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41.
In this paper, by employing linear algebra methods we obtain the following main results:
- (i) Let and be two disjoint subsets of such that Suppose that is a family of subsets of such that for every pair and for every i. Then Furthermore, we extend this theorem to k‐wise L‐intersecting and obtain the corresponding result on two cross L‐intersecting families. These results show that Snevily's conjectures proposed by Snevily (2003) are true under some restricted conditions. This result also gets an improvement of a theorem of Liu and Hwang (2013).
- (ii) Let p be a prime and let and be two subsets of such that or and Suppose that is a family of subsets of [n] such that (1) for every pair (2) for every i. Then This result improves the existing upper bound substantially.
42.
William N. Traves 《Proceedings of the American Mathematical Society》1999,127(8):2245-2248
The notion of D-simplicity is used to give a short proof that varieties whose normalization is smooth satisfy Ishibashi's extension of Nakai's conjecture to arbitrary characteristic. This gives a new proof of Nakai's conjecture for curves and Stanley-Reisner rings.
43.
44.
45.
关于低阶K群的若干问题 总被引:1,自引:0,他引:1
本文主要介绍了低阶K群K_0,K_1,K_2及与它们相关的Bass-Quillen猜测、Birch-Tate猜测研究的最新进展.K_0与K_1方面主要通过对Bass~Quillen猜测研究说明K_0,K_1的作用,同时也给出了一些多项式环上投射模自同构群的计算公式.在K_2群方面,我们主要介绍了域上K_2群,代数整数环上K_2群以及著名的Birch-Tate猜想.并且也给出了K_2群一些计算方面的结果. 相似文献
46.
本文旨在介绍Fermat最后定量的历史和Wiles最近所给的证明。首先简介了其在代数数论的发展过程中所起的作用,然后介绍椭圆曲线的基本概念,叙述Taniyama-Weil猜想,即任一椭圆曲线都是模的。进而介绍Ribet的工作。他证明了若Taniyama-Weil猜想对半稳定的椭圆曲线成立则Fermat最后定理成立。最后介绍了l-adic Galois表示的概念及Wiles定理,即半稳定的椭圆曲线都 相似文献
47.
Baha-Eldin Khaledi Subhash Kochar 《Annals of the Institute of Statistical Mathematics》2001,53(3):620-630
Consider a multivariate mixture model where the random variables X
1, ..., X
n
given (1, ...,
n
), are conditionally independent. Conditions are obtained under which different kinds of positive dependence hold among X
i
's. The results obtained are applied to a variety of problems including the concomitants of order statistics and of record values; and to frailty models. 相似文献
48.
Varghese Mathai 《Geometriae Dedicata》2003,99(1):1-15
We outline a twisted analogue of the Mishchenko–Kasparov approach to prove the Novikov conjecture on the homotopy invariance of the higher signatures. Using our approach, we give a new and simple proof of the homotopy invariance of the higher signatures associated to all cohomology classes of the classifying space that belong to the subring of the cohomology ring of the classifying space that is generated by cohomology classes of degree less than or equal to 2, a result that was first established by Connes and Gromov and Moscovici using other methods. A key new ingredient is the construction of a tautological C*
r
(, )-bundle and connection, which can be used to construct a C*
r
(, )-index that lies in the Grothendieck group of C*
r
(, ), where is a multiplier on the discrete group corresponding to a degree 2 cohomology class. We also utilise a main result of Hilsum and Skandalis to establish our theorem. 相似文献
49.
卢广存 《数学物理学报(B辑英文版)》2002,22(4)
In this note a symplectic capacity of Hofer-Zehnder type that is only invariant under C1-symplectomorphisms is defined and all computation formulae for Hofer-Zehnder symplectic capacity obtained at present are proved still holding for it. As a consequence some results on Weinstein conjecture are generalized to C1-smooth hypersurface of contact type. 相似文献
50.
Let Xn,n 1,be a sequence of independent random variables satisfying P(Xn = O) = 1 - P(Xn = an) = 1 - 1/pn,where an,n 1,is a sequence of real numbers,andpn isthenthprime,setFN(x)=P(N∑Xnn=1 x).The authors investigate a conjecture of Erdos in probabilistic number theory and show that in order for the sequence FN to be weakly convergent,it is both sufficient and necessary that there exist three numbers x0 and x1 < x2 such that limsup(FN(x2) -FN(x1)) > 0 holds,and Lo =N→∞ lim FN(x0) exists.Moreover,the authors point ont that they can also obtain the same N→∞ result in the weakened case of liminfP(Xn = 0) > 0.n→∞ 相似文献