一类规划问题所给最优性必要条件的注记

本文指出了一类规划问题所给最优性必要条件中所存在的问题。对于一些带有附加项，（如（x^TDx)^1/2‖Sx‖p）的单目标规划问题一般都给出了一个类似集合Z^0 ，并以“Z^0为空集”作为一个前提条件。本文指出此条件太强，并论证了当只有Z^0为空集时，就可推出强最优性必要条件，而不必要求“x^0是最优解”。     

Orthomanganated arenes in synthesis VII. Transition-metal mediated formation of a P?P bond; the X-ray crystal structure of Mn2(μ-η1, η1-Ph2PPPh2)(μ-Cl)2(CO)6

The reaction of PPh₂Cl with orthomanganated acetophenone, 2′-CH₃C(O)C₆H₄Mn(CO)₄, gives Mn₂(μ-η₁,η¹-Ph₂PPPh₂)(μ-Cl)₂(CO)₆. An X-ray structure determination [triclinic, space group P1 , a = 10.908(4) Å, b = 11.756(3) Å, c = 12.186(3) Å, α = 96.20(2)°, β = 99.51(2)°, γ = 96.52(2)°] shows two Mn(CO)₃ groups held together by two bridging Cl ligands, and further bridged by a Ph₂P? PPh₂ group prepared in situ.     

Extraction chromatographic separation of carrier-free Tb and Pm generated in (p,xn)-type nuclear reactions

The nuclear reactions of (p, xn)-type, E_p=100–120 MeV, on Gd and Nd have been used to produce highly radioactive preparations of Tb and Pm enriched with neutron-deficient isotopes. Under comparable conditions the yields of practically all isotopes are considerably higher than in Tb and Gd spallation reactions at E_p=660 MeV. The radioactivity of screened¹⁵⁴Tb and¹⁵⁶Tb isotopes has been increased more than 40 times. Tb and Pm were separated from gram amounts of the target-elements by the extraction chromatography technique with undiluted di-(2-ethylhexyl) phosphoric acid as stationary phase. The radiochemical method developed was also applied to separate the radiochemically pure preparation of¹⁶¹Tb from Gd oxide irradiated with thermal neutrons.     

Semiclassical quantization of three-dimensional quasi-Landau resonances under strong-field mixing

Three-dimensional “regular” quasi-Landau resonances, recently discovered experimentally in the Balmer spectrum of the highly excited hydrogen atom around the ionization limit in external static homogeneous magnetic fields, are investigated theoretically by extending previous classical trajectory calculations to semi-classically. Employing the EBK-method for multidimensional non-separable systems, closed trajectories of the excited electron with the proton as origin are quantized by numerical quadrature of the two-dimensional EBK-integral in cylindrical coordinates. The results are resonances with quantum numbersn=1, 2,... for each closed classical trajectory as functions of both the excitation energyE and field strengthB. The calculations include in particular also the classically chaotic region around the ionization limit with experimentally accessible fields, just the region which has so far defied exact quantum mechanical solution. Based on simple physical arguments for the motion of the highly excited electron, an analytic relation is derived for the (E, B)-dependence of the regular three-dimensional resonances which fits quantitatively the numerical EBK-results.     

Determination of phthalate monoesters in human milk,consumer milk,and infant formula by tandem mass spectrometry (LC–MS–MS)

Daily exposure of humans to phthalates may be a health risk because animal experiments have shown these compounds can affect the differentiation and function of the reproductive system. Because milk is the main source of nutrition for infants, knowledge of phthalate levels is important for exposure and risk assessment. Here we describe the development and validation of a quantitative analytical procedure for determination of phthalate metabolites in human milk. The phthalate monoesters investigated were: monomethyl phthalate (mMP), monoethyl phthalate (mEP), mono-n-butyl phthalate (mBP), monobenzyl phthalate (mBzP), mono-(2-ethylhexyl) phthalate (mEHP), and monoisononyl phthalate (mNP). The method is based on liquid extraction with a mixture of ethyl acetate and cyclohexane (95:5) followed by two-step solid-phase extraction (SPE). Detection and quantification of the phthalate monoesters were accomplished by high-pressure liquid chromatography using a Betasil phenyl column (100 mm×2.1 mm×3 m) and triple tandem mass spectrometry (LC–MS–MS). Detection limits were in the range 0.01 to 0.5 g L^–1 and method variation was from 5 to 15%. Analysis of 36 milk samples showed that all these phthalates were present, albeit at different concentrations. Median values (g L^–1) obtained were 0.11 (mMP), 0.95 (mEP), 3.5 (mBP), 0.8 (mBzP), 9.5 (mEHP), and 101 (mNP). We also analysed seven samples of consumer milk and ten samples of infant formula. Only mBP and mEHP were detected in these samples, in the ranges 0.6–3.9 g L^–1 (mBP) and 5.6–9.9 g L^–1 (mEHP).     

Determination of one-dimensional crystal structures using the double Patterson function

The properties and previous use of the double Patterson function in x-ray crystallography are briefly reviewed followed by an account of a new iterative technique, based on the double Patterson, which is being developed by the author. The technique starts with an approximation to the double Patterson which does not require phases, then improves the approximation by making it conform to the known projections and known magnitudes of the Fourier coefficients. The latter are 3-phase structure invariants and estimating their phases is an important step in the direct determination of structure factor phases. Tests carried out on one-dimensional centro-symmetric structures show that the technique is successful. At best, it determines correct phases for all 3-phase invariants. At worst, it fails to improve on the estimate of all phases being zero. It consistently does very much better than the B_{3, 0} formula which is also based on the double Patterson. Further development is necessary to apply the technique to non-centrosymmetric structures and to real structures in three dimensions.