Effect of surface modes on the six-dimensional molecule-surface scattering dynamics of H2-Cu(100) and D2-Cu(111) systems

We include the phonon modes originating from the three layers of Cu(100)/Cu(111) surface atoms on the dynamics of molecular [H(2)(v,j)/D(2)(v,j)] degrees of freedom (DOFs) through a mean field approach, where the surface temperature is incorporated into the effective Hamiltonian (potential) either by considering Boltzmann probability (BP) or by including the Bose-Einstein probability (BEP) factor for the initial state distribution of the surface modes. The formulation of effective potential has been carried out by invoking the expression of transition probabilities for phonon modes known from the "stochastic" treatment of linearly forced harmonic oscillator (LFHO). We perform four-dimensional (4D?2D) as well as six-dimensional (6D) quantum dynamics on a parametrically time and temperature-dependent effective Hamiltonian to calculate elastic/inelastic scattering cross-section of the scattered molecule for the H(2)(v,j)-Cu(100) system, and dissociative chemisorption-physisorption for both H(2)(v,j)-Cu(100) and D(2)(v,j)-Cu(111) systems. Calculated sticking probabilities by either 4D?2D or 6D quantum dynamics on an effective potential constructed by using BP factor for the initial state distribution of the phonon modes could not show any surface temperature dependence. In the BEP case, (a) both 4D?2D and 6D quantum dynamics demonstrate that the phonon modes of the Cu(100) surface affect the state-to-state transition probabilities of the scattered H(2) molecule substantially, and (b) the sticking probabilities due to the collision of H(2) on Cu(100) and D(2) on Cu(111) surfaces show noticeable and substantial change, respectively, as function of surface temperature only when the quantum dynamics of all six molecular DOFs are treated in a fully correlated manner (6D).     

Effect of counterions on the activity of lipase in cationic water-in-oil microemulsions

This paper delineates how the different counterions affect the physicochemical properties of the aqueous aggregates and thereby the lipase activities at the interface of cationic water-in-oil microemulsions. To this end, we have synthesized a series of cetyltrimethylammonium-based surfactants, 1-14, having aliphatic, aliphatic with aromatic substitution at the alpha position, and aromatic carboxylate anion as the counterion. The physicochemical characterizations of these aqueous aggregates were done by conductometric, tensiometric, fluorometric techniques to determine counterion binding (beta), critical micelle concentration (cmc), and micropolarity at the microenvironment. It has been found that the activity of lipase mainly increases with hydrophobicity (which is directly proportional to the counterion binding (beta) of the surfactant) of the counterion and reaches a maximum when the beta value is around 0.5. Increase in hydrophobicity as well as beta leads to the attachment of more counterions at interface resulting in enhancement of interfacial area. Consequently, the enzyme may attain flexible secondary conformation at the augmented surface area and also allow larger population of substrates and enzyme molecules at the interface leading to the enhancement in lipase activity. After an optimum value of beta, further increase probably produces a steric crowding at the interface, hindering the smooth occupancy of enzyme and the substrate in this region leading to decrease of enzyme activity, while molecular surface area of the counterion did not show any virtual influence on the lipase activity. Thus, the variation in the counterion structure and hydrophobicity plays a crucial role in modulating the lipase activity.     

A new generalization of Aczél’s inequality and its applications to an improvement of Bellman’s inequality

A new generalized version of Aczél’s inequality is proved. This is a unified generalization of some known results. Moreover, the result is applied to the improvement of the well-known Bellman’s inequality.     

On transient development of surface waves

Summary An initial value investigation into the development of two-dimensional surface waves generated by a harmonically oscillating pressure acting on the free surface of a fluid of limited, unlimited and very shallow depth is made in this paper in considerable detail. A rigorous mathematical treatment of the problem is given with the aid of integral transform technique in conjunction with asymptotic methods. The limiting behaviour of the asymptotic solution as timet tends to infinity has been given due attention. It is shown that the ultimate steady state is attained in the case of physically realisable pressure distributions. Finally, a discussion of the wave motions including the main predictions of this theory is presented in some detail. A careful consideration has also been given to examine the validity of Lighthill's prediction regarding the steady state.     

Synthesis of homochiral bis (oxazolinyl) pyridine type ligands for asymmetric cyclopropanation reactions

Homochiral bis(oxazolinyl)pyridine type ligands were synthesized from (S)-valine and converted into their Cu(II) complexes. Reduction of these Cu(II) complexes into Cu(I) with diazoesters was studied by uv-vis and epr spectroscopy. The enantioselective cyclopropanation reaction was carried out using styrene as a model substrate.     

A brief historical introduction to matrices and their applications

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer’s Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical networks. It contains a wide variety of important materials accessible to college and even high school students and teachers at all levels.     

One-pot Sonogashira coupling,hydroamination of alkyne and intramolecular CH arylation reactions toward the synthesis of indole-fused benzosultams

A one-pot Sonogashira coupling, hydroamination of alkyne and CH arylation reactions for the synthesis of indole-fused benzosultams are described. This method allows access to a variety of indole-fused seven membered benzosultams in good to excellent yields. The free indolyl nitrogen containing indole-fused benzosultams are also prepared by this method. The structures of the synthesized compounds are confirmed by single crystal XRD studies.     

Photodynamic efficacy of chlorin p6: a pH dependent study in aqueous and lipid environment

Photodynamic efficacy of chlorin p6, a potential candidate of photodynamic therapy (PDT), has been studied at pH 5.0, 6.0 and 7.6 in aqueous and lipid environment. Increased chlorin p6 mediated photodynamic bleaching of N,N-dimethyl-4-nitrosoaniline (RNO), a measure of singlet oxygen yield, was obtained at higher pH. Rate of photodynamic bleaching of RNO was also higher at higher pH and the rate decreased with lowering in pH of irradiated solution. Photodynamic oxidation of tryptophan was also found to be higher at higher pH. Diminished oxidation of RNO was obtained with decrease in pH of irradiated solution. Both, RNO bleaching and tryptophan oxidation was significantly reduced by sodium azide, a known quencher of singlet oxygen. At lower pH, chlorin p6 mediated photodynamic malondialdehyde (MDA) and lipid hydroperoxide formation in egg lecithin liposome was higher. At higher pH chlorin p6 was found to be photodynamically more effective in aqueous environment whereas at lower pH chlorin p6 was photodynamically more effective in hydrophobic environment.