In this paper, we give a necessary and sufficient solvable condition for diagonal cubic equation with prime variable in arithmetic progressions and the outline of the proof.
Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly...Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes, which implicitly proves Goldbach’s Conjecture for 2n as well.展开更多
The oldest Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. The recent proof [1] connected Goldbach’s Conjecture with the fact...The oldest Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. The recent proof [1] connected Goldbach’s Conjecture with the fact that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes. The present paper contains explicit additional and complementary details of the proof, insisting on the existence and the number of Goldbach’s representations of even positive integers as sums of pairs of primes.展开更多
A necessary and sufficient solvable condition for diagonal quadratic equation with prime variables in arithmetic progressions is given, and the best qualitative bound for small solutions of the equation is obtained,
以紫花苜蓿种子为材料,3种无机盐溶液KNO3、CaCl2、K2HPO4为引发剂,浓度为2%、4%,进行引发处理,研究不同无机盐溶液引发对紫花苜蓿种子活力及幼苗抗逆性的影响,结果表明,适宜的无机盐溶液引发处理能明显提高紫花苜蓿种子活力及幼苗抗逆...以紫花苜蓿种子为材料,3种无机盐溶液KNO3、CaCl2、K2HPO4为引发剂,浓度为2%、4%,进行引发处理,研究不同无机盐溶液引发对紫花苜蓿种子活力及幼苗抗逆性的影响,结果表明,适宜的无机盐溶液引发处理能明显提高紫花苜蓿种子活力及幼苗抗逆性,显著提高幼苗SOD、POD、CAT的活性和叶绿素含量,显著降低幼苗丙二醛含量。其中,2%KNO312 h;2%CaCl224 h;2%K2HPO412 h 3种引发处理的效果最为明显。展开更多
基金Supported by the National Natural Science Foundation of China(10471104)
文摘In this paper, we give a necessary and sufficient solvable condition for diagonal cubic equation with prime variable in arithmetic progressions and the outline of the proof.
文摘Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes, which implicitly proves Goldbach’s Conjecture for 2n as well.
文摘The oldest Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. The recent proof [1] connected Goldbach’s Conjecture with the fact that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes. The present paper contains explicit additional and complementary details of the proof, insisting on the existence and the number of Goldbach’s representations of even positive integers as sums of pairs of primes.
基金supported partially by the National Natural Science Foundation of China (Grant No.10671056)
文摘A necessary and sufficient solvable condition for diagonal quadratic equation with prime variables in arithmetic progressions is given, and the best qualitative bound for small solutions of the equation is obtained,
文摘以紫花苜蓿种子为材料,3种无机盐溶液KNO3、CaCl2、K2HPO4为引发剂,浓度为2%、4%,进行引发处理,研究不同无机盐溶液引发对紫花苜蓿种子活力及幼苗抗逆性的影响,结果表明,适宜的无机盐溶液引发处理能明显提高紫花苜蓿种子活力及幼苗抗逆性,显著提高幼苗SOD、POD、CAT的活性和叶绿素含量,显著降低幼苗丙二醛含量。其中,2%KNO312 h;2%CaCl224 h;2%K2HPO412 h 3种引发处理的效果最为明显。
