A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES

In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extersion of a known theorem in the corresponding non-random case.     

Analytical design of photonic band-gap fibers and their dispersion characteristics

The paper essentially deals with the analysis of photonic band-gap fibers in analogy with the electron wave motion in periodic crystal lattice. As such, the analyses are based on Bloch formulation. The dispersion characteristics of such fibers are presented by considering some illustrative values of design parameters. The effect of design parameters on the dispersion characteristics is also presented in terms of the variation of widths of allowed and forbidden bands of band-gap fibers. It is found that the number of allowed bands increases with the increase in difference between refractive indices of different layers. Further, widths of the allowed and forbidden bands increase with the increase in layer thickness.     

Nuclear symmetry energy effects in finite nuclei and neutron star

Within a relativistic mean-field model with nonlinear isoscalar–isovector coupling, we explore the possibility of constraining the density dependence of nuclear symmetry energy from a systematic study of the neutron skin thickness of finite nuclei and neutron star properties. We find the present skin data supports a rather stiff symmetry energy at subsaturation densities that corresponds to a soft symmetry energy at supranormal densities. Correlation between the skin of ²⁰⁸Pb and the neutron star masses and radii with kaon condensation has been studied. We find that ²⁰⁸Pb skin estimate suggest star radii that reveals considerable model dependence. Thus precise measurements of neutron star radii in conjunction with skin thickness of heavy nuclei could provide significant constraint on the density dependence of symmetry energy.     

Vibrational spectroscopy of bio-molecules: an algebraic approach

Porphyrins have received numerous considerable attentions during recent years because of their great biological importance. The most interesting areas of current research in molecular spectroscopy are the study of the vibrational ground and excited states of polyatomic molecules especially for the Metalloporphyrins. In this paper, we have calculated the fundamental and extrapolated vibrational energy levels of Magnesium, Nickel, Copper, Zinc, Metalloporphyrin molecules using U (2) algebraic model Hamiltonian. The results obtained by this method are in good agreement with the experimental data. This study gives a general approach for solving the vibrational spectra of Metalloporphyrin molecules.     

On vector variational-like inequalities and vector optimization problems with (<Emphasis Type="Italic">G</Emphasis>, <Emphasis Type="Italic">α</Emphasis>)-invexity

The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.     

Applicability and effectiveness of classifications models for achieving the twin objectives of growth and outreach of microfinance institutions

Measuring performance of microfinance institutions (MFIs) is challenging as MFIs must achieve the twin objectives of outreach and sustainability. We propose a new measure to capture the performance of MFIs by placing their twin achievements in a 2 × 2 grid of a classification matrix. To make a dichotomous classification, MFIs that meet both their twin objectives are classified as ‘1’ and MFIs who could not meet their dual objectives simultaneously are designated as ‘0’. Six classifiers are applied to analyze the operating and financial characteristics of MFIs that can offer a predictive modeling solution in achieving their objectives and the results of the classifiers are comprehended using technique for order preference by similarity to ideal solution to identify an appropriate classifier based on ranking of measures of performance. Out of six classifiers applied in the study, kernel lab-support vector machines achieved highest accuracy and lowest classification error rate that discriminates the best achievement of the MFIs’ twin objective. MFIs can use both these steps to identify whether they are on the right path to attaining their multiple objectives from their operating characteristics.     

Scaling law of poly(ethylene oxide) chain permeation through a nanoporous wall

This paper presents a study of the permeation of poly(ethylene oxide) (PEO) chains through the nanoporous wall of hollow polymeric capsules prepared by self-assembly of polyelectrolytes. We employ the method of pulsed field gradient (PFG) NMR diffusion to distinguish chains in different sites, i.e., in the capsule interior and free chains in the dispersion, by their respective diffusion coefficient. From a variation of the observation time, the time scale of the molecular exchange between both sites and thus the permeation rate constant is extracted from a two-site exchange model. Permeation rate constants show two different regimes with a different dependence on chain length. This suggests a transition between two different mechanisms of permeation as the molecular weight is increased. In either regime, the permeation time can be described by a scaling law tau approximately N (b) , with b = (4)/ 3 for short chains and b = (1)/ 3 for long chains. We discuss these exponents, which clearly differ from the theoretical predictions for chain translocation.     

DNA-templated assemblies of nickel hexacyanoferrate crystals

We report here the synthesis of nickel hexacyanoferrate (NiHCF) crystals using calf thymus DNA (CT-DNA) as a template. The double-stranded CT-DNA has been used as a template to self-assemble NiHCF crystals and to produce aggregates having different morphologies at different temperatures. The guided self-assembly behavior of DNA was studied at different temperatures by scanning electron microscopy. The cube-shaped crystals of NiHCF with an average diameter of 400 nm are observed along the DNA framework at room temperature; however, at higher temperatures, the morphology of NiHCF changed from open tubular to dendrimer. The intermediate temperatures show long chains (up to many micrometers) and spherical structures of NiHCF crystals. The micrometer long DNA template plays a key role in the formation of extended arrays of NiHCF crystals, suggesting that the templating action is retained even at the higher temperatures.     

Hydro­gen‐bonded adducts of ferrocene‐1,1′‐diyl­bis­(di­phenyl­methanol): monomeric and dimeric 1:1 adducts with 1,2‐bis(4‐pyridyl)­ethane and 1,2‐­diamino­ethane

In ferrocene‐1,1′‐diyl­bis­(di­phenyl­methanol)–4,4′‐ethyl­enedi­pyridine (1/1), [Fe(C₁₈H₁₅O)₂]·C₁₂H₁₂N₂, there is an intra­molecular O—H?O hydrogen bond in the ferrocenediol component and a single O—H?N hydrogen bond linking the two components into a finite monomeric adduct. Ferrocene‐1,1′‐diyl­bis­(di­phenyl­methanol)–ethyl­enedi­amine (1/1), [Fe(C₁₈H₁₅O)₂]·C₂H₈N₂, crystallizes with Z′ = 2 in space group P, and there are two independent four‐component aggregates in the structure, both of which are centrosymmetric. In the first type of aggregate, the molecular components are linked by O—H?N and N—H?O hydrogen bonds, in which both di­amine N atoms participate; in the second type of aggregate, the di­amine component is disordered over two sets of sites, but only one N atom is involved in the hydrogen bonding.     

Covalence reduction factors of four-coordinated pseudo-tetrahedral paramagnetic compounds inD 2d symmetry

Theoretical expressions for the covalence reduction factors of orbital angular momentum and spin-orbit coupling in pseudo-tetrahedral four-coordinated paramagnetic complexes withD _2d symmetry, denoted ask's andR's respectively, have been derived. p ]The mixing coefficients in the antibonding MO's for the CuCl ₄ ^2- ion in three complexes are estimated using suitable approximations. It is shown thatk's must be less thanR's in Tinkham's approximation. Certain misconceptions existing in the literature regarding the value of the integral 〈p _u |???u|s〉 have been clarified.