General strategy for a short and efficient synthesis of 3-hydroxy-4-methylprolines (HMP)

The non-proteinogenic amino acid 3-hydroxy-4-methylproline (HMP) is an active constituent of some potent antimicrobials including echinocandins, nostopeptins, pneumocandins, sporiofungin and mulundocandins. A synthesis has been achieved in 10 steps with 29% overall yield; the Evans’ aldol reaction using Crimmins’ modified method was pivotal to the success of the strategy.     

High pressure X-ray diffraction study of CdAl2Se4 and Raman study of AAl2Se4 (A=Hg, Zn) and CdAl2X4 (X=Se, S)

We report the results of an X-ray diffraction study of CdAl₂Se₄ and of Raman studies of HgAl₂Se₄ and ZnAl₂Se₄ at room temperature, and of CdAl₂S₄ and CdAl₂Se₄ at 80 K at high pressure. The ambient pressure phase of CdAl₂Se₄ is stable up to a pressure of 9.1 GPa above which a phase transition to a disordered rock salt phase is observed. A fit of the volume pressure data to a Birch-Murnaghan type equation of state yields a bulk modulus of 52.1 GPa. The relative volume change at the phase transition at ∼9 GPa is about 10%. The analysis of the Raman data of HgAl₂Se₄ and ZnAl₂Se₄ reveals a general trend observed for different defect chalcopyrite materials. The line widths of the Raman peaks change at intermediate pressures between 4 and 6 GPa as an indication of the pressure induced two stage order-disorder transition observed in these materials. In addition, we include results of a low temperature Raman study of CdAl₂S₄ and CdAl₂Se₄, which shows a very weak temperature dependence of the Raman-active phonon modes.     

Selective quenching of tryptophanyl fluorescence in bovine serum albumin by the iodide ion

Modified Stern-Volmer equation is obeyed by bovine serum albumin (BSA)-iodide system showing selective quenching of tryptophanyl fluorescence of BSA. The fraction of accessible protein fluorescence is 0.56 and the effective Stern-Volmer constant is 290 M^-1 at pH 7.4 in 0.005 M phosphate buffer at 25°C. Collisional quenching is operative both in the BSA -I⁻¹ system and the model system, tryptophan-I⁻¹. It is supported by the observed relationship between the ratio of quenching rate constants (k _q ) and diffusion coefficients and alsok _q with bulk viscosity.     

On algebras of Toeplitz fuzzy matrices

In this paper, necessary and sufficient conditions are given for a product of Toeplitz fuzzy matrices to be Toeplitz. As an application, a criterion for normality of Toeplitz fuzzy matrices is derived and conditions are deduced for symmetric idempotency of Toeplitz fuzzy matrices. We discuss similar results for Hankel fuzzy matrices. Keywords: Fuzzy matrix, Toeplitz and Hankel matrices.     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

Bi-large neutrino mixings by radiative magnification

Starting with the unification hypothesis of mixings of quarks and leptons and small quark-like mixings at the see-saw scale, we find that two large mixings for ν_e —νx03BC; andv _μ—v _τ at the weak scale are obtained as a result of renormalization group evolution and radiative magnification if the three neutrinos are quasi degenerate in masses and possess the same CP parity. We also find thatU _e3 remains small and well within the CHOOZ-Palo Verde bound since the correspondingV _ub for CKM mixing is very small. Several testable pedictions are pointed out.     

Amine-templated metal squarates

Two layered amine-templated cobalt squarates, [C₆N₂H₁₄]₂[Co₂(C₄O₄)₃(H₂O)₄], I, and [C₃N₂H₅]₂[Co₂(C₄O₄)₃(H₂O)₄], II, have been prepared under hydrothermal conditions. Both I and II contain chains formed by dimers comprising two cobalt atoms bound to the squarate units, the chains being connected through hydrogen bond interactions. An amine-templated cobalt squarate of the formula [C₄N₂H₁₂][Co(C₄O₄)₂(H₂O)₄][H₂O]₂, III, as well as its Ni, Zn and Cd analogues have been prepared by room temperature reactions. III has a layered architecture wherein the cobalt-squarate monomers are linked by the amine molecules. Co and Zn analogues of [Ni(C₄O₄)(H₂O)₂(C₃N₂H₄)] with ligating imidazole units have also been prepared and characterized.