Proof of semialgebraic covering mapping cylinder conjecture with semialgebraic covering homotopy theorem

In this paper we prove the semialgebraic version of Palais' covering homotopy theorem, and use this to prove Bredon's covering mapping cylinder conjecture positively in the semialgebraic category. Bredon's conjecture was originally stated in the topological category, and a topological version of our semialgebraic proof of the conjecture answers the original topological conjecture for topological G-spaces over “simplicial” mapping cylinders.     

New aspect in transient magnetic fields using heavy ion beams

Transient field precessions have been measured with the first excited 2 ₁ ⁺ -state as probe for ions of²⁸Si traversing Fe at v_ion?1v₀ and 13v₀(v₀=c/137) and⁶²Ni being stopped in Fe. The degree of polarization deduced for the Si ions, p_1s=0.19(6), is consistent with low-velocity data. There is clear evidence that the field strength is attenuated by heavy ion beams. For the⁶²Ni(2 ₁ ⁺ ) state at 1.173 MeV a g-factor value of g=0.34(7) was obtained in good agreement with a previous result.     

Acetic anhydride as a synthetic reagent

Acetic anhydride has been used widely in synthetic organic chemistry, especially in syntheses and transformations of heterocyclic compounds. These utilities are reviewed under the following classification.     

Synthesis of pyrimido[4,5-e][1,4]oxazepin-5-ones

Eighteen novel pyrimido[4,5-e][1,4]oxazepin-5-ones were prepared directly via the reaction of either ethyl 4-chloro-2-phenyl-5-pyrimidinecarboxylate (Ia) or ethyl 4-chloro-2-m-chlorophenyl-5-pyrimidinecarboxylate (Ib) with a variety of substituted 2-(alkylamino)ethanols. A typical example was the preparation of 8,9-dihydro-9-methyl-2-phenylpyrimido[4,5-e][1,4]-oxazepin-5(7H)-one (IIa) from the reaction of Ia with 2-(methylamino)ethanol. Hydrolytic cleavage of the lactone ring in IIa with sodium hydroxide solution, followed by acidification with hydrochloric acid afforded 4-[(2-hydroxyethyl)methylamino]-2-phenyl-5-pyrimidinecarboxylic acid (IV). Reactions of IIa with concentrated ammonium hydroxide or hydrazine also caused cleavage of the lactone ring, giving the corresponding amide (V) or hydrazide (VI), respectively. Structural assignments were supported by infrared and nuclear magnetic resonance spectra.     

FFC-1离子交换纤维对酸碱有害气体吸附性能的研究

系统考察了不同直径及反离子形式的FFC-1聚羧酸离子交换纤维对酸碱有害气体的穿透吸附,各种温、湿度条件下的吸水率,以及作为有害气体吸附滤除材料的重复使用与再生性能。研究表明:FFC-1纤维直径的减小有利于提高对有害气体的动态吸附容量。在体系温度、相对湿度分别为15℃、50%时,以3D腈纶为起始原料的钠型FFC-1离子交换纤维的吸水率≥350mg/g.纤维;对SO2的穿透吸附容量可达200mg/g.纤维。FFC-1离子交换纤维具有良好的重复使用与再生能力,经20次再生循环使用后,纤维交换容量未见明显变化。     

Synthesis of 5,6,8,9,14,14a-hexahydroisoquino[1,2-b][3]benzazepines

Syntheses of 5,6,8,9,14,14a-hexahydroisoquino[1,2-b][3]benzazepine-2,3,11,12-tetrol and related compounds are described. Key steps involve an initial construction of the isoquinoline ring under the Bischler-Napieralski conditions, which is followed by the building of the azepine ring via an intramolecular lactam formation on to the isoquinoline nucleus.     

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...     

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.