Separable programming/duality approach to solving the multi-product Newsboy/Gardener Problem with linear constraints

The Gardener Problem is an extension of the multi-product Newsboy Problem with constraints. It deals with situations where not only the demand is random but also the yield (the supply). Separable programming and duality approaches are utilized to solve the constrained Newsboy/Gardener Problem. The solution methodologies are developed for the common probability distribution functions for the demand, and uniform distribution for the supply, rendering exact and approximate solutions to the problem. Numerical examples are given and when applicable, the performance of the developed approach is compared to those of existing works in this arena. The results reveal that the developed solution methods efficiently converge to the optimal or near optimum solutions. Also, a salient feature of the proposed methodologies is that they can utilize readily available commercial software to solve the considered problems. This feature facilitates the portability of the developed models to the classroom environment.     

A highly effective synthesis of 2-alkynyl-7-azaindoles: Pd/C-mediated alkynylation of heteroaryl halides in water

The reaction of 4-chloro-2-iodo-7-azaindole with terminal alkynes was investigated using 10% Pd/C-PPh₃-CuI as a catalyst system in water. This study afforded a new, mild and selective process for the preparation of 2-alkynyl-4-chloro-7-azaindole in good yields via C-C bond forming reaction. The resulting chloro derivative can be functionalized further via another Pd-mediated C-C bond forming reaction with arylboronic acid.     

Magnetism of Fe in SrFe2As2: Local investigation by time differential perturbed angular distribution (TDPAD) spectroscopy

Employing the γ-ray perturbed angular distribution technique, we have measured the magnetic hyperfine field of ⁵⁴Fe in tetragonal and orthorhombic structural phases of SrFe₂As₂. In the tetragonal phase, the magnetic response of ⁵⁴Fe shows Curie-Weiss type local susceptibility, indicating the presence of localized moment on Fe. The temperature dependence of the hyperfine field of ⁵⁴Fe reflects quasi-two dimensional first order magnetic transition at 200 K. Our data indicate that Fe moments in the magnetically ordered phase of SrFe₂As₂ may be canted out of the ab-plane.     

Laminar flow separation in an axi-symmetric sudden smooth expanded circular tube

This paper concerns with the investigation of laminar flow separation and its consequences in a tube over a smooth expansion under the axi-symmetric approximations. A co-ordinate stretching has been made to map the expanded tube into a straight tube. The two-dimensional unsteady Navier-Stokes equations are solved approximately by using primitive variables in staggered grid. A thorough quantitative analysis is performed through numerical simulations of the desired quantities such as wall shear stress, axial velocity, pressure distribution etc. These quantities are presented graphically and their consequences in the flow field are analysed in details. The dependence of the flow field on the physical parameter like expansion height d and on the Reynolds number has been investigated in details. It is interesting to note that the peak value of wall shear stress decreases with increasing height of expansion and also with the increasing Reynolds number.     

Baryon inhomogeneities due to cosmic string wakes at the quark-hadron transition

Baryon inhomogeneities generated during the quark-hadron transition may alter the abundances of light elements if they persist up to the time of nucleosynthesis. These inhomogeneities survive up to the nucleosynthesis epoch if they are separated by a distance of at least a few metres. In this work we present a model where large sheets of these inhomogeneities separated by a distance of a few km are formed by cosmic string wakes during the quark-hadron transition. The effect of these sheets on nucleosynthesis will also put constraints on the various cosmic string parameters.     

Analysis of blood flow through a modelled artery with an aneurysm

The intention of the present work is to carry out a systematic analysis of flow features in a tube, modelled as artery, having a local aneurysm in presence of haematocrit. The arterial model is treated to be axi-symmetric and rigid. The blood, flowing through the modelled artery, is treated to be Newtonian and non-homogeneous. For a thorough quantitative analysis of the flow characteristics such as wall pressure, flow velocity, wall shear stress, the unsteady incompressible Navier-Stokes equations in cylindrical polar co-ordinates under the laminar flow conditions are solved by using the finite-difference method. Finally, the numerical illustrations presented in this paper provide an effective measure to estimate the combined influence of haematocrit and aneurysm on flow characteristics. It is found that the magnitude of wall shear stress and also the length of separation increase with increasing values of the haematocrit parameter. The length of flow separation increases but the peak value of wall shear stress decreases with the increasing length of aneurysm. The peak value of wall shear stress as well as the length of separation increases with the increasing height of the aneurysm.     

Chaotic thermal convection of couple-stress fluid layer

In this work we study the pattern of bifurcations and intermittent-chaos of non-Newtonian couple-stress shallow fluid layer subject to heating from below. The couple-stress parameter delays onset of convection, synchronizes chaotic behavior, and decreases the heat transfer . Some global aspects of the dynamics such as homoclinic bifurcations and transition to chaos are explored. The effects of particle size on the intermittent-chaos regime at particular normalized Rayleigh number, say \(r=166.1\), are investigated. With the increase in couple-stress parameter, the present Lorenz-like system synchronizes to a steady state via a series of periodic solutions interspersed with intervals of chaotic behaviors.     

Effect of iron doping concentration on magnetic properties of ZnO nanoparticles

The ZnO:Fe nanoparticles of mean size 3-10 nm were synthesized at room temperature by simple co-precipitation method. The crystallite structure, morphology and size estimation were performed by X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM). The wurtzite structure of ZnO gradually degrades with the increasing Fe doping concentration. The magnetic behavior of the nanoparticles of ZnO with varying Fe doping concentration was investigated using a vibrating sample magnetometer (VSM). Initially these nanoparticles showed strong ferromagnetic behavior, however at higher doping percentage of Fe, the ferromagnetic behavior was suppressed and paramagnetic nature was observed. The enhanced antiferromagnetic interaction between neighboring Fe-Fe ions suppressed the ferromagnetism at higher doping concentrations of Fe. Room-temperature Mössbauer spectroscopy investigation showed Fe³⁺ nature of the iron atom in ZnO matrix.     

Valence fluctuation in Ce2Co3Ge5 and crystal field effect in Pr2Co3Ge5

Polycrystalline samples of ternary rare-earth germanides R₂Co₃Ge₅ (R=La, Ce and Pr) have been prepared and investigated by means of magnetic susceptibility, isothermal magnetization, electrical resistivity and specific heat measurements. All these compounds crystallize in orthorhombic U₂Co₃Si₅ structure (space group Ibam). No evidence of magnetic or superconducting transition is observed in any of these compounds down to 2 K. The unit cell volume of Ce₂Co₃Ge₅ deviates from the expected lanthanide contraction, indicating non trivalent state of Ce ions in this compound. The reduced value of effective moment (μ_eff≈0.95 μ_B) compared to that expected for trivalent Ce ions further supports valence-fluctuating nature of Ce in Ce₂Co₃Ge₅. The observed temperature dependence of magnetic susceptibility is consistent with the ionic interconfiguration fluctuation (ICF) model. Although no sharp anomaly due to a phase transition is seen, a broad Schottky-type anomaly is observed in the magnetic part of specific heat of Pr₂Co₃Ge₅. An analysis of C_mag data suggests a singlet ground state in Pr₂Co₃Ge₅ separated from the singlet first excited state by 22 K and a doublet second excited state at 73 K.     

Highly sensitive method for the determination of omeprazole in human plasma by liquid chromatography-electrospray ionization tandem mass spectrometry: application to a clinical pharmacokinetic study

A highly sensitive, rapid assay method has been developed and validated for the estimation of omeprazole (OPZ) in human plasma with liquid chromatography coupled to tandem mass spectrometry with electrospray ionization in the positive-ion mode. The assay procedure involves alkalinization of plasma followed by simple liquid-liquid extraction of OPZ and lansoprazole (internal standard, IS) from human plasma with acetonitrile. Chromatographic separation was achieved with 0.01 M ammonium acetate:acetonitrile (40:60, v/v) at a flow rate of 0.25 mL/min on an Inertsil ODS 3 column with a total run time 2.5 min. The MS/MS ion transitions monitored were 346.1 --> 198.1 for OPZ and 370.1 --> 252.1 for IS. Method validation and clinical sample analysis were performed as per FDA guidelines and the results met the acceptance criteria. The lower limit of quantitation achieved was 0.05 ng/mL and the linearity was observed from 0.05 to 10.0 ng/mL. The intra-day and inter-day precisions were in the ranges 2.09-8.56 and 5.29-8.19%, respectively. This novel method has been applied to a pharmacokinetic study of OPZ in humans.