Inner sequence based invariant subspaces in

A closed subspace is said to be invariant if it is invariant under the Toeplitz operators and . Invariant subspaces of are well-known to be very complicated. So discovering some good examples of invariant subspaces will be beneficial to the general study. This paper studies a type of invariant subspace constructed through a sequence of inner functions. It will be shown that this type of invariant subspace has direct connections with the Jordan operator. Related calculations also give rise to a simple upper bound for , where are zeros of a Blaschke product.

     

Synthesis of polymers in aqueous solutions: Synthesis of polysulfide by reaction of bis(4‐mercaptophenyl) sulfide with bis(4‐chloro‐3‐nitrophenyl) sulfone using various bases in aqueous solutions

The polycondensation of bis(4‐mercaptophenyl) sulfide (BMPS) with bis(4‐chloro‐3‐nitrophenyl) sulfone (BCNPS) was examined using various organic or inorganic bases in mixed solvents of N‐methyl‐2‐pyrrolidone (NMP) with water or in plain water. The reaction of BMPS with BCNPS proceeded smoothly to give the corresponding polysulfide in mixed solvents of NMP with water at 60 °C using 1,8‐diazabicyclo[5.4.0]undecene‐7 as a base, although the rate of the reaction decreased gradually as the water in the solvent increased. Polysulfide can also be obtained by reaction in plain water using appropriate organic bases such as tripropylamine (TPA) or quinoline. The polysulfide with a number‐average molecular weight of 45,100 was synthesized in 62% yield when the reaction of BMPS with BCNPS was performed using TPA as a base at 60 °C for 48 h in plain water. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3399–3404, 2000     

In situ CP MAS NMR spectroscopy under continuous-flow conditions to monitor real time dynamics during propene polymerization over a supported Ziegler catalyst

In situ propene polymerization was observed using CP MAS (cross polarization with magic angle spinning) ¹³C NMR spectroscopy under the conditions of continuously flowing propene through a supported Ziegler catalyst treated with triethylaluminium. The signals at 44, 26, and 22 ppm attributed to the CH₂, CH, and CH₃ groups of polypropene, respectively, were found to appear upon exposure to the propene flow (0.1 L/min). An increase in intensities of these lines was observed for 30 min, then they remained approximately constant. The cross-polarization parameters of nascent polypropene, measured using standard techniques, were close to those of typical crystalline polypropene. The technique has a great potential as an effective tool for the investigation of the polypropene formation on the Ziegler catalyst.     

A compact permanent‐magnet system for measuring magnetic circular dichroism in resonant inelastic soft X‐ray scattering

A compact and portable magnet system for measuring magnetic dichroism in resonant inelastic soft X‐ray scattering (SX‐RIXS) has been developed at the beamline BL07LSU in SPring‐8. A magnetic circuit composed of Nd–Fe–B permanent magnets, which realised ～0.25 T at the center of an 11 mm gap, was rotatable around the axis perpendicular to the X‐ray scattering plane. Using the system, a SX‐RIXS spectrum was obtained under the application of the magnetic field at an angle parallel, nearly 45° or perpendicular to the incident X‐rays. A dedicated sample stage was also designed to be as compact as possible, making it possible to perform SX‐RIXS measurements at arbitrary incident angles by rotating the sample stage in the gap between the magnetic poles. This system enables facile studies of magnetic dichroism in SX‐RIXS for various experimental geometries of the sample and the magnetic field. A brief demonstration of the application is presented.     

Detector area expansion at iNSE neutron spin echo spectrometer

Expansion of a detection area is an effective method to increase the measurement efficiency of a neutron spin echo (NSE) spectrometer as well as other spectrometers. For this purpose, we installed a new π/2 spin flipper and Fresnel coil of iNSE spectrometer at JRR-3, Tokai, Japan, for wide-area data acquisition. In this study, we propose a data reduction method to correct the phase inhomogeneity due to the path difference of neutrons on the large detection area. This method can convert many NSE signals at small areas to one NSE signal at a large area with taking the phase offset due to the phase inhomogeneity into account. The measurement efficiency increased by approximately one order of magnitude as a result of the detection area expansion.     

Creation and application of psychoactive designer drugs data library using liquid chromatography with photodiode array spectrophotometry detector and gas chromatography-mass spectrometry

In order to quickly confirm a potentially hazardous psychoactive designer drug (a compound in which part of the molecular structure of a stimulant or narcotic has been modified), we created a psychoactive drugs data library by performing analysis using liquid chromatography with photodiode array spectrophotometry (LC/PDA) and gas chromatography-mass spectrometry (GC/MS). The data in this library consist of the LC capacity factor (k′) ratios in relation to the internal standard, the ultraviolet (UV) spectra and the MS spectra of 104 compounds. By performing a comparative study of the data in this report with the analytical data for commercial and illegal drug products, it is possible to quickly identify the psychoactive designer drugs in 205 purchased products by using the library. Further, it is possible to analogize the structure of drugs for which there is no matching data in the library using similar data.Furthermore, when structural isomers of controlled substances have detected from the presented library, similarity of their biological effects on human will be predicted, thus leading to regulate their public circulation. Examples of these types of isomers include, for instance, the narcotic 3,4,5-trimethoxyamphetamine (TMA) and its positional isomers 2,4,5-trimethoxyamphetamine (TMA-2) and 2,4,6-trimethoxyamphetamine (TMA-6), or the narcotic 1-(3-chlorophenyl)piperazine (3CPP) and its isomers 1-(o-chlorophenyl)piperazine (2CPP) and 1-(p-chlorophenyl)piperazine (4CPP). Differentiation of these compounds is necessary in regulating them, and we report here the results of a study of a method to confirm these compounds using the present library.     

Precise determination of hyperfine interactions and second-order doppler shift in <Superscript>149</Superscript>Sm Mössbauer transition

We have succeeded in precisely determining the hyperfine interactions, particularly the isomer shifts, in the ¹⁴⁹Sm Mössbauer transition. The difference in the nuclear radii between the ground and excited states is critical for the determination of isomer shifts but is relatively small in ¹⁴⁹Sm. Therefore, the precise determination by ¹⁴⁹Sm Mössbauer spectroscopy is difficult. The recent development of synchrotron-radiation-based Mössbauer spectroscopy allows the isomer shifts to be determined more precisely than previously with the help of wellcollimated synchrotron radiation. In particular, the time-window effect assists the precise determination of hyperfine interactions in the ¹⁴⁹Sm Mössbauer transition because this effect enables us to measure spectra with higher energy resolution than natural linewidth determined by the lifetime of the excited states. Meanwhile, highenergy-resolution measurements to determine center shifts by SR-based Mössbauer spectroscopy enable us to observe the second-order Doppler shift, which has not been discussed, particularly for heavy Mössbauer nuclei. We have discussed the precise determination of isomer shifts and the observation of the second-order Doppler shift using ¹⁴⁹Sm synchrotron-radiation-based Mössbauer spectroscopy.     

In-Line Reactions and Ionizations of Vaporized Diphenylchloroarsine and Diphenylcyanoarsine in Atmospheric Pressure Chemical Ionization Mass Spectrometry

We propose detecting a fragment ion (Ph₂As⁺) using counter-flow introduction atmospheric pressure chemical ionization ion trap mass spectrometry for sensitive air monitoring of chemical warfare vomiting agents diphenylchloroarsine (DA) and diphenylcyanoarsine (DC). The liquid sample containing of DA, DC, and bis(diphenylarsine)oxide (BDPAO) was heated in a dry air line, and the generated vapor was mixed into the humidified air flowing through the sampling line of a mass spectrometer. Humidity effect on the air monitoring was investigated by varying the humidity of the analyzed air sample. Evidence of the in-line conversion of DA and DC to diphenylarsine hydroxide (DPAH) and then BDPAO was obtained by comparing the chronograms of various ions from the beginning of heating. Multiple-stage mass spectrometry revealed that the protonated molecule (MH⁺) of DA, DC, DPAH, and BDPAO could produce Ph₂As⁺ through their in-source fragmentation. Among the signals of the ions that were investigated, the Ph₂As⁺ signal was the most intense and increased to reach a plateau with the increased air humidity, whereas the MH⁺ signal of DA decreased. It was suggested that DA and DC were converted in-line into BDPAO, which was a major source of Ph₂As⁺.

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Are Unsaturated Isocyanides so Different from the Corresponding Nitriles?

Simple unsaturated and cyclopropylic isocyanides are synthesized by an efficient and simple approach. These compounds with gradually increasing distance between the unsaturated moiety and the isonitrile group are studied by UV photoelectron spectroscopy and quantum chemical calculations, and also compared to the corresponding nitriles. The first photoelectron band of the unsaturated compounds is linked to removal of an electron from the HOMO, which corresponds to CC multiple-bond ionization in antibonding interaction with the π-isocyanide bond (in the same plane) for conjugated systems, or in antibonding interaction with the pseudo-π-CH(2) group for isolated systems. For the 1-ethenyl derivatives, both cyano and isocyano groups act as a π-electron acceptor from the vinyl group, but the isocyano π system is much more strongly destabilized (ionization energies (IEs) shift to smaller values) by vinyl (3.12 eV) than the cyano π system is (2.70 eV). In comparison with the 1-ethynyl derivatives, a less pronounced destabilization (2.69 eV) of π(NC) by the ethynyl system (1.86 eV for π(CN)), and nearly the same order of magnitude of the energetic gap between the total antibonding (π(CC)-π(NC)) and the total bonding (π(CC)+π(NC)) IEs for ethenyl and ethynyl compounds are noted. The huge values of these last-named data for H(2)C=CH-NC (3.85 eV) and for HC≡C-NC (4.04 eV) reflect the strong interaction between the unsaturated carbon-carbon moiety and the isocyanide group, and thus more efficient conjugation than for the corresponding nitriles.     

Vector WIMP miracle

Weakly interacting massive particle (WIMP) is well known to be a good candidate for dark matter, and it is also predicted by many new physics models beyond the standard model at the TeV scale. We found that, if the WIMP is a vector particle (spin-one particle) which is associated with some gauge symmetry broken at the TeV scale, the Higgs mass is often predicted to be 120–125 GeV, which is very consistent with the result of Higgs searches recently reported by ATLAS and CMS Collaborations at the Large Hadron Collider experiment. In this Letter, we consider the vector WIMP using a non-linear sigma model in order to confirm this result as general as possible in a bottom-up approach. Near-future prospects to detect the vector WIMP at both direct and indirect detection experiments of dark matter are also discussed.