果蔬中L—抗坏血酸的示波计时电位K3Fe（CN）6滴定法研究

本文报导的方法是在南京大学高鸿教授研究的K_3Fe(CN)_6示波极谱滴定法(在PH8的K_2HPO_4—KH_2PO_4—KBr底液中,用0.04660mol/LK_3Fe(CN)_6标准溶液对纯抗坏血酸测定)的基础上,考虑到L—抗坏血酸(以下简称V_e)在碱性、中性介质中稳定性差,如用于V_e含量很微的果蔬测定,对结果影响大。本文改为H_2C_2O_4—KBr的酸性介质作底液,用     

Synthesis of 1,2,3,4,8,9,10,11-octahydro-[1,4] diazepino[6,5,4-jk ]earbazole and related compounds

1,2,3,4,8,9,10,11-Octahydro[1,4]diazepino[6,5,4-jk]earbazole (VIa) was synthesized from 2,3,4,5-tetrahydro-1H-benzodiazepine (la) via the route shown in Scheme 1. Other compounds which were prepared similarly are 3-acetyl-6-chloro-1,2,3,4,8,9,10,11-octahydro[1,4]diazepino-[6,5,4-jk]carbazole(Vb) and 3-methyl-1,2,3,4,8,9,10,11-octahydro[1,4]diazepino[6,5,4-jk]carb-azole (VIII). Chemical transformations which were carried out with VI and 3-acetyl-1,2,3,4,8,9, 10,11-octahydro[1,4]diazepino[6,5,4-jk]carbazole (Va) are also described.     

Improperly efficient solutions in a class of vector optimization problems

Journal of Global Optimization - Improperly efficient solutions in the sense of Geoffrion in linear fractional vector optimization problems with unbounded constraint sets are studied systematically...     

Levin methods for highly oscillatory integrals with singularities

In this paper,new Levin methods are presented for calculating oscillatory integrals with algebraic and/or logarithmic singularities.To avoid singularities,the technique of singularity separation is applied and then the singular ODE occurring in classic Levin methods is converted into two kinds of non-singular ODEs.The solutions of one can be obtained explicitly,while the other kind of ODEs can be solved efficiently by collocation methods.The proposed methods can attain arbitrarily high asymptotic orders and also enjoy superalgebraic convergence with respect to the number of collocation points.Several numerical experiments are presented to validate the efficiency of the proposed methods.     

Estimation of a quantile in some nonstandard cases

A necessary condition for the asymptotic normality of the sample quantile estimator isf(Q(p))=F(Q(p))>0, whereQ(p) is thep-th quantile of the distribution functionF(x). In this paper, we estimate a quantile by a kernel quantile estimator when this condition is violated. We have shown that the kernel quantile estimator is asymptotically normal in some nonstandard cases. The optimal convergence rate of the mean squared error for the kernel estimator is obtained with respect to the asymptotically optimal bandwidth. A law of the iterated logarithm is also established.This research was partially supported by the new faculty award from the University of Oregon.     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

An exponent bound on skew Hadamard abelian difference sets

A difference setD in a groupG is called a skew Hadamard difference set (or an antisymmetric difference set) if and only ifG is the disjoint union ofD, D(^–1), and {1}, whereD(^–1)={d^–1|dD}. In this note, we obtain an exponent bound for non-elementary abelian groupG which admits a skew Hadamard difference set. This improves the bound obtained previously by Johnsen, Camion and Mann.     

Nonabelian orbifolds and the boson-fermion correspondence

For a positive integerl divisible by 8 there is a (bosonic) holomorphic vertex operator algebra (VOA) associated to the spin lattice _l . For a broad class of finite groupsG of automorphisms of we prove the existence and uniqueness of irreducibleg-twisted -modules and establish the modular-invariance of the partition functionsZ(g, h, ) for commuting elements inG. In particular, for any finite group there are infinitely many holomorphic VOAs admittingG for which these properties hold. The proof is facilitated by a boson-fermion correspondence which gives a VOA isomorphism between and a certain fermionic construction, and which extends work of Frenkel and others.Supported by NSA grant MDA904-92-H-3099.Supported by NSF grant DMS-9122030.