A set of n points in the plane determines a total C 2 n distances (some of them may be the same).Let r n be the ratio of the maximum distance to the minimum distance, and R n be the greatest lower bound for r n. ...A set of n points in the plane determines a total C 2 n distances (some of them may be the same).Let r n be the ratio of the maximum distance to the minimum distance, and R n be the greatest lower bound for r n. By using the mathematical software Mathematica,the author gets the following results in this paper.R 12 ≤2.99496..., R 13 ≤cscπ10.展开更多
In this work, join and meet algebraic structure which exists in non-near-linear finite geometry are discussed. Lines in non-near-linear finite geometry ?were expressed as products of lines in near-linear finite geomet...In this work, join and meet algebraic structure which exists in non-near-linear finite geometry are discussed. Lines in non-near-linear finite geometry ?were expressed as products of lines in near-linear finite geometry ?(where?p?is a prime). An existence of lattice between any pair of near-linear finite geometry ?of ?is confirmed. For q|d, a one-to-one correspondence between the set of subgeometry ?of ?and finite geometry ?from the subsets of the set {D(d)}?of divisors of d?(where each divisor represents a finite geometry) and set of subsystems {∏(q)}?(with variables in Zq) of a finite quantum system ∏(d)?with variables in Zd?and a finite system from the subsets of the set of divisors of d?is established.展开更多
文摘A set of n points in the plane determines a total C 2 n distances (some of them may be the same).Let r n be the ratio of the maximum distance to the minimum distance, and R n be the greatest lower bound for r n. By using the mathematical software Mathematica,the author gets the following results in this paper.R 12 ≤2.99496..., R 13 ≤cscπ10.
文摘In this work, join and meet algebraic structure which exists in non-near-linear finite geometry are discussed. Lines in non-near-linear finite geometry ?were expressed as products of lines in near-linear finite geometry ?(where?p?is a prime). An existence of lattice between any pair of near-linear finite geometry ?of ?is confirmed. For q|d, a one-to-one correspondence between the set of subgeometry ?of ?and finite geometry ?from the subsets of the set {D(d)}?of divisors of d?(where each divisor represents a finite geometry) and set of subsystems {∏(q)}?(with variables in Zq) of a finite quantum system ∏(d)?with variables in Zd?and a finite system from the subsets of the set of divisors of d?is established.
