Quasi-invariants and generalized Killing vectors-II

We consider here the problem of the existence of a quasi-invariant which is linear in the momenta for Hamiltonians in three degrees of freedom. We show that such quasi-invariants are more constrained in their structure than in the two degrees of freedom case. We also show that some of these quasi-invariants have to be interpreted as ‘pseudo-translations’, i.e., as translations in a non-orthogonal system of coordinates.     

Crystallization kinetics of SrBi<Subscript>2</Subscript>B<Subscript>2</Subscript>O<Subscript>7</Subscript> glasses by non-isothermal methods

In the photomicrocalorimetric module designed by Johansson and Wadsö for a commercial Thermometric TAM heat conduction batch microcalorimeter, the incident light from an external xenon lamp was divided by a beam splitter and directed to the two vessels of the differential system by light guides ideally to give zero heat flow. In practice this proved difficult and so to improve the balance between the vessels in terms of the incident light heat output as well as potentially to give more versatility regarding the choice of wavelengths, the xenon lamp-based system was replaced in the first stage by a pair of cold white LEDs embedded directly in the test and reference vessels. The LEDs had independent electrical circuits to achieve the balance by manual adjustment. As a second stage, the test vessel was equipped with PTFE tubing for changing the liquid phase in it while it was in the middle thermal equilibrium position. This improved the reproducibility of the results.     

Stereoselective total synthesis of (+)-strictifolione and (6R)-6-[(4R,6R)-4,6-dihydroxy-10-phenyldec-1-enyl]-5,6-dihydro-2H-pyran-2-one by Prins reaction and olefin cross-metathesis

Prins and olefin cross-metathesis reactions were used as the key steps for the stereoselective total synthesis of (+)-strictifolione and (6R)-6-[(4R,6R)-4,6-dihydroxy-10-phenyldec-1-enyl]-5,6-dihydro-2H-pyran-2-one. Removal of MOM protecting groups under neutral conditions using CeCl₃·7H₂O is an attractive addition to the present strategy.     

Generation of aperiodic tilings with fivefold symmetry by the method of intersecting decagons and diffraction from finite size tilings

A method for generating aperiodic tilings with five fold symmetry is discussed here. Basic patterns formed within decagons can be used to fill two dimensional space, by matching such suitable patterns. It appears to be possible to generate perfect tilings without retracing already established coordinates imposing conditions at the initial stages of generating them. Various possible ways to generate tilings, when perfectness is not required, are discussed. The calculated diffraction patterns for some representative finite size tilings are shown. There are subtle differences in the intensities of peaks in the diffraction patterns corresponding to different finite size tilings constructed using intersecting decagons. These effects persist for a larger number of scatterers in weak peaks than in strong peaks. They are unaffected by an introduction of systematic disorder. These effects could be termed as the finite size boundary effects. There are also small shifts in the peak positions owing to the finite size effects. The possibility of formation of large approximate square cells in large tilings is shown.     

Palladium-catalyzed convenient one-pot synthesis of multi-substituted 2-pyrones via transesterification and alkenylation of enynoates

An efficient one-pot protocol for the synthesis of multi-substituted 2-pyrone derivatives from internal alkynes and unactivated alkenes is reported. The methodology involves difunctionalization of internal alkynes by using Pd(II) as a catalyst alongwith X-Phos as ligand via 6-endo transesterification and subsequent alkenylation pathway. Notable features include simple and easily available starting materials, including a range of unactivated alkenes, reduced synthetic steps and mild reaction conditions with high efficiency.     

Synthesis,characterization, DNA cleavage and in vitro antimicrobial activities of copper(II) complexes of Schiff bases containing a 2,4-disubstituted thiazole

Six Cu(II) complexes of Schiff base ligands of arylidene-2-(4-(4-bromo/methoxy-phenyl)thiazol-2-yl) hydrazines have been synthesized, characterized and screened for DNA cleavage and antimicrobial activities. The chemical structures of the complexes were deduced by physicochemical and spectroscopic methods. Elemental analyses indicated that the stoichiometry of the complexes is CuL₂ (L = Schiff base ligand). The DNA cleavage activities of the complexes were evaluated by agarose gel electrophoresis in the presence and absence of oxidant (H₂O₂) and free radical scavenger (DMSO). All the six complexes showed significant nuclease activity in the presence of H₂O₂, and two of the complexes showed moderate nuclease activity even in the absence of oxidant. The complexes did not show nuclease activity in the presence of free radical scavenger. The compounds were tested for activity against selected bacteria and fungi.     

Stereoselective total synthesis of (+)-anamarine via cross-metathesis protocol

A convergent stereoselective total synthesis of (+)-anamarine via cross-metathesis (CM) protocol starting from 2-butyn-1,4-diol and vinyl lactone is reported. Other key features of the strategy include the use of Sharpless asymmetric epoxidation, Sharpless dihydroxylation, and Red-Al reduction.     

Volatile oil composition of Pogostemon heyneanus and comparison of its composition with patchouli oil

The volatile oil of the leaves of Pogostemon heyneanus Benth. (Lamiaceae) was analyzed by GC and GC-MS. Twenty-six components representing 96.0% of the oil were identified. The major components of the oil were acetophenone (51.0%), beta-pinene (5.3%), (E)-nerolidol (5.4%), and patchouli alcohol (14.0%). Comparison of the compositions of the oils of P. heyneanus and P. cablin (Blanco) Benth. (Patchouli oil) showed wide variation between them. Though 13 sesquiterpenes and oxygenated sesquiterpenes were detected in both oils, their concentrations in the oils differed widely. Acetophenone, benzoyl acetone and (E)-nerolidol present in the oil of P. heyneanus were not detected in patchouli oil.     

Collective modes in the loop ordered phase of cuprate superconductors

We show that the two branches of collective modes discovered recently in underdoped cuprates with a large spectral weight are a necessary consequence of the loop-current state. Such a state has been shown in earlier experiments to be consistent with the symmetry of the order parameter competing with superconductivity in four families of cuprates. We also predict a third branch of excitations which cannot be discovered by neutron scattering but may be discovered by other techniques. Using parameters to fit the observed modes, we show that quantum fluctuations change the direction of the effective moments in the ground state to lie at an angle to the c axis as observed in experiments.