Discussion of substantially identical gel points among multiallyl monomers based on characterization of resultant network polymer precursors consisting of oligomeric primary polymer chains

No difference in the actual gel points was substantially observed among three isomeric diallyl phthalates such as diallyl phthalate (DAP), diallyl isophthalate, and diallyl terephthalate (DAT); this interesting gelation behavior was discussed further in terms of the correlation between gelation and the difference in cyclization modes, and also, the difference in reactivity between the uncyclized and cyclized radicals for cross‐linking. In the present work, we tried to extend the preceding discussion to the polymerization of triallyl trimellitate (TAT) because the molecular structure of TAT is presumed to essentially involve the characteristics of three isomeric diallyl phthalates and, therefore, the enhanced gelation was expected in TAT polymerization. However, no enhancement of gelation was observed. For a full understanding of the gelation in multiallyl cross‐linking polymerization, we explored further the polymerizations of DAP, DAT, and TAT, especially focusing on the characterization of resultant network polymer precursors (NPPs) using SEC‐MALLS‐viscometry providing the correlation of [η] versus M_w of fractionated samples. Notably, the structure of NPP consisting of oligomeric primary polymer chains generated from specific allyl polymerization would become core‐shell type dendritic with the progress of polymerization. The correlation between delayed gelation and decreased reactivity of dendritic NPP for intermolecular cross‐linking is discussed. Conclusively, the reactivity for intermolecular cross‐linking between NPPs decreased with the progress of polymerization leading to a delayed gelation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2871–2881, 2009     

Absolutely continuous invariant measures for expanding piecewise linear maps

We prove the existence of absolutely continuous invariant measures for arbitrary expanding piecewise linear maps on bounded polyhedral domains in Euclidean spaces ℝ ^d . Oblatum 6-V-1999 & 8-VI-2000?Published online: 11 October 2000     

Affine geometric crystals and limit of perfect crystals

For every non-exceptional affine Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra-discretization is isomorphic to the limit of certain perfect crystals of the Langlands dual affine Lie algebra.

     

Conformational and Intermolecular Interaction Dynamics of Photolyase/Cryptochrome Proteins Monitored by the Time‐Resolved Diffusion Technique

Cryptochrome (CRY), a blue light sensor protein, possesses a similar domain structure to photolyase (PHR) that, upon absorption of light, repairs DNA damage. In this review, we compare the reaction dynamics of these systems by monitoring the reaction kinetics of conformational change and intermolecular interaction change based on time‐dependent diffusion coefficient measurements obtained by using the pulsed laser‐induced transient grating technique. Using this method, time‐dependent biomolecular interactions, such as transient dissociation reactions in solution, have been successfully detected in real time. Conformational change in (6‐4) PHR has not been detected after the photoexcitation by monitoring the diffusion coefficient. However, the repaired DNA dissociates from PHR with a time constant of 50 μs, which must relate to a minor conformational change. However, CRY exhibits a considerable diffusion change with a time constant of 400 ms, which indicates that the protein–solvent interaction is changed by the conformational change. The C‐terminal domain of CRY is shown to be responsible for this change.     

Influence of the glucosylated β-cyclodextrin inclusion on sulfur trioxide spin-adduct stabilizations and spin-trapping rate processes for DMPO-type spin traps

The effect of CD-inclusion on spin-trapping rates and spin-adduct decay rates for sulfur trioxide radical anion (SO₃ ^??) was investigated. SO₃ ^?? radical was produced with UV photolysis of sodium sulfite in basic aqueous solution, and spin-trapped with various spin traps, i.e., PBN (α-phenyl-N-t-butylnitrone), DMPO (5,5-dimethyl pyrroline-1-oxide), and three other phosphoryl DMPO-type spin traps. A modified β-CD, 6-O-α-d-glucosyl-β-cyclodextrin (G-β-CD) having better inclusion properties than β-CD, was employed. Upon adding excess G-β-CD, decay rates of SO₃ ^?? radical adducts significantly decreased in most spin traps. Half-lives of SO₃ ^?? radical adducts of phosphoryl spin traps were one to two orders of magnitude longer than that of PBN or DMPO, and the G-β-CD addition further extended the half-life time. The spin traps containing phosphoryl-group all showed higher SO₃ ^?? trapping rates than those of PBN and DMPO, but two phosphoryl spin traps achieved slower trapping rates by G-β-CD addition. In addition, the structures of CD-inclusion complexes of spin traps were established by means of 1D and 2D NMR measurements. Based on the results, the influences of inclusion on the spin-trapping rate processes and spin-adduct stabilizations were discussed. We conclude that substituents in DMPO-type spin traps may be modified to provide best spin-trapping capabilities in the presence or absence of CD.     

Hydrofluoroarylation of alkynes with fluoroarenes

A combination of Ni(cod)(2) and PCyp(3) is found to be an effective catalyst for chemoselective activation of the C-H bond of fluoroarenes over C-F bonds followed by insertion of alkynes to allow direct alkenylation of the electron-deficient arenes. The characteristics of the reactions are: a C-H bond ortho to a fluorine substituent is selectively activated; the reactivity of fluorobenzenes is roughly proportional to the number of fluorine atoms. The reaction conditions tolerate a broad range of both alkynes and fluoroarenes containing both electron-withdrawing and -donating groups, thus allowing efficient synthesis of a variety of substituted ethenes containing a fluoroaryl motif in high regio- and stereoselective manners. Mechanistic studies including both labeling experiments and stoichiometric reactions reveal that oxidative addition of C-H bonds in fluoroarenes to nickel(0) is kinetically highly facile whereas that of C-F bonds is thermodynamically favoured.     

Lumped parameter models representing impedance functions at the interface of a rod on a viscoelastic medium

In this study, a lumped parameter model that properly simulates the impedance characteristics at the extremity of a uniform, isotropic, homogeneous rod on a viscoelastic medium is proposed. The lumped parameter model consists of springs, dashpots, and so-called “gyro-mass elements”. The gyro-mass elements generate a reaction force proportional to the relative acceleration of the nodes between which they are placed. This model consists of units arranged in series, each unit consisting of a spring, a damper, and a gyro-mass element arranged in parallel. A formula is proposed for determining the properties of the elements in the units calculated from a closed-form solution based on a modal expansion. The impedance function simulated by the proposed model shows good agreement with the rigorous impedance function derived from the differential equation of motion of the rod. The results obtained by employing this model in some example applications show that the accuracy of the model is appreciably high when compared with conventional finite element models. A great advantage of this model is that a significant reduction of the number of degrees of freedom can be achieved for solving recent vibration problems with high-frequency excitations, such as ultrasonic vibrations.     

Efficient decoherence-free entanglement distribution over lossy quantum channels

We propose and demonstrate a scheme for boosting the efficiency of entanglement distribution based on a decoherence-free subspace over lossy quantum channels. By using backward propagation of a coherent light, our scheme achieves an entanglement-sharing rate that is proportional to the transmittance T of the quantum channel in spite of encoding qubits in multipartite systems for the decoherence-free subspace. We experimentally show that highly entangled states, which can violate the Clauser-Horne-Shimony-Holt inequality, are distributed at a rate proportional to T.     

Stable rigged configurations for quantum affine algebras of nonexceptional types

For an affine algebra of nonexceptional type in the large rank we show the fermionic formula depends only on the attachment of the node 0 of the Dynkin diagram to the rest, and the fermionic formula of not type A can be expressed as a sum of that of type A with Littlewood–Richardson coefficients. Combining this result with Kirillov et al. (2002) [13] and Lecouvey et al. (2011) [18] we settle the X=M conjecture under the large rank hypothesis.