Energy estimates for regularly hyperbolic operators with log-Lipschitz coefficients

Using the method of Colombini–Lerner, we derive the energy estimates for regularly hyperbolic equations with log-Lipschitz coefficients.     

Precise Synthesis of New Triblock Co- and Terpolymers by a Methodology Combining Living Anionic Polymers with a Specially Designed Linking Reaction

Five A-B-A′, A-C-A′, B-A-B′, C-A-C′, and C-B-C′ triblock terpolymers with block orders difficult to synthesize by sequential polymerization have been successfully synthesized by a new methodology combining living anionic polymers with a specially designed linking reaction using α-phenylacrylate as the reaction site. Here, A(A′), B(B′), and C(C′) represent groups of polymers (having chain-end anions with different nucleophilicities), which are only polymerizable from A(A′) to B(B′) to C(C′) via sequential polymerization. The corresponding polymers are polystyrene (A) and poly(α-methylstyrene) (A′), poly(2-vinylpyridine) (B) and poly(4-vinylpyridine) (B′) and polymers from methacrylate type monomers like poly(methyl methacrylate) (C), poly(tert-butyl methacrylate) (C′), poly(2-hydroxyethyl methacrylate) (C′), poly(2,3-dihydroxypropyl methacrylate) (C′), and poly(ferrocenylmethyl methacrylate) (C′). Furthermore, three synthetically difficult B-A-B, C-A-C, and C-B-C triblock copolymers with molecular asymmetry in both side blocks have also been synthesized by the developed methodology. All of the polymers thus synthesized are quite new triblock terpolymers and copolymers with well-defined structures, i.e., precisely controlled molecular weights, compositions and narrow molecular weight distributions (M_w/M_n ≤ 1.05).     

Library‐directed Solution‐ and Solid‐phase Synthesis of 2,4‐Disubstituted Pyridines: One‐pot Approach through 6 π‐Azaelectrocyclization

An efficient one‐pot synthetic procedure for the synthesis of 2,4‐disubstituted pyridines has been successfully established. The method proceeds through a 6π‐azaelectrocyclization‐aromatization sequence. Using this method, a wide variety of pyridine structures substituted at the 2‐position have been rapidly constructed from vinyl stannanes, vinyl iodide, sulfonamide, and a palladium catalyst. The method was further applied to the solid‐phase synthesis wherein the use of a “traceless” sulfonamide linker enabled the rapid preparation of a small library of pyridines with high purity, without any chromatographic separation.     

Broué's conjecture for non-principal 3-blocks of finite groups

In representation theory of finite groups, there is a well-known and important conjecture due to M. Broué. He conjectures that, for any prime p, if a p-block A of a finite group G has an abelian defect group D, then A and its Brauer correspondent p-block B of N_G(D) are derived equivalent. We demonstrate in this paper that Broué's conjecture holds for two non-principal 3-blocks A with elementary abelian defect group D of order 9 of the O'Nan simple group and the Higman-Sims simple group. Moreover, we determine these two non-principal block algebras over a splitting field of characteristic 3 up to Morita equivalence.     

Photoinduced ground-state singlet biradical--novel insight into the photochromic compounds of biindenylidenediones

The biindenylidenedione derivative (A) developed a biradical accompanied by the simultaneous photocolor development on UV or sunlight irradiation; the former of which showed antiferromagnetic behavior on account of the singlet ground state and a thermally accessible triplet state.     

Estimation of sialic acid in a sialoglycan and a sialoglycoprotein by capillary electrophoresis with in-capillary sialidase digestion

An example of application of in-capillary derivatization for CE, obtained by using the throughout-capillary format, is presented. Introduction of a sialoglycan (N-acetylneuraminyllactose) or a sialoglycoprotein (bovine serum fetuin) sample to a running buffer (pH 5.0) containing N-acetylneuraminidase followed by application of a voltage resulted in the release of N-acetylneuraminic acid (NANA) which could be estimated by CE with UV detection. Two-step application of voltages (5 and 20 kV) was proved to be more effective for rapid estimation of the released NANA. This format (modified throughout-capillary format) allowed differential estimation of the NANA present in the sample as an impurity and the NANA released from the substrate at the picomol level, and thereby reliable micro assay of the sialidase activity. It also allowed estimation of the rate constant of this enzymatic reaction.     

Triple quantum nutation in the two-level NMR system in the rotating frame

The authors present the detailed theory and the new results associated with the triple quantum (TQ) nutation and the line narrowing effect of the TQ resonance in the two-level NMR system which we reported previously. The TQ resonance is induced in the spin-locked system by the oscillating field produced by the sinusoidal phase modulation (PM) of the RF field. The theory predicts that the TQ nutation is accompanied by several higher frequency oscillations and we detected them experimentally by improving the detection system. These higher frequency oscillations are due to the fluctuation of the angle between the transverse or effective field causing the TQ nutation and the RF field. We obtain the result that the modulation index 2phim of the PM is the key parameter that essentially controls the conditions of the TQ resonance and the narrowing effect. Under the exact TQ resonance, the ratio of the TQ resonance frequency to the Larmor frequency of the RF field depends only on phim, and the secular part of the magnetic dipole Hamiltonian of a like spin system in the triply rotating frame disappears at a particular value of phim. The condition is different from that of the well-known magic angle condition.