An identification of the connections of Quillen and Beilinson-Schechtman

Given a family of Riemann surfaces and a holomorphic vector bundle Beilinson and Schechtman construct a canonical connection on the associated determinant bundle. We prove the conjecture which states that their connection coincides with the Quillen connection. This is done by reducing to the case where along fibers are invertible. Both connection forms become more accessible in this case.Supported in part by N.S.F. Grant No. DMS-9201022Supported in part by National Science Council of Republic of China Grant No. NSC 82-0208-M-002-125-T, and NSERC of Canada Grant No. OGP 0121883     

三元Ⅲ─V半导体合金的基态有序结构

利用了自旋１／２二维Ｉｓｉｎｇ模型及其“不等式方法”,确定了三元Ⅲ─Ｖ半导体会金（００１）面外延生长中的二维平面基态有序结构和基态相图,并通过层状叠加得到了合金中可能出现的长程有序结构,较好地说明了实验发现的（００１）衬底外延生长中的长程有序现象．     

Nuclear gluon shadowing via continuum lepton pairs inp+A collisions at\sqrt s = 200 A GeV

The dilepton spectra from open charm decay inp+A reactions at $\sqrt s = 200$ AGeV are proposed to constrain gluon shadowing in nuclei. We show that the required measurements are feasible at RHIC.     

A finiteness theorem for maximal independent sets

Denote bymi(G) the number of maximal independent sets ofG. This paper studies the setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG K ₁) or duplicated vertices. We determineS(1), S(2), andS(3) and prove that |V(G)| 2 ^k–1 +k – 2 for anyG inS(k) andk 2; consequently,S(k) is finite for anyk. Supported in part by the National Science Council under grant NSC 83-0208-M009-050     

Extremal functions for Moser's inequality

Let be a bounded smooth domain in , and a function with compact support in . Moser's inequality states that there is a constant , depending only on the dimension , such that

where is the Lebesgue measure of , and the surface area of the unit ball in . We prove in this paper that there are extremal functions for this inequality. In other words, we show that the

is attained. Earlier results include Carleson-Chang (1986, is a ball in any dimension) and Flucher (1992, is any domain in 2-dimensions).