A formula for angular and hyperangular integration

A formula is derived which allows angular or hyperangular integration to be performed on any function of the coordinates of a D-dimensional space, provided that it is possible to expand the function as a polynomial in the coordinates x₁,x₂,...,x_d. The expansion need not be carried out for the formula to be applied. This revised version was published online in July 2006 with corrections to the Cover Date.     

Selective Transport of Lead(II) and Strontium(II) Through a Crown Ether-Based Polymer Inclusion Membrane Containing Dialkylnaphthalenesulfonic Acid

New polymer inclusion membranes (PIMs) containing 18-membered crownethers and dialkylnaphthalenesulfonic acid are proposed for Sr2+ and Pb2+removal from nitric acid solutions. The influence of source phasecomposition and stripping agents was characterized and permeabilitycoefficients were calculated. The PIMs are easy to prepare and may be usefulin separation and concentration procedures for these cations from complexmixtures such as nuclear waste. Long-term stability was obtained for atleast several weeks of constant use during which no significant change ofpermeability was observed.     

Compartmentalized polymerization initiated by oil-soluble initiators. Calculation of average number of radicals per particle

Expressions for calculating the stationary state distribution of radicals in compartmentalized systems with a constant number of reaction loci containing an oil-soluble initiator are given. Besides pairwise formation of radicals in the particles, desorption and reabsorption, water phase termination, solubility of the initiator in the aqueous phase, and the possibility of formation of a single radical species are taken into consideration. The calculation is based on a probabilistic analysis leading to a third-order recurrence relation solved using confluent, hypergeometric Kummer functions. Some calculated curves illustrating the de-pendence of the average number of radicals per particle on various relevant parameters are included. © 1995 John Wiley & Sons, Inc.     

Complexes of chromium(III), manganese(II) and nickel(II) with methylhydrazinecarboxylate and 1,1-dimethylhydrazinecarboxylate ligands

Summary New complexes of chromium(III), manganese(II) and nickel(II) with methylhydrazinecarboxylate (MeCz) and of manganese(II) and nickel(II) with 1,1-dimethylhydra-zinecarboxylate (Me₂Cz) were prepared by reacting salts of the metals with CO₂-saturated solutions of the hydrazines in EtOH. The compounds [Cr(MeCz)₃]·2H₂O, Ni(MeCz)₂(H₂O)₃·MMH, Mn(MeCz)₂(H₂O)₂(MMH = monomethylhydrazine) and M(Me₂Cz)₂(H₂O)₂ (M = Mn or Ni) were investigated using d.t.a., t.g.a., electronic and i.r. spectroscopy and by magnetic susceptibility measurements.     

Benzannelated analogs of phenanthro[1,2-b]- and [2,1-b]thiophene: Synthesis and structural characterization by two-dimensional NMR and X-ray techniques

Syntheses of benzo[3,4]phenanthro[1,2-b]thiophene, benzo[3,4]phenanthro[2,1-b]thiophene and their 1-methyl analogs are reported as potential constituents of solvent refined coal liquids and for mutagenicity testing. The attempted synthesis of the 13-methyl analogs which gave the 11-methyl isomers is also described. Total assignments of the ¹H- and ¹³C-nmr spectra based on long range optimized heteronuclear protoncarbon two-dimensional chemical shift correlation are reported. Carbon assignments obtained for benzo[3,4]-phenanthro[1,2-b]thiophene using this approach were confirmed with a 125 MHz ¹³C–¹³C INADEQUATE spectrum. X-Ray crystal structures were determined for benzo[3,4]phenanthro[1,2-b]thiophene and 1-methyl-benzo[3,4]phenanthro[2,1-b]thiophene. Both molecules were helically distorted from planarity. Close intramolecular contacts between the bay region H1–H13 and ClMe-H13 of 2.03 and 2.28 Å, respectively, were responsible for the distortions. There were no close intermolecular contacts of <3.5Å. both molecules refined to an R value of <0.05.     

Field evaluations of the VDmax approach for substantiation of a 25 kGy sterilization dose and its application to other preselected doses

The International and European standards for radiation sterilization require evidence of the effectiveness of a minimum sterilization dose of 25 kGy but do not provide detailed guidance on how this evidence can be generated. An approach, designated VD_max, has recently been described and computer evaluated to provide safe and unambiguous substantiation of a 25 kGy sterilization dose. The approach has been further developed into a practical method, which has been subjected to field evaluations at three manufacturing facilities which produce different types of medical devices. The three facilities each used a different overall evaluation strategy: Facility A used VD_max for quarterly dose audits; Facility B compared VD_max and Method 1 in side-by-side parallel experiments; and Facility C, a new facility at start-up, used VD_max for initial substantiation of 25 kGy and subsequent quarterly dose audits. A common element at all three facilities was the use of 10 product units for irradiation in the verification dose experiment.

The field evaluations of the VD_max method were successful at all three facilities; they included many different types of medical devices/product families with a wide range of average bioburden and sample item portion values used in the verification dose experiments. Overall, around 500 verification dose experiments were performed and no failures were observed. In the side-by-side parallel experiments, the outcomes of the VD_max experiments were consistent with the outcomes observed with Method 1.

The VD_max approach has been extended to sterilization doses >25 and <25 kGy; verification doses have been derived for sterilization doses of 15, 20, 30, and 35 kGy. Widespread application of the VD_max method for doses other than 25 kGy must await controlled field evaluations and the development of appropriate specifications/standards.     

Acetonitrile derivatives as carbonyl synthons. One-pot preparation of diheteroaryl ketones via a strategy of sequential SNAr substitution and oxidation

The anion of 2-aryl acetonitrile derivatives reacted with a variety of heteroaryl chlorides or bromides in an S(N)Ar manifold to afford intermediate anions which were susceptible to oxidation. The addition of sodium peroxide and aqueous NH(4)OAc solution effected oxidation to afford aryl heteroaryl ketones in good yields. Aryl acetonitrile derivatives are thus umpolung-type synthons of the corresponding aryl carbonyl functionality.     

Theoretical method for full ab initio calculation of DNA/RNA-ligand interaction energy

In this paper, we further develop the molecular fractionation with conjugate caps (MFCC) scheme for quantum mechanical computation of DNA-ligand interaction energy. We study three oligonuclear acid interaction systems: dinucleotide dCG/water, trinucleotide dCGT/water, and a Watson-Crick paired DNA segment, dCGT/dGCA. Using the basic MFCC approach, the nucleotide chains are cut at each phosphate group and a pair of conjugate caps (concaps) are inserted. Five cap molecules have been tested among which the dimethyl phosphate anion is proposed to be the standard concap for application. For each system, one-dimensional interaction potential curves are computed using the MFCC method and the calculated interaction energies are found to be in excellent agreement with corresponding results obtained from the full system ab initio calculations. The current study extends the application of the MFCC method to ab initio calculations for DNA- or RNA-ligand interaction energies.     

Electrochemistry and photoelectron spectroscopy of oxomolybdenum(V) complexes with phenoxide ligands: effect of para substituents on redox potentials,heterogeneous electron transfer rates,and ionization energies

Complexes of the form (Tp*)MoOCl(p-OC(6)H(4)X) and (Tp*)MoO(p-OC(6)H(4)X)(2) (Tp* = hydrotris(3,5-dimethyl-1-pyrazolyl)borate and X = OEt, OMe, Et, Me, H, F, Cl, Br, I, and CN) were examined by electrochemical techniques and gas-phase photoelectron spectroscopy to probe the effect of the remote substituent (X) on electron-transfer reactions at the oxomolybdenum core. Cyclic voltammetry revealed that all of these neutral Mo(V) compounds undergo a quasireversible one-electron oxidation (Mo(VI)/Mo(V)) and a quasireversible one-electron reduction (Mo(V)/Mo(IV)) at potentials that linearly depend on the electronic influence (Hammett sigma(p) parameter) of X. The first ionization energies for (Tp*)MoO(p-OC(6)H(4)X)(2) (X = OEt, OMe, H, F, and CN) were determined by photoelectron spectroscopy. A nearly linear correlation was found for the Mo(VI)/Mo(V) oxidation potentials in solution and the gas-phase ionization energies. Calculated heterogeneous electron-transfer rate constants show a slight systematic dependence on the substituent.     

Thermal isomerization of cis,anti,cis-tricyclo[6.3.0.0(2,7)]undec-3-ene to endo-tricyclo[5.2.2.0(2,6)]undec-8-ene

[reaction: see text] The gas-phase thermal isomerization of cis,anti,cis-tricyclo[6.3.0.0(2,7)]undec-3-ene (1) to endo-tricyclo[5.2.2.0(2,6)]undec-8-ene (2) at 315 degrees C occurs cleanly through a symmetry-forbidden [1,3] suprafacial,retention (sr) pathway.