Determination of lead by selective chelatometric titration with HEDTA after separation as its sulphate by an improved method of precipitation

A selective titrimetric determination of Pb after separation by a modified method of precipitation as its sulphate is proposed. Pb(II), present as the perchlorate, is precipitated by gentle boiling in 3.6M H(2)SO(4) presaturated with PbSO(4) and free from any extraneous anions. The customary time-consuming evaporation to fumes of sulphuric acid is dispensed with. The precipitate is collected, and dissolved in excess of HEDTA, the surplus of which is back-titrated with Zn(II) at pH 5.0-5.5. Use of Catechol Violet and Xylenol Orange as a mixed indicator gives a sharper end-point. The standard deviation of the proposed method for 60 mg of lead is 0.35 mg. The method has been successfully used to determine Pb in non-ferrous alloys.     

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...     

On bandwidth sums of graphs

ＯＮＢＡＮＤＷＩＤＴＨＳＵＭＳＯＦＧＲＡＰＨＳＹＡＯＢＩＮＧ（姚兵）;ＷＡＮＧＪＩＡＮＦＡＮＧ（王建方）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＮｏｒｉｈｗｅｓｔｅｔｅｒｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ,Ｌａｎｚｈｏｕ７３００７０,Ｃｈｉ...     

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.