Continuity at the extreme points

We prove that a bounded convex lower semicontinuous function defined on a convex compact set K is continuous at a dense subset of extreme points. If there is a bounded strictly convex lower semicontinuous function on K, then the set of extreme points contains a dense completely metrizable subset.     

Arbitrary oscillatory Stokes flow past a porous sphere using Brinkman model

The present paper deals with the hydrodynamics of a porous sphere placed in an arbitrary oscillatory Stokes flow. Unsteady Stokes equation is used for the flow outside the porous sphere and Brinkman equation is used for the flow inside the porous sphere. Corresponding Faxén’s law for drag and torque is derived and compared with few existing results in some special cases. Examples like uniform flow, oscillatory shear flow and oscillating Stokeslet are discussed. Also, translational oscillation of a weakly permeable sphere is discussed.     

High performing magnesium aluminate-coated separator for lithium batteries

A high performing and thermally stable magnesium aluminate (MgAl₂O₄) coated on both sides of Celgard 2320 for applications in lithium batteries was prepared. The MgAl₂O₄-coated membrane was thermally stable up to 440 °C and capable of up-taking electrolytes up to 250%. The contact angle of MgAl₂O₄-coated membrane was lower (21°) than that of uncoated membrane. The MgAl₂O₄-coated ceramic separator exhibited appreciable ionic conductivity and better compatibility with lithium metal anode. Finally, a 2032-type coin cell comprising Li/MgAl₂O₄-coated separator/LiFePO₄ was assembled and its charge-discharge behavior was analyzed at 0.1, 0.5, and 1 C-rates. A stable discharge capacity was achieved even at 1 C-rate which qualifies this MgAl₂O₄-coated membrane for lithium battery applications.

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Stereoselective synthesis and applications of nitrogen substituted donor-acceptor cyclopropanes (N-DACs) in the divergent synthesis of azacycles

A new, highly stereoselective intramolecular cyclopropanation of vinylogous carbamates with carbenes in the presence of Cu(acac)(2) as the catalyst has been developed for the construction of cyclopropapyrrolidinones. The 'syn' isomer of N-DAC can be converted to the 'anti' isomer by simple silica gel treatment. Regioselective cleavage of each of the cyclopropane bonds of these two acceptor substituted N-DACs led to a diverse array of azacycles.     

Metal ions as cofactors for aggregation of therapeutic peptide salmon calcitonin

The effects of multivalent metal ions (Cu(2+)/Zn(2+)/Al(3+)) on the aggregation of salmon calcitonin (sCT)--a therapeutic peptide used worldwide in the treatment of osteoporosis and Paget's disease--have been studied in vitro using NMR (both solution state and solid state), TEM, ThT-fluorescence, and FT-IR spectroscopy. Overall, the various results indicated that the metal-ions-induced conformational transitions in the peptide--mostly toward the β-sheet--facilitate the aggregation of sCT in solution. First, the solution NMR has been used to check the interaction between the peptide and the metal ions. Following this, the formation and characterization of calcitonin aggregates has been performed using TEM, solid state NMR, and FT-IR spectroscopy. The TEM and ThT-fluorescence results revealed that the sCT peptide incubated with Cu(2+) and Zn(2+) metal ions (in aqueous environment) forms globular aggregates, while that with Al(3+) ions forms fibrils. The solid state NMR and FT-IR studies revealed the presence of a substantial amount of β-sheet content in sCT aggregates (formed in the presence of these metal ions) compared to the monomeric sCT, indicating that the metal binding is concomitant with conformational changes. The present study becomes crucial while prescribing this drug peptide under physio-pathological conditions associated with an abnormal accumulation of metal ions (Cu(2+)/Zn(2+)/Al(3+)) in the body (i.e., abnormal metal ion homeostasis).     

An empirical approach to the theory of particle and nuclear phenomena: Review and some new ideas

Experimental data on masses and lifetimes of unstable particles falls into a pattern, a brief review of some interesting consequences is presented here. From the experience in semiclassical methods and recent advances in quantum chromodynamics, it is proposed that an appropriate generalization of the Gutzwiller trace formula for field theories may lead to a systematic semiclassical chromodynamics theory. The theory can be developed to get appropriate dynamics leading to an explanation of pattern discovered in the empirical data.     

The Euler Class Group of a Noetherian Ring

For a commutative Noetherian ring A of finite Krull dimension containing the field of rational numbers, an Abelian group called the Euler class group is defined. An element of this group is attached to a projective A-module of rank = dim A and it is shown that the vanishing of this element is necessary and sufficient for P to split off a free summand of rank 1. As one of the applications of this result, it is shown that for any n-dimensional real affine domain, a projective module of rank n (with trivial determinant), all of whose generic sections have n generated vanishing ideals, necessarily splits off a free direct summand of rank 1.     

Purification of 233U from Thorium and Iron in the Reprocessing of Irradiated Thorium Oxide Rods

A two step precipitation using ammonium carbonate and oxalic acid as the precipitants for thorium and iron is developed for the purification of ²³³U. Ammonium carbonate is added to the feed to increase the pH of the solution. The effect of pH on the solubility of U, Th and Fe in an excess of ammonium carbonate is studied. This indicates that the solubility of Th and Fe is minimum at pH 7 and the recovery of uranium is maximum. The effect of the concentration of thorium and iron on the recovery of uranium at pH 7 is studied. This indicates that the ammonium carbonate precipitation tolerates 2 g/l of thorium and 10 g/l of iron keeping losses of uranium to a minimum. If the feed solution contains more than a tolerable concentration of thorium the precipitation is followed in two steps: (1) Bulk of the thorium is removed by oxalate precipitation, (2) the remaining thorium and iron in the supernatant are removed by ammonium carbonate precipitation. A flow sheet is proposed for the purification of ²³³U from thorium and iron present in a strip product concentrate obtained during the reprocessing of irradiated thorium rods.     

AN UNCONDITIONALLY STABLE HYBRID FE-FD SCHEME FOR SOLVING A 3-D HEAT TRANSPORT EQUATION IN A CYLINDRICAL THIN FILM WITH SUB-MICROSCALE THICKNESS

Heat transport at the microscale is of vital importance in microtechnology applications.The heat transport equation is different from the traditional heat transport equation since a second order derivative of temperature with respect to time and a third-order mixed derivative of temperature with respect to space and time are introduced. In this study,we develop a hybrid finite element-finite difference (FE-FD) scheme with two levels in time for the three dimensional heat transport equation in a cylindrical thin film with submicroscale thickness. It is shown that the scheme is unconditionally stable. The scheme is then employed to obtain the temperature rise in a sub-microscale cylindrical gold film. The method can be applied to obtain the temperature rise in any thin films with sub-microscale thickness, where the geometry in the planar direction is arbitrary.     

Bed of polydisperse viscous spherical drops under thermocapillary effects

Viscous flow past an ensemble of polydisperse spherical drops is investigated under thermocapillary effects. We assume that the collection of spherical drops behaves as a porous media and estimates the hydrodynamic interactions analytically via the so- called cell model that is defined around a specific representative particle. In this method, the hydrodynamic interactions are assumed to be accounted by suitable boundary conditions on a fictitious fluid envelope surrounding the representative particle. The force calculated on this representative particle will then be extended to a bed of spherical drops visualized as a Darcy porous bed. Thus, the “effective bed permeability” of such a porous bed will be computed as a function of various parameters and then will be compared with Carman–Kozeny relation. We use cell model approach to a packed bed of spherical drops of uniform size (monodisperse spherical drops) and then extend the work for a packed bed of polydisperse spherical drops, for a specific parameters. Our results show a good agreement with the Carman–Kozeny relation for the case of monodisperse spherical drops. The prediction of overall bed permeability using our present model agrees well with the Carman–Kozeny relation when the packing size distribution is narrow, whereas a small deviation can be noted when the size distribution becomes broader.