Diffeomorphism classification of smooth weighted complete intersections

Xn(d1, . . . , dr-1, dr; w) and Xn(e1, . . . , er-1, dr; w) are two complex odd-dimensional smooth weighted complete intersections defined in a smooth weighted hypersurface Xn+r-1(dr; w). We prove that they are diffeomorphic if and only if they have the same total degree d, the Pontrjagin classes and the Euler characteristic, under the following assumptions: the weights w = (ω0, . . . , ωn+r) are pairwise relatively prime and odd, νp(d/dr) ≥ 2n+1/ 2(p-1) + 1 for all primes p with p(p-1) ≤ n + 1, where νp(d/dr) satisfies d/dr =Ⅱp prime pνp (d/dr).     

算术级数中的奇数Goldbach问题(Ⅱ)

本文考察了几乎所有模的算术级数中的奇数Goldbach问题．证明了对几乎所有的模r≤N1/6-ε,充分大的正奇数N可表为三个素数之和,其中每个素数取在模r 的满足必要同余条件的任意剩余系中．     

算术级数中的奇数Goldbach问题

本文给出了算术级数的模的精确数值上界,在该算术级数中奇数Goldbach问题可解。我们的结果蕴含了Linnik常数的一个数值上界。     

正奇数边形任何三条对角线形内不共点

文[1]中作者证明了：当n为素数时，正n边形的任何三条或三条以上对角线在形内不共点．本文证明当n为奇数时，这一结论仍然成立．从而完全解决了猜想whc57．本文沿用文[1]记号．     

安道什猜想推广奇数解问题的几个新结论

安道什猜想的推广没有正奇数适合方程：ｘｘ１１·ｘｘ２２…ｘｘｋｋ＝ｚｚ（ｋ≥２）①当ｋ＝２时，即为安道什猜想：没有正奇数适合方程ｘｘ·ｙｙ＝ｚｚ．文［１］中笔者已给出了①的反例，此后笔者对此又作了进一步的研究，虽没能完全解决这一问题，但从不同的角度得...     

L（Ω, μ） CANNOT ISOMETRICALLY CONTAIN SOME THREE-DIMENSIONAL SUBSPACES OF AM-SPACES

This article presents a novel method to prove that: let E be an AM-space and if dim E≥3, then there does not exist any odd subtractive isometric mapping from the unit sphere S(E) into S[L(Ω,μ)]. In particular, there does not exist any real linear isometry from E into L(Ω,μ).     

浅谈平方数计算

笔者最近发现，平方数的计算，就是要看底数为几就用几个从1起按顺序排列的奇数相加之和。