Characterizations based on conditional expectations of the doubled truncated distribution

The expression of the continuous distribution function F(x) is obtained whenever % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaerbhv2BYDwAHbacfiGaa8xBaiaabIcacaWG4bGaaiilaiaadMha% caqGPaGaa8hiaiaab2dacaWFGaGaa8xraiaa-HcacaWFybGaa8hiai% aa-XhacaWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bca% cqGHKjYOcaWFGaGaa8xEaiaa-Lcaaaa!53EE!\[m{\rm{(}}x,y{\rm{)}} {\rm{ = }} E(X | x \le X \le y)\]is known. Moreover, we obtain the necessary and sufficient conditions so that any function m: ² is the conditional expectation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGOaGaamiwaerbhv2BYDwAHbacfiGaa8hiaiaacYha% caWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bcacqGHKj% YOcaWFGaGaa8xEaiaacMcaaaa!4D0D!\[E(X | x \le X \le y)\]of a random variable X with continuous distribution function. Furthermore, we relate m(x,y) to order statistics.     

Simultaneous determination of propranolol and pindolol by synchronous spectrofluorimetry

A completely automated method to determine the most common parameters in cured meat products is proposed. The approach to full automation is based on the coupling of a robotic station for development of preliminary operations (namely weighing of the sample, grinding, leaching, filtration and transport to the aspiration zone) and a continuous unsegmented manifold for derivatisation and spectrophotometric monitoring of the reaction coloured products. This assembly works in an unattended fashion thus eliminating the bottleneck produced by the determination of these parameters in routine laboratories. The good agreement between results obtained by the proposed method and those from conventional methods for target analytes confirms its excellent performance and usefulness.     

Structure of a styrylbenzoselenazole platinum(II) complex: [NEt4][Pt(nsbse)Br3]

Tetraethylammonium tribromo[2-(2-chloro-5-nitrostyryl)benzoselenazole] platinate (II), [(C₂H₅)₄N][PtBr₃(C₁₅H₉ClN₂O₂Se)], is monoclinic, in space groupP2₁/c, witha=9.496(2),b=20.321(7),c=15.166(3)Å,=100.18(1)°,V=2880(2)ų,M _r =928.72,Z=4,D _x =2.141 g cm^–3, (MoK)=0.71073 Å,=104.1 cm^–1,F(000)=1752,T=298 K. The structure was solved by direct methods and refined toR=0.032 for 2626 unique observed reflections withI>3(I). The [Pt(nsbse)Br₃)] unit has square-planar geometry about the Pt atom, with the nsbse coordinated to the Pt through the N of the selenazole ring. The ligand molecule is non-planar, with a dihedral angle of 61.6(2)° between the benzoselenazole and phenyl rings. The dihedral angles between the PtBr₃ plane and the benzoselenazole and phenyl planes are 105.2(1) and 80.7(1)°, respectively.     

Stereochemistry of contiguous cyclopropane formation from cascade cyclization of a skipped dienyl homoallyl triflate

Solvolysis of asymmetric homoallylic triflates bearing a terminal stannyl substituent gives disubstituted cyclopropanes and bicyclopropanes bearing differentiated termini in high enantiopurity.     

FeCp]+-induced hexafunctionalization of hexamethylbenzene with dendrons for the direct synthesis of redox-active iron-centered metallodendrimers

Phenol tri- and nonaallyl dendrons (3 and 7, respectively) were functionalized at the focal position to give the new triallyl dendrons 4 and 6 and the nonaallyl dendrons 11 and 13 that contain a iodoalkyl or a bromobenzyl termini. All these dendrons were used for the [FeCp]+-induced hexafunctionalization of hexamethylbenzene in [FeCp(eta6-C6Me6)][PF6] (1) under mild conditions in the presence of KOH. These reactions directly yielded the 18-allyl and 54-allyl dendrimers 9, 10, and 14 with a [FeCp(eta6-arene)]+ unit located at the dendrimer core. Cyclic voltammetry studies were recorded in THF and DMF with these metallodendrimers and compared with those of analogous dendrimers or complexes of smaller size that contain a [FeCp(eta6-arene)]+ unit at the core. The decreased rate of heterogeneous electron transfer when the dendritic size increases first disclosed by Diederich and Gross is confirmed. The variation of the redox potential of the Fe(II/I) redox system with increasing dendritic size is negligible even in a solvent of high dielectric constant such as DMF. This trend is attributed to fact that the involved "redox" orbital is buried on the metal center, well protected by the shell of alkyl chains (electron-reservoir nature), unlike in ferrocene. The chemical irreversibility increases in THF as the dendrimer size increases, due to more facile ligand substitution with THF at the 19-electron level when the chain bulk increases.     

Reaction of monocyclic ferrocenyl-4,5-dihydropyrazoles with β-dicarbonyl compounds

Monocyclic 3- and 5-ferrocenyl-4,5-dihydropyrazoles with a free NH group in the molecule react with acetylacetone to form the corresponding enaminocarbonyl compounds. The latter were isolated as a single isomer, presumably E. 3-Ferrocenyldihydropyrazoles and 5-ferrocenyl-3-(p-methoxyphenyl)-4,5-dihydropyrazole analogously react with acetoacetic ester. 5-Ferrocenyl-3-phenyl-, 3-(p-bromophenyl)-5-ferrocenyl, and 3,5-diferrocenyl-4,5-dihydropyrazoles react with acetoacetic ester to form acetoacetylpyrazolides.Translated from Zhurnal Obshchei Khimii, Vol. 74, No. 12, 2004, pp. 1942–1947.Original Russian Text Copyright © 2004 by E. Klimova, Vazquez Lopez, T. Klimova, Martinez Garcia, Meleshonkova, Ruiz Ramirez.This revised version was published online in April 2005 with a corrected cover date.     

New butenolides in plantlets of Virola surinamensis (Myristicaceae)

A phytochemical investigation in plantlets of the Brazilian medicinal tree Virola surinamensis resulted in the isolation and structural determination of four new compounds: 3-hydroxy-4-methyl-2-(11'-piperonyl-n-undecyl)-butenolide; 3-hydroxy-4-methyl-2-(7'-piperonyl-n-heptyl)-butanolide; 9'-(3,4-methylenedioxy-phenyl)-nonanoic acid and 13'-(3,4-methylene-dioxyphenyl)-tridecanoic acid. Thirteen compounds previously isolated from seeds and adult plants were also reported.