Counterexamples in optimal quadrature

It is widely believed that order of exactness is a good measure of the quality of an algorithm for numerical quadrature. We show that this is not the case, by exhibiting a situation in which the optimal algorithm does not even integrate constants exactly. We also show that there are situations in which the penalty for using equidistant nodes is unbounded. Finally, we show that the complexity of obtaining an -approximation can be an arbitrary function of , i.e., there is no hardest quadrature problem.     

纳米级NiTiO3粉体的合成

以Ｈ２ＴｉＯ３，Ｈ２Ｏ２及ＮｉＣｌ２为主要原料，用化学共沉淀法制备了纳米级ＮｉＴｉＯ３。确定了反应物Ｈ２ＴｉＯ３，Ｈ２Ｏ２，ＮＨ３的最佳摩尔比为１：８：２，用不同的退火温度和退火时间对样品处理得到相应粒径的纳米级粉体。     

Synthesen von α,β-ungesättigten 2-(2-Oxo-benzazolin-3-yl)-3-hydroxy-dithio-carbonsäure-alkylestern und entsprechend substituierten Keten-S,S-acetalen sowie deren Kristall- und Molekülstruktur

Summary The new alkyl 2-(2-oxo-benzazoline-3-yl)-3-hydroxy dithiocrotonates and dithiocinnamates4 and the corresponding ketene dithioacetals2 and5 are obtained by dithiocarboxylation of the 3-acceptormethyl substituted benzazoline-2-ones1 or3. Alkylation at room temperature gives compounds4 whereas at higher alkylation temperature2 or5 are formed. The results of X-ray analyses performed for methyl 3-hydroxy-p-chloro-dithiocinnamate4d and of N-[1-(4-chloro-benzoyl)-2,2-bis(methylthio)-vinyl]-benzothiazoline-2-one5e are discussed.

     

Fluorinated triazinones from hexafluoroacetone ethoxycarbonylimine

The behavior of hexafluoroacetone ethoxycarbonylimine in cyclocondensation with different binucleophiles of the amidine type, viz., amino derivatives of N- and N,S-heterocycles, was studied. A preparative method for the synthesis of previously unknown annelated 2,2-bis(trifluoromethyl)-1,3,5-triazinones was developed.     

First synthesis of α-aminophosphonates from natural porphyrin derivatives by the Kabachnik—Fields reaction

A preparative procedure is proposed for the synthesis of α-aminophosphonates of natural porphyrins by the microwave-assisted Kabachnik—Fields reaction.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 256–259, January, 2005.     

Comparative performance of MM3(92) and two TINKER MM3 versions for the modeling of carbohydrates

The 1992 version of MM3 was largely used for modeling mono-, di-, and trisaccharides. In later versions of MM3 improvements were made in some parameters that may be important for carbohydrates. This corrected MM3 force field is part of the Tinker package, freely available (as its 4.1 version), and included in the Chem 3D Ultra 8.0 package (as the 3.7 version). The latter version lacks the corrections to the standard bond lengths produced by electronegativity and anomeric effects, whereas the Tinker 4.1 version only lacks the latter correction. The present work compares the performance of the three MM3 versions (and in some cases, DFT and/or HF/ab initio procedures) on several carbohydrate model problems as the chair and rotamer equilibria in 2-hydroxy- and 2-methoxytetrahydropyran, hydrogen bonding in cis-2,3-dihydroxytetrahydropyran, and the potential energy surfaces around the glycosidic bonds of two sulfated disaccharides and two trisaccharides. Tinker MM3 can be used accurately to estimate carbohydrate energies and geometries, and-with the help of some programming-to pursue studies on the potential energy surfaces of di- and trisaccharides. In most cases results obtained using the three MM3 versions are similar, although large energy differences are obtained when comparing a rotameric distribution around a O-C-O-H dihedral, which is almost forced to the exo-anomeric position by the Tinker versions. In other systems smaller energy differences are found, but they can nevertheless lead to a different global minimum when comparing conformers of similar energy. MM3(92) establishes better the differences between the bond lengths in both anomers, as an expected expression of the anomeric correction.     

无保护流体室温燐光法测定吲哚-3-丁酸的研究

在仅以碘化钾为重原子微扰剂、亚硫酸钠为除氧剂及无任何保护性介质存在的水溶液中 ,吲哚_3_丁酸 (IBA)能发射很强的室温光 (RTP) ;详细研究了分析测定条件及有机溶剂对RTP的影响 ;在最大光波长λex/λem =281/447nm处 ,光强度与IBA浓度在2.0×10 -7～1.0×10 -5mol/L范围内呈良好的线性关系 ,检出限4.3×10-8 mol/L ;方法直接用于强化水样和土壤中IBA的测定 ,回收率96 %～104 % ,相对标准偏差2.37 %～3.97 %。     

Alkylation of 6-(3-Indolyl)indolo[2,3-b]carbazole

The methylation and allylation of 6-(3-indolyl)indolo[2,3-b]carbazole were studied, and its trimethyl and mono-, di-, and triallyl derivatives were obtained.     

Total synthesis of 3,3′:4′,3″-ter-1,2,5-thiadiazole using a synthetic utility of S4N4·SbCl5 complex

3,3′:4′,3″-Ter-1,2,5-thiadiazole, an useful oligoheterocyclic compound, has been accomplished in seven steps from 1-(5-methyl-3-isoxazolyl)ethanone or diethyl acetylenedicarboxylate using a synthetic utility of tetrasulfur tetranitride antimony pentachloride (S₄N₄·SbCl₅) complex to make a 1,2,5-thiadiazole ring.     

Interaction of (1-phenylethyl)indole-2-carbonitrile with C-nucleophiles

Methods of obtaining ketones and enamino esters have been developed on the basis of reactions of 1-(1-phenylethyl)indole-2-carbonitrile with organomagnesium and organozinc compounds. Removal of a benzyl group from the indole nitrogen atom by the Grignard reagent has been discovered. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1179–1183, August, 2006.