An Enhancement of the Drezner—Wesolowsky Algorithm for Single-Facility Location with Maximin of Rectilinear Distance

In this note, we examine the algorithm of Drezner and Wesolowsky for locating a facility with maximin rectilinear distance to a given set of demand points. The concept of the closest-point constraint is introduced as a technique for increasing the efficiency of the algorithm. This potential increase in efficiency is demonstrated by an example.     

The synthesis of 1,4-diazacycl[3,2,2]azine

The diazaanalog of “cycl[3,2,2]azine”, “1,4-diazacycl[3,2,2]azine” (1,4,7b-triazacyclopent-[cd]indene) and its 2-methyl derivative were prepared. These compounds are subject to facile acid-catalyzed hydrolysis affording substituted imidazo[1,2-a]pyridines.     

Template synthesis in the nickel(II)–thiocarbohydrazide–propanone triple system

The complexing process proceeding in the Ni^II–thiocarbohydrazide (H₂N–H–NC(=S)–NH–NH₂)–propanone triple system in EtOH solution and nickel(II)hexacyanoferrate(II) gelatin-immobilized matrix has been studied. It has been found that in the first case, template synthesis leading, as a minimum, to formation of three coordination compounds of Ni^II with (N,N,S,S)-donor tetradentate ligands having NiL¹, NiL² and NiL³compositions where L¹ is 4,6,6-trimethyl-2,3,7,8-tetraazanonen-3-di(thiohydrazide)-1,9, L² is 4,6,6,12-tetrametyl-1,9-dithio-2,3,7,8,10,11-hexaazatridekadien-3,11-hydrazide-1 and L³ is 2,8,10,10,16-pentamethyl-5,13-dithio-3,4,6,7,11,12,14,15-octaazaheptadekatrien-2,7,15 is observed, whereas in the gelatin-immobilized matrix, a complexing process in the system considered does not occur.     

Chemische Vitamin D<Subscript>3</Subscript>-Bestimmung in Lebertran

The different aspects of Vitamin D₃ determination and the data reported in the literature are discussed. The spectrophotometric determination of Vitamin D₃ in cod-liver oil is carried out after the alkaline saponification, extraction of unsaponified parts, precipitation of accompanying sterols and the column- and thin-layer chromatographic purification and separation of vitamin D₃ on 40 cm plates from other vitamins. The dyestuff α-naphtholbenzein is suited well as standard substance for the better location and identification of vitamin D₃ zone on the thin-layer plate. The results obtained from the chemical method were checked through the simultaneous biological determination.     

Ab initio studies of the allylic hydroxylation: DFT calculation on the reaction of 2-methyl-2-butene with selenium dioxide

The mechanism of the allylic oxidation of 2-methyl-2-butene with selenium dioxide has been investigated by ab initio quantum mechanics. Transition states for two major steps (an ene reaction and a [2,3]-sigmatropic rearrangement) of this reaction have been optimized by the B3LYP/6-311+G(d,p) method. A comparison of the energies of the transition states shows that the anti-endo and syn-endo approaches are the efficient routes in the ene reaction and the methyl (C4) group is sited in a pseudo-equatorial environment in cyclic transition states during the [2,3]-rearrangement. Calculations also show the kind of the terminal alkyl (C4) substituents may control (E)-selectivity in the formation of the allylic alcohols.     

The Chow rings for 3-dimensional toric varieties with one bad isolated singularity

The properties of a toric variety have strong connection with the combinatorial structure of the corresponding fan and the relations among the generators. Using this fact, we have described explicitly the Chow ring for aQ-factorial toric variety as the Stanley-Reisner ring for the corresponding fan modulo the linear equivalence relation. In this paper, we calculate the Chow ring for 3-dimensionalQ-factorial toric varieties having one bad isolated singularity.