l1 solution of linear inequalities

The numerical solution of a possible inconsistent system oflinear inequalities in the l₁ sense is considered. The non-differentiablel₁ norm minimization problem is approximated by a piecewisequadratic Huber smooth function. A continuation algorithm isdesigned to find an l₁ solution of the inequality system. Inthe case where the linear inequality system is consistent, asolution is obtained by solving any smoothed problem. Otherwise,the algorithm is shown to terminate in a finite number of iterations.We also consider an alternative smoothing scheme which sharessimilar properties with the first one, but results in an improvedcomputational performance of the continuation algorithm on inconsistentsystems. Numerical experiments are conducted to test the efficiencyof the algorithm.     

Vibrational properties of thymine,uracil and their isotopomers

Density functional theory (DFT) calculations using the B3LYP/6‐311G(d,p) basis set of ten isotopomers of thymine and four isotopomers of uracil, including the natural abundance isotopomers, are reported. Comparison of the calculated wavenumber shifts upon hydrogen, carbon and nitrogen isotopic substitution with those from experimental Raman and infrared measurements show good agreement in both the direction and the magnitude of the shift. These results are contrasted to previously reported calculations and discussed in the context of assigning the normal modes of thymine and uracil. Copyright © 2007 John Wiley & Sons, Ltd.     

Spin-dependent level density in interacting boson-fermion-fermion model

The level density of the odd-odd nucleus¹³² Pr is investigated in the interacting boson-fermion-fermion model (IBFFM) which accounts for collectivity and complex interaction between quasiparticle and collective modes. The IBFFM total level density is fitted by a Gaussian and its tail is also fitted by Bethe formula and constant temperature Fermi gas model. The IBFFM spin-dependent level densities show high-spin reductions with respect to Bethe formula. This can be well accounted for by a modified spin-dependent level density formula.     

Magnetic-field dependent optically detected ESR in the photoexcited triplet states of bridged Zr(IV) metallocenes

We report on the magnetic-field-dependent optically detected magnetic resonance (ODMR) spectra for polycrystalline samples of the bridged Zr(IV) metallocenes, Me₂Si<(Cp₂)ZrCl₂ ( (dimethylsilylbis(cyclopentadienyl)zirconium-dichloride) and Me₂C<(Cp₂)ZrCl₂ (iso-propylidenebis(cyclopentadienyl)zirconium-dichloride). ODMR spectra at zero magnetic field were recorded by frequency sweeping a microwave source from 0.1 to 10 GHz with the sample contained in a microwave helix. ODMR spectra at finite magnetic fields were recorded with the sample contained in either a helix or a slotted-tube resonator with a fixed microwave frequency and sweeping the magnetic field. For all experiments, the sample and microwave probes were contained in an immersion dewar cryostat, and the temperature was held at about 2 K. All three zero field ODMR transitions (2|E|, and |D| − |E| and |D|+|E|) were observed in the frequency-swept ODMR spectra recorded at zero and small magnetic fields. The zero-field frequency-swept spectra allowed the determination ofD andE values uniquely. For frequency-swept small-field ODMR spectra recorded at successively higher magnetic fields, each of the ODMR line intensities was observed to increase with increasing magnetic field. This intensity increase was observed for all three ODMR lines, reflecting an increase in the total intensity rather than simply a change in the polarization of the triplet sublevels. The latter would result in a change in the relative intensities of the ODMR lines but would not change simultaneously the intensities of all three lines. The ODMR line intensities increase in proportion toB ⁿ, wheren<1. This field dependence is weaker than the expected proportionalB ² dependence from the Zeeman effect, which likely originates from the magnetic field dependence of the spin relaxation rates between the triplet sublevels. Magnetic-field-swept ODMR spectra recorded at fixed microwave frequencies in the X-band frequency range (9.8 GHz) do not show all three expected classic Pake powder pattern line shape profiles, exhibited by the molecules with their magneticZ, Y, andX axes parallel to the external magnetic field. In particular, the intensity for molecular magneticY-axes parallel to the external magnetic field is completely suppressed. In addition, an external magnetic field dependence in field-swept ODMR spectra was observed, which results in a linear decrease of the ODMR intensity with increasing strength of the external magnetic field over and above that would be expected in a polycrystalline spectrum. The data are analyzed by simulation of the continuous-wave ESR spectrum with the eigenvalues and eigenvectors of the spin Hamiltonian matrix characterizing the triplet state exhibiting the ODMR spectrum, in conjunction with homotopy, as a function of the orientations of the magnetic axes of the various molecules in a polycrystalline sample. This approach is useful to interpret the experimentally observed ODMR transition frequencies andg-values but does not take the amplitudes in the ODMR spectrum. The corrections required to modify the continuous-wave ESR spectral amplitudes that reproduce the observed ODMR amplitudes are effects associated with the ODMR processes.     

Ionic conductivity and tensile properties of hydroxyethyl and hydroxypropyl chitosan membranes

Hydroxyethyl chitosan and hydroxypropyl chitosan were prepared through the reaction of alkali‐chitosan with 2‐chloroethanol and propylene epoxide, respectively. Fourier transform infrared and ¹³C NMR measurements were made to examine the substitution on the chitosan unit. According to a comparison of the peak areas between the modified chitosan and unmodified chitosan and the integration of peak areas of ¹H NMR spectra, for both modified chitosans, the maximum degree of substitution was less than 25%. The ionic conductivity and mechanical properties of modified chitosan membranes were investigated. In comparison with the unmodified chitosan membrane, hydrated hydroxyethyl and hydroxypropyl chitosan membranes with a higher degree of substitution showed an increase in ionic conductivity of about one order of magnitude; moreover, the crystallinity of hydroxyethyl and hydroxypropyl chitosan membranes was remarkably reduced, and their swelling indices increased significantly. However, these modified membranes did not exhibit significant changes in their tensile strength and breaking elongation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1379–1397, 2004     

Dead Ends and Detours En Route to Total Syntheses of the 1990s A list of abbreviations can be found at the end of the article

From the very beginning organic chemistry and total synthesis have been intimately joined. In fact, one of the first things that freshmen in organic chemistry learn is how to join two molecules together to obtain a more complex one. Of course they still have a long way to go to become fully mature synthetic chemists, but they must have the primary instinct to build molecules, as synthesis is the essence of organic chemistry. With the different points of view that actually coexist in the chemical community about the maturity of the science (art, or both) of organic synthesis, it is clear that nowadays we know how to make almost all of the most complex molecules ever isolated. The primary question is how easy is it to accomplish? For the readers of papers describing the total synthesis of either simple or complex molecules, it appears that the routes followed are, most of the time, smooth and free of troubles. The synthetic scheme written on paper is, apparently, done in the laboratory with few, if any, modifications and these, essentially, seem to be based on finding the optimal experimental conditions to effect the desired reaction. Failures in the planned synthetic scheme to achieve the goal, detours imposed by unexpected reactivity, or the absence of reactivity are almost never discussed, since they may diminish the value of the work reported. This review attempts to look at total synthesis from a different side; it will focus on troubles found during the synthetic work that cause detours from the original synthetic plan, or on the dead ends that eventually may force redesign. From there, the evolution from the original route to the final successful one that achieves the synthetic target will be presented. The syntheses discussed in this paper have been selected because they contain explicit information about the failures of the original synthetic plan, together with the evolution of the final route to the target molecule. Therefore, they contain a lot of useful negative information that may otherwise be lost.     

Air-clad optical fibre filament for generating broadband radiation

A simple broadband optical source is demonstrated by using a high numerical aperture air-clad optical fibre to collect broadband emission of blackbody radiation from the fibre during exposure to high intensity electric arcs.