A comprehensive note on: An inventory model under two levels of trade credit and limited storage space derived without derivatives

In 2006, Huang proposed an inventory model with two warehouses when the supplier offers the retailer a permissible delay of M periods, and the retailer also provides its customers a permissible delay of N periods. He then solved it without derivatives. In this note, we extend his model to complement the shortcomings of his model. In contrast to the complicated and tedious quadratic–algebraic method suggested by Huang, we propose a simple arithmetic–geometric method to solve the inventory problem. Finally, we run computer programs for several numerical examples to illustrate the proposed model and obtain some managerial implications.     

Small-angle neutron scattering study of sodium cholate and sodium deoxycholate interacting micelles in aqueous medium

Small angle neutron scattering (SANS) measurements of D₂O solutions (0.1 M) of sodium cholate (NaC) and sodium deoxycholate (NaDC) were carried out atT= 298 K. Under compositions very much above the critical micelle concentration (CMC), the bile salt micelle size growths were monitored by adopting Hayter-Penfold type analysis of the scattering data. NaC and NaDC solutions show presence of correlation peaks atQ = 0.12 and 0.1 ?_-1 respectively. Monodisperse ellipsoids of the micelles produce best fits. For NaC and NaDC systems, aggregation number (9.0, 16.0), fraction of the free counterions per micelle (0.79, 0.62), semi-minor (8.0 ?) and semi-major axes (18.4, 31.7 ?) values for the micelles were deduced. Extent of micellar growth was studied using ESR correlation time measurements on a suitable probe incorporating NaC and NaDC micelles. The growth parameter (axial ratio) values were found to be 2.3 and 4.0 for NaC and NaDC systems respectively. The values agree with those of SANS.     

Temperature dependent small-angle neutron scattering of CTABr—magnetic fluid emulsion

Small-angle neutron scattering studies have been carried out to check the structural integrity of citryltrimethylammonium bromide (CTABr) micelles in a magnetic fluid for different magnetic fluid concentrations at two different temperatures 303 and 333 K. It is found that the CTABr micelles grow with increasing magnetic fluid concentration and there is a decrease in the micellar size with increase in temperature.     

Small-angle neutron scattering from micellar solutions

Micellar solutions are the suspension of the colloidal aggregates of the sur-factant molecules in aqueous solutions. The structure (shape and size) and the interaction of these aggregates, referred to as micelles, depend on the molecular architecture of the surfactant molecule, presence of additives and the solution conditions such as temperature, concentration etc. This paper gives the usefulness of small-angle neutron scattering to the study of micellar solutions with some of our recent results.     

Multidimensional modified fractional calculus operators involving a general class of polynomials

In the present work, we introduce and study essentially a class of multi-dimensional modified fractional calculus operators involving a general class of polynomials in the kernel. These operators are considered in the space of functionsM _γ (R ₊ ⁿ ). Some mapping properties and fractional differential formulas are obtained. Also images of some elementary and special functions are established.     

Small-angle neutron scattering studies on water soluble complexes of poly(ethylene glycol)-based cationic random copolymer and SDS

The interaction of cationic random copolymers of methoxy poly(ethylene glycol) monomethacrylate and (3-(methacryloylamino)propyl) trimethylammonium chloride with oppositely charged surfactant, sodium dodecyl sulphate, and the influence of surfactant association on the polymer conformation have been investigated by small-angle neutron scattering. SANS data showed a positive indication of the formation of RCPSDS complexes. Even though the complete structure of the polyion complexes could not be ascertained, the results obtained give us the information on the local structure in these polymer-surfactant systems. The data were analysed using the log-normal distribution of the polydispersed spherical aggregate model for the local structure in these complexes. For all the systems the median radius and the polydispersity were found to be in the range of 20 ± 2 Å and 0.6 ± 0.05, respectively.     

Self-injection length in La0.7Ca0.3MnO3-YBa2Cu3O7-δ ferromagnet-superconductor multilayer thin films

We have carried out extensive studies on the self-injection problem in barrierless heterojunctions between La_0.7Ca_0.3MnO₃ (LCMO) and YBa₂Cu₃O_7-δ (YBCO) thin films. The heterojunctions were formed in situ by sequentially growing LCMO and YBCO films on 〈100〉 LaAlO₃ (LAO) substrate using a pulsed laser deposition (PLD) system. YBCO micro-bridges with 64 μm width were patterned both on the LAO (control) and LCMO side of the substrate. Critical current, I _c, was measured at 77 K on both the control side as well as the LCMO side for different YBCO film thickness. It was observed that while the control side showed a J _c of ∼ 2 × 10⁶ A/cm², the LCMO side showed about half the value for the same thickness (1800 ?). The difference in J _c indicates that a certain thickness of YBCO has become ‘effectively’ normal due to self-injection. From the measurement of J _c at two different thicknesses (1800 ? and 1500 ?) of YBCO films both on the LAO as well as the LCMO side, the value of self-injection length (at 77 K) was estimated to be ∼ 900 ?. To the authors’ best knowledge, this is the first time that self-injection length has been quantified. A control experiment carried out with LaNiO₃ deposited by PLD on YBCO did not show any evidence of self-injection.     

Electrical and photo-electrical properties of a chalcopyrite semiconductor AgInSe2

In this paper we report the electrical and photoelectrical properties of AgInSe₂. Nyquist plots for AgInSe₂, obtained at different temperatures, are perfect arcs of a semicircle with their centres lying below the abscissa at an angleα. Finite values ofα (the distribution parameter) clearly indicate a multirelaxation behaviour. Transient and steady state photoconductivity of AgInSe₂ has been studied at different temperatures and illumination levels. The lnI _ph vs lnF curves at different temperatures follow the empirical relation:I _ph ∝F ^γ. Values of γ are close to 0.5 at all the temperatures, suggesting a bimolecular recombination. Decay of the photocurrent, when the illumination is switched off, shows that during decay, photocurrent has two components, i.e. a fast decay in the beginning and a slow decay thereafter. Decay time constant for slow decay process decreases with increasing temperature, suggesting that recombination is a thermally activated process in the temperature range studied.