Positivity of Lyapunov Exponents for a Continuous Matrix-Valued Anderson Model

We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all energies in (2, +∞) except those in a discrete set, which leads to absence of absolutely continuous spectrum in (2, +∞). This result is an improvement of a previous result with Stolz. The methods, based upon a result by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a criterion by Goldsheid and Margulis, allow for singular Bernoulli distributions.      

Assignment of the EPR spectrum of 5,5-dimethyl-1-pyrroline N-oxide (DMPO) superoxide spin adduct

[structure: see text] Spin trapping consists of using a nitrone or a nitroso compound to "trap" an unstable free radical as a long-lived nitroxide that can be characterized by electron paramagnetic resonance (EPR) spectroscopy. The formation of DMPO-OOH, the spin adduct resulting from trapping superoxide (O(2)(*)(-)) with 5,5-dimethyl-1-pyrroline N-oxide (DMPO), has been exploited to detect the generation of superoxide in a wide variety of biological and chemical systems. The 12-line EPR spectrum of DMPO-OOH has been either reported or mentioned in more than a thousand papers. It has been interpreted as resulting from the following couplings: A(N) approximately 1.42 mT, A(H)beta approximately 1.134 mT, and A(H)gamma(1H) approximately 0.125 mT. However, the DMPO-OOH EPR spectrum has an asymmetry that cannot be reproduced when the spectrum is calculated considering a single species. Recently, it was proposed that the 0.125 mT splitting was misassigned and actually results from the superimposition of two individual EPR spectra associated with different conformers of DMPO-OOH. We have prepared 5,5-dimethyl-[3,3-(2)H(2)]-1-pyrroline N-oxide (DMPO-d(2)), and we showed that the EPR spectrum of the corresponding superoxide spin adduct is composed of only six lines, in agreement with the assignment of the 0.125 mT splitting to a gamma-splitting from a hydrogen atom bonded to carbon 3 of DMPO. This result was supported by DFT calculations including water solvation, and the asymmetry of the DMPO-OOH EPR spectrum was nicely reproduced assuming a chemical exchange between two conformers.     

Properties of block and graft copolymers of polybutadiene with small complexed poly(4-vinylpyridine) segments

Various diblocks, triblocks and a graft copolymer of butadiene with 4-vinylpyridine short blocks have been prepared. They were complexed with ZnCl₂ to give ionomer-like materials. For all copolymers, the T_g of the elastomeric block (?84°C to ?91°C) was unchanged by complexation. For all diblocks and triblocks with short blocks (DP _n ～ 3) the storage modulus was only slightly increased by comparison with uncomplexed materials. For the graft copolymer even with short blocks the material is less sensitive to temperature after complexation. For triblocks, when the DP _n of the vinylpyridine blocks was high enough (15 units), complexes were associated in multiplets of large size and the elastomeric properties were retained up to 200°C.     

Glass open-tubular capillary columns with chemically bonded methyl-phenyl siloxane stationary phases of tailor made polarity

Summary The previously described method yielding apolar, chemically bonded methyl polysiloxane glass capillary columns was extended to the production of capillary systems of controlled polarity. The approach involved prior synthesis of a reactive methyl-phenyl polysiloxane polymer by copolymerisation of a mixture of dimethyl and diphenyl chlorosilanes. The polymer was then chemically bonded to the capillary glass surface to yield remarkably stable, high resolution analytical systems which were shown to be particularly well suited to the separation of biochemical mixtures at the subnanogram level. The principle of copolymerisation of differently substituted silanes confers to the method a considerable flexibility which could be used to devise polar capillary systems tailor made for a given analytical problem.     

Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model

For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t ^–(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1.     

Synthesis,characterization and biological activity of some 1,2,4‐triazine derivatives

4‐Amino‐6‐methyl‐3‐(2H)‐thioxo‐5‐(4H)‐oxo‐1,2,4‐triazine ( 1 ) was condensed with 2‐methyl (or phenyl)‐4H‐3,1‐benzoxazin‐4‐one ( 5a,b ) in boiling acetic acid to give compounds 8‐11 . Reacting 1 with chloroacetyl chloride afforded the corresponding chloroacetamido and triazinothiadiazine derivatives 12 and 13 . Condensing 2 with succinic anhydride and/or phthalic anhydride yielded compounds 14 and 15 . Benzoylation of 4‐amino‐6‐methyl‐3‐(2H)‐thioxo‐5‐(4H)‐oxo‐2‐(2,3,4,5‐tetra‐O‐acetyl‐α‐D‐glucopyra‐nosyl)‐1,2,4‐triazine ( 19 ) afforded the corresponding 4‐N,N‐dibenzoyl derivative 20 . Deblocking of the N‐2 glycoside 21 and the S‐glycoside 22 by methanolic ammonia gave compounds 23 and 24 . Acetylation of 4‐amino glycoside 25a afforded the corresponding 4‐mono‐ and 4‐diacetyl derivatives 26 and 27 . Deamination of 25a,b yielded compounds 28a,b . Methylation of compound 28b afforded the corresponding N4‐ and S‐methyl derivatives 29 and 30 .     

Offline estimation of 2D crystal lattice parameters by processing the electron diffraction image

Electron diffraction provides useful information about the internal composition of materials and has been in the use of material scientists for more than fifty years. In order to extract useful information from offline diffraction images, they are manually analyzed by using some photometric technique. Manual analysis is however a cumbersome, laborious and difficult task. To reduce the labors of material scientists one can employ image processing techniques to perform automated analysis, due to the well established popularity and clear evidence of widely used image processing techniques. In this work an image processing technique is being proposed for the extraction of 2D unit cell information from diffraction images on one hand and finding the 2D point group contained by the lattices on the other. The technique employs a morphological shrinking operation to find the center of each spot in the underlying preprocessed diffraction image. This is followed by the extraction of eight points with reference to the spot produced by the transmitted electron beam. The resultant nine points, i.e. the extracted eight plus the reference spot generated by the transmitted electron beam, are then subjected to symmetry operations, rotation symmetry and mirror symmetry, in polar coordinate system, to classify the point group of the lattice produced by the electron diffraction. One of the difficult task, even in manual analysis, is to ascertain the exact spot where the transmitted electron beam hit the sample at the time of realization of the image. This has been accurately and intuitively done by employing the notion that the transmitted spot must have greater number of pixels, with the highest gray value, among the diffracted spots. The proposed strategy has been applied to a sample set of various images and the results shows that the technique is efficient in determining the unit cell in 2D and classify the point group with good accuracy.