Conformational analysis of some acrylates using dipole moment calculations by CNDO/force method

CNDO MO calculations are carried out for four acrylates, H₂C=C (R₁)-COO (R₂) with R₁=H, Me and R₂=Me, Et for dipole moment determination using the Pople-Segal expression.⁷ Energy minimization for various conformers in each molecular system was achieved by the gradient method. Dipole moments for comparatively stable conformers of each of the molecules considered are reported. Theoretically calculated energy values are used to arrive at the equilibrium geometry and the corresponding dipole moments are compared with the experimental values in each system considered.     

Biological and catalytic evaluation of Ru(II)‐p‐cymene complexes of Schiff base ligands: Impact of ligand appended moiety on photo‐induced DNA and protein cleavage,cytotoxicity and C‐H activation

Two organometallic Ru(II)‐p‐cymene complexes of the type [Ru(η⁶‐p‐cymene)(L)Cl]PF₆ 1 and 2 , where L is N,N‐bis(4‐isopropylbenzylidene)ethane‐1,2‐diamine (bien, L1 ) or N,N‐bis (pyren‐2‐ylmethylene)ethane‐1,2‐diamine (bpen, L2 ) have been prepared and characterized well. Because of appended pyrenyl groups in coordinated bpen ligand, the complex 2 exhibits higher DNA and protein binding than complex 1 in which isopropylbenzyl groups are incorporated. Interestingly, the luminescent characteristic complex 2 is unique in displaying DNA cleavage after light activation by UVA light at 365 nm through oxygen dependent mechanism. AFM analysis attests the photo‐induced DNA fragmentation ability of complex 2 . Also, the complex 2 cleaves the protein after light exposure in a non‐specific manner suggesting that it can act as a protein photo cleaving agent. In contrast to the trend of DNA and protein interaction of complexes, the complex 1 exhibits cytotoxic activity against human breast carcinoma ( MCF‐7 ) and liver carcinoma ( HepG2 ) with potency higher than that of complex 2 due to enhanced hydrophobicity of isopropyl groups present in p‐cymene and bien ligands. Indeed, complex 2 is inactive against MCF‐7 and HepG2 cancer cell lines even up to 200 μM concentration. The AO/EB staining assay reveals that the complex 1 is able to induce late apoptotic mode of cell death in breast cancer cells, which is further confirmed by inter‐nucleosomal DNA cleavage. Furthermore, the complexes 1 and 2 are evaluated for their catalytic activities and found to be working well for the β‐carboline directed C–H arylation to afford the desired products in good yield (40–47%).     

Axisymmetric Thermoelastic Interactions without Energy Dissipation in an Unbounded Body with Cylindrical Cavity

The linear theory of thermoelasticity without energy dissipation is employed to study thermoelastic interactions in a homogeneous and isotropic unbounded body containing a cylindrical cavity. The interactions are supposed to be due to a constant step in radial stress or temperature applied to the boundary of the acvity, which is maintained at a constant temperature or zero radial stress (as the case may be). By using the Laplace transform technique, it is found that the interactions consist of two coupled waves both of which propagate with a finite speed but with no attenuation. The discontinuities that occurs at the wavefronts are computed. Numerical results applicable to a copper-like material are presented.     

Quantum mechanics in finite dimensions

We explicitly compute, following the method of Weyl, the commutator [Q, P] of the position operatorQ and the momentum operatorP of a particle when the dimension of the space on which they act is finite with a discrete spectrum; and we show that in the limit of a continuous spectrum with the dimension going to infinity this reduces to the usual relation of Heisenberg.     

On the number of Fourier coefficients that determine a Hilbert modular form

We estimate the number of Fourier coefficients that determine a Hilbert modular cusp form of arbitrary weight and level. The method is spectral (Rayleigh quotient) and avoids the use of the maximum principle.

     

Analysis of scattered-light methods in photoelasticity

The use of scattered light for nondestructive analysis of general photoelastic models is becoming quite common and, during the last few years, several methods have appeared in the literature to determine the directions of the secondary principal stresses and their differences at any general point. Among the methods suggested, some are mentioned as “exact” and some “approximate”. Even the exact methods have limitations in their applicability for a generally stressed model. The present discussion attempts to bring out the inaccuracies involved in the various exact methods. Also, a few modifications to improve the accuracy and a new method called the Mini-max method are proposed. References 1, 2 and 3 give the general methods and the derivations of equations used in the present analysis.     

Nucleation and growth mechanism for the electropolymerization of aniline on highly oriented pyrolytic graphite at higher potentials

In this work, the nucleation and growth mechanism for the electropolymerization of aniline was investigated at higher potentials on highly oriented pyrolytic graphite by potentiostatic current-time transient and atomic force microscopic (AFM) measurements. The electrochemical data fitted to the theoretical curves for the nucleation and growth suggest that electropolymerization of aniline follows the three-dimensional growth and progressive nucleation mechanism. These results were also compared with the results obtained at lower potentials. The results obtained from transient analysis, at higher potentials, were in good agreement with the results of AFM images. Electronic Publication     

Finite-dimensional quantum mechanics of a particle

This paper analyzes the possible implications of interpreting the finitedimensional representations of canonically conjugate quantum mechanical position, and momentum operators of a particle consistent with Weyl's form of Heisenberg's commutation relation as the actual position, and momentum operators of the particle when it is confined to move within a finite spatial domain, and regarding the application of current quantum mechanical formalism based on Heisenberg's relation to such a situation as an asymptotic approximation. In the resulting quantum mechanical formalism the discrete and finite position and momentum spectra of a particle depend on its rest mass and the spatial domain of confinement. Such a finite-dimensional quantum mechanics may be very suitable for describing the physics of particles confined to move within very small regions of space.     

Graph splicing systems

In this paper, extended graph splicing systems are defined. It is shown that when strings are represented as linear graphs, any recursively enumerable set can be generated by an extended graph splicing system. It is also shown that the computational completeness of extended graph splicing systems can be proved under some constraints too.