Synthesis and Reactions of Some New Pyrrolylfuro[2,3‐d]Pyrimidines and Pyrrolopyrazinofuropyrimidines

5‐Amino‐4‐methyl‐2‐phenyl‐6‐substitutedfuro[2,3‐d]pyrimidines ( 2a‐c ) were reacted with 2,5‐dimethoxytetrahydrfuran to afford the pyrrolyl derivatives 3a‐c . Compound 3a was chosen as intermediate for the synthesis of poly fused heterocycles incorporated furopyrimidines moiety 4–11 . Some of the synthesized compounds were screened for their antibacterial and antifungal activities.     

On the Discrete Hardy Inequality

Necessary and sufficient conditions for the boundedness of thediscrete Hardy operator of the form , from to when 0 < q < 1 <p , is given.     

Robust optimization in countably infinite linear programs

A robust optimization framework for countably infinite linear programs (CILPs) is developed. It is shown that a particular robust counterpart of a nominal CILP can be reformulated as another CILP. A bound on the probability of constraint violation is derived. A convergent algorithm for solving this robust CILP is proposed.     

Adjoint L-Values and Primes of Congruence for Hilbert Modular Forms

Let f be a primitive Hilbert modular cusp form of arbitrary level and parallel weight k, defined over a totally real number field F. We define a finite set of primes that depends on the weight and level of f, the field F, and the torsion in the boundary cohomology groups of the Borel–Serre compactification of the underlying Hilbert-Blumenthal variety. We show that, outside , any prime that divides the algebraic part of the value at s=1 of the adjoint L-function of f is a congruence prime for f. In special cases we identify the boundary primes in terms of expressions of the form , where is a totally positive unit of F.     

Structural,optical and electrical properties of undoped and Si-doped AlxGa1−xN thin films on Si (1 1 1) substrate grown by PA-MBE

We have studied the structural properties of undoped and Si-doped Al_xGa_1?xN/GaN/AlN on Si (1 1 1) substrate prepared by plasma-assisted molecular beam epitaxy (PA-MBE) using high-resolution X-ray diffraction (HR-XRD) and atomic force microscopy (AFM). In comparison with undoped AlGaN, the roughness and dislocation density on the surface of the AlGaN layer decrease with Si doping. Full width half maximum (FWHM) of the undoped and Si-doped samples were equal to 0.69° and 0.52°, respectively. This indicates that the Si doping improves the crystalline quality of the Al_xGa_1?xN layer compared with the undoped one. Raman scattering measurement reveals that the optical phonon modes of A₁(LO) and E₂(H) of the AlGaN show a one-mode and two-modes behavior, respectively. The Fourier-transform infrared reflectance (FTIR) investigation confirms the one-mode (two-mode) behavior of the LO (TO) phonon in our samples. This is in good agreement with Raman measurement. Finally, the barrier height (Φ_B) of undoped and Si-doped Al_xGa_1?xN samples was found to be 0.86 and 0.74 eV, respectively.     

Dynamic lot-sizing in sequential online retail auctions

Retailers often conduct non-overlapping sequential online auctions as a revenue generation and inventory clearing tool. We build a stochastic dynamic programming model for the seller’s lot-size decision problem in these auctions. The model incorporates a random number of participating bidders in each auction, allows for any bid distribution, and is not restricted to any specific price-determination mechanism. Using stochastic monotonicity/stochastic concavity and supermodularity arguments, we present a complete structural characterization of optimal lot-sizing policies under a second order condition on the single-auction expected revenue function. We show that a monotone staircase with unit jumps policy is optimal and provide a simple inequality to determine the locations of these staircase jumps. Our analytical examples demonstrate that the second order condition is met in common online auction mechanisms. We also present numerical experiments and sensitivity analyses using real online auction data.     

Studies on photoinduced effects in pulse-electrodeposited Ag/Hg-1212/CdSe hetero-nanostructures

Metal/superconductor/semiconductor (Ag/Hg-1212/CdSe) hetero-nanostructures have been fabricated using pulse-electrodeposition technique and are characterized by X-ray diffraction (XRD), full-width at half-maximum (FWHM) and scanning electron microscopy (SEM) studies. The junction capacitance of Ag/Hg-1212, Hg-1212/CdSe and Ag/Hg-1212/CdSe heterojunctions is measured in dark and under laser irradiation at room temperature. The nature of the junction formed and built-in-junction potentials were determined. The increase in carrier concentration across the junction due to photo-irradiation has been observed.     

Effect of laser irradiation of C-V characteristics of electrodeposited Ag/Tl-2223/CdSe hetero-nanostructures

One of the innovative technological directions for the high-temperature superconductors has been persued by fabricating the heteroepitaxial multilayer structures such as superconductor-semiconductor heterostructures. In the present investigation, metal/superconductor/semiconductor (Ag/Tl-2223/CdSe) hetero-nanostructures have successfully been fabricated using dc electrodeposition technique and were characterized by X-ray diffraction (XRD), full-width at half-maximum (FWHM) and scanning electron microscopy (SEM) studies. The measurement of junction capacitance as a function of biasing voltage was used for the estimation of junction built-in-potential (V _D) and to study the charge distribution in a heterojunction. The Mott-Schottky plots were measured for each junction in dark and under the photo-irradiation. The effect of laser irradiation on C-V characteristics of hetero-nanostructure has been studied.