Structural and dielectric behaviour of non-aqueous lyotropic mixtures: influence of amphiphile chain lengths and counter ions

This study highlights the effects of amphiphile chain length and counter ions on the self-assembly and dielectric behaviour of non-aqueous lyotropic liquid crystals. Two-dimensional hexagonal mesophase is seen for short-chain length sodium dodecyl sulphate, while lamellar and multiwall lamellar mesophases are noticed for long-chain length cetyltrimethylammonium bromide and polyoxyethylene (20) sorbitan monolaurate amphiphiles in the non-aqueous domains of ethylene glycol. A strong influence of amphiphile counter ions is seen on static dielectric constant, loss factor, relaxation frequency and relaxation time of these lyotropic mixtures. Refractive indices of these lyotropic phases are also highlighted.     

Effect of solvent polarity on the self-assembly and dielectric dynamics of non-aqueous lyotropic liquid crystalline phases

Binary mixtures comprising cetylpyridinium chloride and non-aqueous solvents of varying polarity [ethylene glycol (ε ~ 37.2) and formamide (ε ~ 109)] were studied via X-ray diffraction, polarisation optical microscopy, differential scanning calorimetry and dielectric spectroscopy. Layered lamellar mesophase was observed in both mixtures. Formamide-based mesophase was found more ordered and stable up to higher temperature (140°C). Ordering and stability of the mesophase was explained considering the higher polarity and dipolar–dipolar interactions of formamide. Dielectric spectroscopy demonstrates the large magnitudes of capacitance and permittivity (Cp ≈ 9 µF and ε ≈ 2428) for mesophase derived from formamide. Dynamical relaxation parameters of both mixtures were discussed and correlated with their structural aspects.     

Mathematical foundations of a cultural project or Ramchandra's treatise “through the unsentimentalised light of mathematics”

The nineteenth century witnessed a number of projects of cultural rapprochement between the knowledge traditions of the East and West. This paper discusses the attempt to render elementary calculus amenable to an Indian audience in the indigenous mathematical idiom, undertaken by an Indian polymath, Ramchandra. The exercise is specifically located in his book A Treatise on the Problems of Maxima and Minima. The paper goes on to discuss the “vocation of failure” of the book within the context of encounter and the pedagogy of mathematics.     

Modeling crack micro-branching using finite elements with embedded strong discontinuities

The emphasis of this work lies in the development of a numerical method which is capable of representing the complex physical phenomena arising in the case of crack branching in brittle materials. In particular, the formation of crack micro-branches needs to be accounted for when it comes to the prediction of the propagation pattern of crack macro-branches which will ultimately lead to the failure of the material. This is achieved by numerically modeling the failure zones within the individual finite elements based on the concept of the embedded finite element method, where all the information with regard to the geometry of the failure zone is stored locally on the element level leading to a very efficient methodology capable of discretely resolving the failure zone. The main feature of the current work is the redundancy of the branching criterion based on crack tip velocity and that both, micro- as well as macro-branches can be modeled. Whether a micro-crack develops into a macro-crack solely depends on the local state of the material as it is outlined based on the application of the proposed numerical scheme on a rectangular block with a pre-existing notch set under tension. A comparison of the oscillatory behavior of the obtained crack tip velocity every time a micro-crack develops with experimental results from the literature is provided. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two-neutrino positron double-beta decay of <Superscript>106</Superscript>Cd for the 0<Superscript>+</Superscript> → 0<Superscript>+</Superscript> transition

The two-neutrino positron double-beta decay of ¹⁰⁶Cd for the 0 ⁺ 0⁺ transition has been studied in the Hartree-Fock-Bogoliubov model in conjunction with the summation method. In the first step, the reliability of the intrinsic wave functions of ¹⁰⁶Cd and ¹⁰⁶Pd nuclei has been tested by comparing the theoretically calculated results for yrast spectra, reduced B(E2: 0⁺ 2⁺) transition probabilities, quadrupole moments Q(2⁺) and gyromagnetic factors g(2⁺) with the available experimental data. In the second step, the nuclear transition matrix element M₂ and the half-life T_1/2² for the 0 ⁺ 0⁺ transition have been calculated with these wave functions. Moreover, we have studied the effect of deformation on the nuclear transition matrix element M₂.     

Intramolecular addition of acyl radicals to alpha-substituted vinylogous carbonates: demonstrating the effect of ring size on acyclic stereocontrol

The level of stereocontrol obtained in the reduction of the free radical derived from the intramolecular addition of an acyl radical to an alpha-branched vinylogous carbonate is dependent upon the ring-size of the cyclic ether.     

A note on the multidimensional Weyl fractional operator

The purpose of the present paper is to establish a connection theorem involving the multidimensional Weyl fractional operator and the classical multidimensional Laplace transform. This provides an extension of a result due to Raina and Koul [6].     

A note on multidimensional modified fractional calculus operators

In the present investigation some new formulas giving the images under multidimensional modified fractional operators of the celebratedH-function of Fox [Trans. Am. Math. Soc. 98 (1961) 395–429] are obtained. Special cases are briefly pointed out and the results are also studied on general spaces of functionsM _γ(R ₊ ⁿ )