A correlational inequality for linear extensions of a poset

Suppose 1, 2, and 3 are pairwise incomparable points in a poset onn≥3 points. LetN (ijk) be the number of linear extensions of the poset in whichi precedesj andj precedesk. Define λ by $$\lambda = \frac{{N(213)N(312)}}{{\left[ {N(123) + N(132)} \right]\left[ {N(231) + N(321)} \right]}}$$ Two applications of the Ahlswede-Daykin evaluation theorem for distributive lattices are used to prove that λ?(n?1)²/(n+1)² for oddn, and λ?(n?2)/(n+2) for evenn. Simple examples show that these bounds are best-possible. Shepp (Annals of Probability, 1982) proved thatP(12)?P(12/13), the so-calledxyz inequality, whereP(ij) is the probability thati precedesj in a randomly chosen linear extension of the poset, thus settling a conjecture of I. Rival and B. Sands. The preceding bounds on λ yield a simple proof ofP(12)<P(12/13), which had also been conjectured by Rival and Sands.     

PA.FPNS: its synthesis and use in spectrophotometric determination of magnesium

A new polymeric chromogenic reagent PA.FPNS has been synthesized by condensing polyallylamine (PA) with 3-(4-formylphenylazo)-4,5-dihydroxynaphthalene-2,7-disulfonic acid (FPNS) and its properties studied. In alkaline media, PA.FPNS reacts with magnesium to form a water-soluble blue complex, whose absorption maximum is at 604 nm. The molar absorptivity (varepsilon) of the complex is 5.2 x 10(4)l mol(-1) cm(-1), which is four times that of the FPNS-Mg complex, and Beer's law is obeyed over the range 0-0.35 mug ml(-1) magnesium. Compared to the corresponding low-molecular-weight FPNS and other chromogenic reagents, PA.FPNS offers considerably improved sensitivity and selectivity for magnesium, which may be attributed to incorporating FPNS into a water-soluble polymer and the effect of the polymeric chain on the reaction microenvironment. Also, a simple and sensitive spectrophotometric method for the determination of magnesium has been developed and applied to water and human fluid samples with satisfactory results.     

Inner-shell and valence-shell electronic excitation of SF6, SeF6 and TeF6 by high energy electron impact: An investigation of potential barrier effects

Inner- and valence-shell electron energy loss spectra of gaseous SF₆, SeF₆ and TeF₆ have been measured at high impact energy (2.0–3.7 keV) and zero degree scattering angle. The resulting inner-shell excitation spectra include F 1s, S 2s and 2p in SF₆: F 1s, Se 3s, 3p and 3d in SeF₆ and F 1s, Te 4s, 4p, 4d and 3d in TeF₆. The results for each of these hexafluorides are interpreted, in the framework of the potential barrier model, as excitations to resonances involving a common manifold of virtual valence (inner-well) orbitals and also to Rydberg (outer-well) orbitals. The below-edge shape resonances in corresponding inner-shell excitation spectra of these hexafluorides show very similar variations in intensities in accord with expectations based on electric-dipole selection rules. This is an indication that these below-edge resonances in SeF₆ and TeF₆ are of the same symmetry as those in SF₆ (i.e. a_1g and t_1u). The continuum (above-edge) shape resonances in SeF₆ also show similar spectral behavior to those of SF₆ and can be understood by including Se 4d and S 3d orbitals in the basis for the respective MO schemes. However, in TeF₆ completely different spectral behavior is observed for the continuum resonances. In particular, there is a dramatic series of intense resonances observed above the Te 3d and 4d edges. The TeF₆ spectrum can only be understood by extending the MO basis set to include the Te 4f orbitals which are even lower lying than the Te 5d orbitals. Therefore, these continuum resonances which are also seen in the F 1 s and Te 3p spectra of TeF₆ are assigned to l=3 (f-type) continuum shape resonances due to involvement of the 4f orbitals rather than the l=2 (d-type) continuum resonances observed in SF₆ and SeF₆. This is the first reported observation of such f-type continuum shape resonances and such considerations will likely prove to be important in the understanding of near-edge spectra of heavy atom containing species. The VSEELS spectra which are very similar for the three hexafluorides also show significant continuum shape resonances. A consideration of both the ISEELS and the VSEELS spectra indicates that there is a weakening of the potential barrier in going through the series from SF₆, SeF₆ to TeF₆.     

Experimental observation of light-induced solitary waves of analyte bands in capillary electrophoresis.

The phenomenon of electrophoresis in free solution has been studied theoretically down to the molecular level for decades. In addition, intermolecular photo-induced proton transfer reactions, which occur in a wide class of molecules (phenols and aminoarenes) as well as proteins (green fluorescent protein), were also studied extensively. However, the study of the effect of light-induced electrophoretic mobility changes of the analytes in electrophoresis was begun only recently. In the present work, capillary zone electrophoresis was chosen as the environment to measure the magnitude of these electrophoretic mobility shifts induced by light. Background electrolytes (running electrolytes) with high refractive indices were developed, allowing the capillary to work like an optical fiber. The experimental conditions for obtaining stable coupling and guided laser light along the liquid core are discussed. Experimental evidence of band compression is observed, leading to a solitary wave behavior of the analyte band (2-naphthol). These solitary waves result from competition between thermal diffusion (dispersion mechanism) and a nonlinear (band compression) effect due to the combined electrophoresis phenomenon and absorption of guided light by the molecules of the band (which are subjected to a "reversible intermolecular proton transfer reaction" as one of their decay routes). The possibilities of applying this effect to different methods and techniques are also discussed.     

N-isobutyloxycarbonylation for improved detection of 3'-hydroxystanozolol and its 17-epimer in doping control

An improved screening method was developed for 3'-hydroxystanozolol and its 17-epimer in human urine involving gas chromatography-mass spectrometry (GC-MS) with N-isobutyloxycarbonyl (isoBOC) and O-trimethylsilyl (TMS) derivatization. A procedure was reported previously for the pentane extraction of many steroids from urine in doping control, but it was not suitable for the detection of stanozolol metabolites. Compared with the n-pentane extraction method, which gave a poor recovery (< 10%), isoBOC extraction resulted in a good recovery (> 80%). The sensitivity and specificity of mixed N-isoBOC-O-TMS derivatization were adequate for the detection of 3'-hydroxystanozolol and its 17-epimer when 3 ml of urine was used with spiking at a level of 2 ng ml-1. When applied to a stanozolol-positive urine sample, the proposed method allowed rapid and sensitive screening for the detection of 3'-hydroxystanozolol and its 17-epimer.     

Titanium alkoxide complexes: condensed phase and gas phase comparisons

The complex [Ti(2,4-dimethyl-2,4-pentanediolate)2]2 (1) has been synthesized from [Ti(OiPr)4] by transesterification with a stoichiometric amount of 2,4-dimethyl-2,4-pentanediol. We have characterized complex 1 in the solid state by single-crystal X-ray diffraction and in the gas phase by desorption chemical ionization mass spectrometry (DCI-MS). The structural and mass spectrometric data show complex 1 to be stable as a dimer in both the solid and gas phases. The retention of dimeric nuclearity in the gas phase sets complex 1 apart from other simple titanium alkoxide complexes [Ti(OiPr)4] and [Ti(OMe)4]4 that give rise to respective families of molecular ions in the DCI-MS experiment. The highest mass molecular ions for Ti alkoxide complexes in the gas phase may reveal the highest nuclearity that these complexes achieve in condensed phases. According to this interpretation the complex [Ti(OiPr)4] is principally dimeric in the gas phase and probably also in the pure liquid phase and should be represented by the formula [Ti(OiPr)4]2.     

Use of low energy photon spectroscopy in activation analysis of noble metals with high-energy bremsstrahlung

Noble metals have been analyzed in high purity copper and a platinum ore to be certified as reference materials. Analyses were performed by photon activation analyses using both conventional gamma and low energy photon spectroscopy. Our values agree very well with those of other laboratories using various analysis methods. Low energy photon spectroscopy is more advantageous than gamma spectroscopy from various points of view.     

The electronic spectrum of the triethylamine-perfluoro-tert-butanol complex

The far-ultraviolet absorption spectrum of the triethylamine-perfluoro-tert-butanol complex has been measured in the gas phase. The photoelectron band of lowest energy has also been determined. It is about 13000 cm^?1 higher than for free triethylamine. Up to at least 60000 cm^?1, the UV spectrum is readily interpreted as a triethylamine spectrum shifted to higher frequencies by about 13000 cm^?1. The bands of lowest frequency are the 3s and 3p Rydberg bands which follow the ionization potential. Up to 60000 cm^?1, no charge transfer type band has been found.     

Synthesis of some 3-Methyl-11H-indolo[3,2-c] [1,8]naphthyridines. A New heterocyclic ring system

Some derivatives of 11H-indolo[3,2-c] [1,8]naphthyridine, a new heterocyclic system, have been prepared using the Fischer indole synthesis on the appropriately phenylhydrazones. The preparation of some substituted 5,6-dihydro-11H-indolo[3,2-c][1,8]naphthyridines is also described.     

The chemical ionization mass spectra of 2-tert-butyl-substituted 1,3-cycloalkanediol diacetates and dimethyl ethers

The chemical ionization (CI) mass spectra of the 2-tert-butyl-substituted 1,3-cyclopentane- and 1,3-cyclohexanediol diacetates and dimethyl ethers have been determined using isobutane and methane as reagent gases. From the differences in the spectra of these compounds, it clearly follows that steric and conformational effects are expresssed in the CI mass spectra. The relative impact of these effects, however, is strongly dependent on diol derivatization and 2-alkyl substitution.