Improved color purity in nano-size Eu-doped YBO3 red phosphor

Nano-size YBO₃:Eu³⁺ phosphor has been synthesized by the co-precipitation method. X-ray diffraction (XRD) pattern confirmed the formation of hexagonal vaterite-type structures of YBO₃:Eu³⁺ nanoparticles. The transmission electron microscopy (TEM) study revealed the formation of spherical YBO₃:Eu³⁺ nanoparticles with size 20-40 nm. The photoluminescence spectra revealed that the ratio of the red emission (⁵D₀-⁷F₂) to the orange emission (⁵D₀-⁷F₁) was much higher in the synthesized nano-size YBO₃:Eu³⁺ phosphor. The improved relative intensity, i.e., higher R/O value of emission peaks, is due to a lower symmetry of crystal field around Eu³⁺ ions.     

Central Limit Theorems for the Energy Density in?the?Sherrington-Kirkpatrick Model

In this paper we consider central limit theorems for various macroscopic observables in the high temperature region of the Sherrington-Kirkpatrick spin glass model. With a particular focus on obtaining a quenched central limit theorem for the energy density of the system with non-zero external field, we show how to combine the mean field cavity method with Stein’s method in the quenched regime. The result for the energy density extends the corresponding result of Comets and Neveu in the case of zero external field.     

Control of amplification without inversion in H2 and LiH molecules: Dependence on relative magnitude of probe and coherent field Rabi frequencies in three-level Λ system

Dependence of amplification without inversion (AWI) on the relative strength of probe and coherent field Rabi frequencies has been studied in H₂ and LiH molecules for three-level Λ configuration. We have derived exact analytical expressions for coherences and populations keeping all the orders of probe field Rabi frequency (G) and coherent field Rabi frequency. (Θ) in the steady state limit. Previously, first-order approximation (i.e. keeping only the first-order term in G) was used and hence AWI was studied for the condition Θ>>G. Here, by using the exact analytical expressions of coherences and populations, we have shown that AWI is maximum when Θ is within the same order of probe field Rabi frequency G irrespective of the choice of different ro-vibrational transitions in both the molecules. However, the shape of the gain profile and the maximum value of gain on the probe field and the absorption on coherent field depend on the choice of different ro-vibrational levels as the upper lasing levels. Effect of bidirectional pumping, homogeneous and inhomogeneous broadening on AWI process has been studied. By solving the density matrix equations numerically it has been shown that both the transient and the steady state AWI can be obtained and the numerical values of coherences and populations at large time are in very good agreement with exact analytical values in the steady state limit. It has been shown that in molecules AWI can be obtained on probe field of smaller wavelength than that of the coherent field which has not been observed in atoms so far.     

Convexifactors, Generalized Convexity, and Optimality Conditions

The recently introduced notion of a convexifactor is further studied, and quasiconvex and pseudoconvex functions are characterized in terms of convexifactors. As an application to a chain rule, a necessary optimality condition is deduced for an inequality constrained mathematical programming problem.     

Scheduling of Jobs in a Hypercube Processing System

When a job is processed in a hypercube multi-processor, it is allocated a cube of processing elements of the requisite size. There are three distinct costs involved in the hypercube scheduling problem: the cost of detecting a free cube (allocation), the cost of migrating jobs and merging the free spaces to accommodate a larger cube request (relocation) and the cost of not meeting the due date (tardiness). Traditionally, research in this area has focused on finding efficient algorithms for allocating a free cube (if any) in the hypercube system. The relocation cost has been treated as an independent cost metric. The role of scheduling has not received much attention and present subcube allocation methods assume a first-come-first-serve (FCFS) approach over the input job set.This paper considers the underlying scheduling issues in a hypercube processing system and shows how techniques other than FCFS scheduling of the incoming jobs can help in reducing the relocation cost and hence the overall subcube resource assignment cost. We discuss five simple and easily implementable dispatching heuristics, and compare their relative performance with the FCFS scheduling rule to demonstrate the advantages of scheduling in subcube allocation.     

Preconcentration and separation of trace amounts of palladium using dithiooxamide functionalized chelating resin followed by its determination using radiotracer technique

The work describes a procedure of preconcentration and separation of trace amounts of Pd(II) by solid phase extraction of the metal ion by dithiooxamide groups incorporated into a matrix of polystyrene-divinylbenzene whereas the determination of palladium has been carried out by radiotracer technique using ¹⁰⁹Pd (T _1/2 = 13.43 hr, E _γ = 311, 647 keV). The experiments were carried out using both batch method and column operation. Parameters such as the amount of resin, effect of pH, equilibration rate, sorption and desorption of metal ions have been studied. The maximum sorption capacity for palladium was found to be 0.10 mmol·g⁻¹ at pH 6.0. The method is rapid, has a good accuracy and can be used routinely.