We analyze the polynomial solutions of the linear differential equation p2(x)y ′′ +p1(x)y ′ + p0(x)y = 0 where pj(x) is a j th -degree polynomial. We discuss all the possible polynomial solutions and their dependence on the parameters of the polynomials pj(x). Special cases are related to known differential equations of mathematical physics. Classes of new soluble problems are exhibited. General results are obtained for weight functions and orthogonality relations.PACS numbers: 33C05, 33C15, 33C45, 33C47, 33D45
We report, for the first time, the intercalation of poly[oligo(ethylene glycol) oxalate] (POEGO) and POEGO lithium salt (LiCF 3 SO 3 ) complex (POEGO-LiCF 3 SO 3 ) into vanadium pentoxide xerogel (V 2 O 5 nH 2 O). The effect of changing the polymer concentration on the interlayer expansion of the layered host was studied, and the optimal intercalation ratio was determined to be 1:2. The intercalates were characterized by powder X-ray diffraction, thermogravimetric analysis, differential scanning calorimetry, Fourier transform infrared spectroscopy, and AC impedance spectroscopy.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.