Under the assumption of sixth power large.sieve mean-value of Dirichlet L-function, we improve Bombieri＇s theorem in short intervals by virtue of the large sieve method and Heath-Brown＇s identity.
In this paper,Oh liver tissue following short interval successive partial hepatectomy as diver and 112h liver tissue following short interval successive partial hepatectomy as test-er,we used suppression subtracted hy...In this paper,Oh liver tissue following short interval successive partial hepatectomy as diver and 112h liver tissue following short interval successive partial hepatectomy as test-er,we used suppression subtracted hybridization method to construct a high efficiency for-ward subtractive library.From the library we randomly picked 80 clones to analysis.After PCR detection,75 clones were sequenced and they represented 53 expressedsequence tags(EST).Among these clones,9 ESTs was 100%homologous to GenBank and 44 ESTs weren't 100%homologous to GenBank,one of these ESTs suggested a novel gene was found no ho-mologous to GenBank.Construction of the subtractive library lied a basis to clone and analy-sis these up-regulated genes in bulk in liver regeneration.展开更多
Preterm birth and suboptimal fetal growth remain significant perinatal challenges worldwide.Recent data indicate that China's perinatal profile has improved due to reductions in preterm birth rates.However,the cou...Preterm birth and suboptimal fetal growth remain significant perinatal challenges worldwide.Recent data indicate that China's perinatal profile has improved due to reductions in preterm birth rates.However,the country has a 6.5%prevalence of small-for-gestational-age(SGA),ranking fifth globally in total SGA birth numbers^([1,2]).展开更多
The main purpose of this paper is to study the mean value properties of the character sums over the interval [1,p/8） by using the mean value theorems of the Dirichlet L-functions, and give an interesting mean value f...The main purpose of this paper is to study the mean value properties of the character sums over the interval [1,p/8） by using the mean value theorems of the Dirichlet L-functions, and give an interesting mean value formula for this study.展开更多
Letk be a positive integer and n a nonnegative integer,0 〈 λ1,...,λk＋1 ≤ 1 be real numbers and w =（λ1,λ2,...,λk＋1）.Let q ≥ max{[1/λi ]：1 ≤ i ≤ k ＋ 1} be a positive integer,and a an integer coprime to ...Letk be a positive integer and n a nonnegative integer,0 〈 λ1,...,λk＋1 ≤ 1 be real numbers and w =（λ1,λ2,...,λk＋1）.Let q ≥ max{[1/λi ]：1 ≤ i ≤ k ＋ 1} be a positive integer,and a an integer coprime to q.Denote by N（a,k,w,q,n） the 2n-th moment of（b1··· bk c） with b1··· bk c ≡ a（mod q）,1 ≤ bi≤λiq（i = 1,...,k）,1 ≤ c ≤λk＋1 q and 2（b1＋ ··· ＋ bk ＋ c）.We first use the properties of trigonometric sum and the estimates of n-dimensional Kloosterman sum to give an interesting asymptotic formula for N（a,k,w,q,n）,which generalized the result of Zhang.Then we use the properties of character sum and the estimates of Dirichlet L-function to sharpen the result of N（a,k,w,q,n） in the case ofw =（1/2,1/2,...,1/2） and n = 0.In order to show our result is close to the best possible,the mean-square value of N（a,k,q） φk（q）/2k＋2and the mean value weighted by the high-dimensional Cochrane sum are studied too.展开更多
Let P（x） denote the greatest prime factor of ∏<sub>x【n≤x+x<sup>1/2</sup></sub>n. In this paper, we shall prove that P（x）】x<sup>0.728</sup>holds true for sufficiently large x.
In this paper, we study Rényi＇s problem and other related problems about the additive functions in short intervals. As corollaries, we improve Ivic＇s results.
Let the arithmetic function a(n) denote the number of non-isomorphic Abeliangroups of order n;k, positive integer, and x≥0. We setA_k(x)= sum from n≤x a(n)=k to (1)andA_k(x;h) =A_k(x+h)-A_k(x). A. Ivice first invest...Let the arithmetic function a(n) denote the number of non-isomorphic Abeliangroups of order n;k, positive integer, and x≥0. We setA_k(x)= sum from n≤x a(n)=k to (1)andA_k(x;h) =A_k(x+h)-A_k(x). A. Ivice first investigated the distribution of the values of finite non-isomorphicAbelian groups in short intervals. E. Kratzel reduced the problem to estimate theerror term △(1, 2, 3;x) in the three-dimensional multiplicative problem, and furtherimproved Ivice’s result.展开更多
As the fast economic development and urban expansion, it is dififcult for traditional methods to monitor land use changes in short time interval. Moreover, remotely sensed data acquired by optical sensors is often lim...As the fast economic development and urban expansion, it is dififcult for traditional methods to monitor land use changes in short time interval. Moreover, remotely sensed data acquired by optical sensors is often limited by bad weathers and cloud cover. SAR images, such as RADARSAT-1, are an ideal tool for weather-proof observation on ground surface. This paper analyzed the results of land use change detections with time lags of 24, 48 and 72 days according to the period of acquisition dates of RADARSAT-1. The results need a compromise between accuracies and efifciencies related to the time lags. For most of the situation, it is sufifcient of using a time lag of 24 days to obtain accuracy of 60%or above. In some cases of months, a time lag of 48 days is needed. For obtaining higher accuracies, longer time lag such as 72 days is needed.展开更多
The authors regret that due to an oversight,the online version of Fig.5 is missing the sign,here is the correct Fig.5 and its caption.Fig.5:(A)Short interval intracortical inhibition(SICI)and(B)Long interval intracort...The authors regret that due to an oversight,the online version of Fig.5 is missing the sign,here is the correct Fig.5 and its caption.Fig.5:(A)Short interval intracortical inhibition(SICI)and(B)Long interval intracortical inhibition(LICI)in active and sham groups(Median,interquartile range,MEP peak to peak amplitude conditioned/test)of hemiplegic CP patients at baseline(pre)and after intervention.展开更多
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.
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_(...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_(1),p_(2),p_(3),p_(4),p_(5)are prime numbers.This expands the previous results.展开更多
It is proved unconditionally that every sufficiently large positive integer satisfying some necessary congruence conditions can be represented as the sum of s almost equal k-th powers of prime numbers for 2 ≤ k ≤ 10...It is proved unconditionally that every sufficiently large positive integer satisfying some necessary congruence conditions can be represented as the sum of s almost equal k-th powers of prime numbers for 2 ≤ k ≤ 10 and s =2k ＋ 1, which gives a short interval version of Hun＇s theorem.展开更多
Let π△ be the automorphic representation of GL（2, QA） associated with Ramanujan modular form A and L（s, π△） the global L-function attached to π△. We study Selberg＇s integral for the automorphic L-function L...Let π△ be the automorphic representation of GL（2, QA） associated with Ramanujan modular form A and L（s, π△） the global L-function attached to π△. We study Selberg＇s integral for the automorphic L-function L（s, π△） under GRH. Our results give the information for the number of primes in short intervals attached to Ramanujan automorphic representation.展开更多
基金Tianyuan Mathematics Foundation (11026075)the NSF (10971119) of Chinathe NSF (ZR2009AQ007) of Shandong Province
文摘Under the assumption of sixth power large.sieve mean-value of Dirichlet L-function, we improve Bombieri＇s theorem in short intervals by virtue of the large sieve method and Heath-Brown＇s identity.
基金supported by the Foundation of Henna Key-stackle S&T Project(No.122031900)
文摘In this paper,Oh liver tissue following short interval successive partial hepatectomy as diver and 112h liver tissue following short interval successive partial hepatectomy as test-er,we used suppression subtracted hybridization method to construct a high efficiency for-ward subtractive library.From the library we randomly picked 80 clones to analysis.After PCR detection,75 clones were sequenced and they represented 53 expressedsequence tags(EST).Among these clones,9 ESTs was 100%homologous to GenBank and 44 ESTs weren't 100%homologous to GenBank,one of these ESTs suggested a novel gene was found no ho-mologous to GenBank.Construction of the subtractive library lied a basis to clone and analy-sis these up-regulated genes in bulk in liver regeneration.
基金funded by the Natural Science Foundation of Hunan Province(grant number 2024JJ5283 to XH)。
文摘Preterm birth and suboptimal fetal growth remain significant perinatal challenges worldwide.Recent data indicate that China's perinatal profile has improved due to reductions in preterm birth rates.However,the country has a 6.5%prevalence of small-for-gestational-age(SGA),ranking fifth globally in total SGA birth numbers^([1,2]).
文摘The main purpose of this paper is to study the mean value properties of the character sums over the interval [1,p/8） by using the mean value theorems of the Dirichlet L-functions, and give an interesting mean value formula for this study.
基金Supported by National Natural Science Foundation of China(Grant Nos.11001218,11201275)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20106101120001)the Natural Science Foundation of Shaanxi Province of China(Grant No.2011JQ1010)
文摘Letk be a positive integer and n a nonnegative integer,0 〈 λ1,...,λk＋1 ≤ 1 be real numbers and w =（λ1,λ2,...,λk＋1）.Let q ≥ max{[1/λi ]：1 ≤ i ≤ k ＋ 1} be a positive integer,and a an integer coprime to q.Denote by N（a,k,w,q,n） the 2n-th moment of（b1··· bk c） with b1··· bk c ≡ a（mod q）,1 ≤ bi≤λiq（i = 1,...,k）,1 ≤ c ≤λk＋1 q and 2（b1＋ ··· ＋ bk ＋ c）.We first use the properties of trigonometric sum and the estimates of n-dimensional Kloosterman sum to give an interesting asymptotic formula for N（a,k,w,q,n）,which generalized the result of Zhang.Then we use the properties of character sum and the estimates of Dirichlet L-function to sharpen the result of N（a,k,w,q,n） in the case ofw =（1/2,1/2,...,1/2） and n = 0.In order to show our result is close to the best possible,the mean-square value of N（a,k,q） φk（q）/2k＋2and the mean value weighted by the high-dimensional Cochrane sum are studied too.
基金Project supported by the Tian Yuan Item in the National Natural Science Foundation of China.
文摘Let P（x） denote the greatest prime factor of ∏<sub>x【n≤x+x<sup>1/2</sup></sub>n. In this paper, we shall prove that P（x）】x<sup>0.728</sup>holds true for sufficiently large x.
基金National Natural Science Foundation of China(10301018)
文摘In this paper, we study Rényi＇s problem and other related problems about the additive functions in short intervals. As corollaries, we improve Ivic＇s results.
文摘Let the arithmetic function a(n) denote the number of non-isomorphic Abeliangroups of order n;k, positive integer, and x≥0. We setA_k(x)= sum from n≤x a(n)=k to (1)andA_k(x;h) =A_k(x+h)-A_k(x). A. Ivice first investigated the distribution of the values of finite non-isomorphicAbelian groups in short intervals. E. Kratzel reduced the problem to estimate theerror term △(1, 2, 3;x) in the three-dimensional multiplicative problem, and furtherimproved Ivice’s result.
基金the Research Grant Council Program of Hong Kong(Grant No.HKU7301/04H,HKU7466/06H)the International Collaborative Program of Science and Technology of Guangzhou Municipal Bureau of Science and Information Technology(Grant No.2012J5100044)
文摘As the fast economic development and urban expansion, it is dififcult for traditional methods to monitor land use changes in short time interval. Moreover, remotely sensed data acquired by optical sensors is often limited by bad weathers and cloud cover. SAR images, such as RADARSAT-1, are an ideal tool for weather-proof observation on ground surface. This paper analyzed the results of land use change detections with time lags of 24, 48 and 72 days according to the period of acquisition dates of RADARSAT-1. The results need a compromise between accuracies and efifciencies related to the time lags. For most of the situation, it is sufifcient of using a time lag of 24 days to obtain accuracy of 60%or above. In some cases of months, a time lag of 48 days is needed. For obtaining higher accuracies, longer time lag such as 72 days is needed.
文摘The authors regret that due to an oversight,the online version of Fig.5 is missing the sign,here is the correct Fig.5 and its caption.Fig.5:(A)Short interval intracortical inhibition(SICI)and(B)Long interval intracortical inhibition(LICI)in active and sham groups(Median,interquartile range,MEP peak to peak amplitude conditioned/test)of hemiplegic CP patients at baseline(pre)and after intervention.
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).
文摘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_(1),p_(2),p_(3),p_(4),p_(5)are prime numbers.This expands the previous results.
基金Supported by National'Natural Science Foundation of China (Grant No. 10701048)
文摘It is proved unconditionally that every sufficiently large positive integer satisfying some necessary congruence conditions can be represented as the sum of s almost equal k-th powers of prime numbers for 2 ≤ k ≤ 10 and s =2k ＋ 1, which gives a short interval version of Hun＇s theorem.
基金Supported by National Natural Science Foundation of China （Grant No. 10571107）Acknowledgements The author expresses her thanks to Professor Jianya Liu and Professor Yangbo Ye for encouragernent, and to Professor Xiumin Ren for valuable suggestions. This work was completed when the author visited The University of Iowa supported by CSC. The author would like to thank Department of Mathematics, The University of Iowa for hospitality and support.
文摘Let π△ be the automorphic representation of GL（2, QA） associated with Ramanujan modular form A and L（s, π△） the global L-function attached to π△. We study Selberg＇s integral for the automorphic L-function L（s, π△） under GRH. Our results give the information for the number of primes in short intervals attached to Ramanujan automorphic representation.
