic forms connected with Fourier coefficients of Maass cusp forms

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

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

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.

Hua's Theorem on Five Almost Equal Prime Squares

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.

Sums of nine almost equal prime cubes

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.

On Sums of Sparse Prime Subsets

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.

An Additive Problem with Primes in Arithmetic Progressions

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.

The Exceptional Set in the Two Prime Squares and a Prime Problem

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.

Some New Results in Waring's Problem

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).