Cayley’s decomposition and pólya’sW-property of ordinary linear differential equations

A proof is given for the equivalence of Pólya’sW- property of a linear differential equationL _n (D) y=0 to the possibility of decomposingL _n (D) ≡ Π _n ¹ [D+λ_i(x)] in a given interval. In this case a set ofn independent solutions form a Chebyshev system in the interval. An application determines intervals of non-oscillation for solutions of linear equations of the second order. Research supported by the National Science Foundation Grant No. GP-3897 with the University of Maryland.     

Effects of slight Fe (III)-doping on structural and optical properties of TiO2 nanoparticles

Journal of Sol-Gel Science and Technology - In this research work, undoped and slight Fe-doped-TiO2 nanoparticles (Fe–TiO2 NPs) were prepared using simple chemical sol–gel method and...