In this article,we have given the definition of the Heilbronn number of n-noncollinear points in the plane. By this, we got the exact value of H5 which is the exact upper bound of H5 (K), where H5 (K) is any Heilbronn...In this article,we have given the definition of the Heilbronn number of n-noncollinear points in the plane. By this, we got the exact value of H5 which is the exact upper bound of H5 (K), where H5 (K) is any Heilbronn number in common sense.展开更多
In this work the authors consider the problem of optimally distributing 8 points inside a unit square so that the smallest area of the(38)triangles formed by them is maximal.Symbolic computations are employed to reduc...In this work the authors consider the problem of optimally distributing 8 points inside a unit square so that the smallest area of the(38)triangles formed by them is maximal.Symbolic computations are employed to reduce the problem into a nonlinear programming problem and find its optimal solution.All computations are done using Maple.展开更多
The present paper proved that if λ1, λ2, λ3 are positive real numbers, λ1/λ2 is irrational. Then, the integer parts of λ1x12＋ λ2x22＋ λ3x34 are prime infinitely often for natural numbers x1, x2, x3.
We show that if λ1 , λ2 , λ3 are non-zero real numbers, not all of the same sign, η is real and λ1 /λ2 is irrational, then there are infinitely many ordered triples of primes (p1 , p2 , p3 ) for which |λ1 p1 + ...We show that if λ1 , λ2 , λ3 are non-zero real numbers, not all of the same sign, η is real and λ1 /λ2 is irrational, then there are infinitely many ordered triples of primes (p1 , p2 , p3 ) for which |λ1 p1 + λ2 p2 + λ3 p2 3 + η| < (max pj )- 1/40 (log max pj ) 4 .展开更多
文摘In this article,we have given the definition of the Heilbronn number of n-noncollinear points in the plane. By this, we got the exact value of H5 which is the exact upper bound of H5 (K), where H5 (K) is any Heilbronn number in common sense.
基金the National Natural Science Foundation of China under Grant Nos.12171159 and 12071282“Digital Silk Road”Shanghai International Joint Lab of Trustworthy Intelligent Software under Grant No.22510750100。
文摘In this work the authors consider the problem of optimally distributing 8 points inside a unit square so that the smallest area of the(38)triangles formed by them is maximal.Symbolic computations are employed to reduce the problem into a nonlinear programming problem and find its optimal solution.All computations are done using Maple.
文摘The present paper proved that if λ1, λ2, λ3 are positive real numbers, λ1/λ2 is irrational. Then, the integer parts of λ1x12＋ λ2x22＋ λ3x34 are prime infinitely often for natural numbers x1, x2, x3.
基金Supported by the NNSF of China(11071070)Supported by the Science Research Plan of Education Department of Henan Province(2011B110002)
文摘We show that if λ1 , λ2 , λ3 are non-zero real numbers, not all of the same sign, η is real and λ1 /λ2 is irrational, then there are infinitely many ordered triples of primes (p1 , p2 , p3 ) for which |λ1 p1 + λ2 p2 + λ3 p2 3 + η| < (max pj )- 1/40 (log max pj ) 4 .
