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.     

Temperature variation of phonon frequency distribution in the fast ion conductor lead fluoride

A weighted phonon frequency distribution has been measured in PbF₂ at temperatures 10, 302, 660 and 910 K, using a neutron scattering technique. At 10 K good agreement is found between the measured distribution and the phonon density-of-states calculated from the low temperature dispersion relation of PbF₂. At the higher temperatures, near the ionic conductivity transition temperature, T_c ～ 700 K, the optic modes are observed to broaden into a high energy tail consistent with strong anharmonicity or extensive disorder. A low energy peak arising from transverse acoustic modes remains well defined even at temperatures above T_c.     

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.