Spectral Characteristics of the Reaction Products of 5-Phenyl-2,3,4-furantrione with o-Diamines

The ¹H and ¹³C NMR and mass spectra of 2-(2-amino-4,5-dimethylphenylcarbamoyl)-3-(hydroxyphenylmethyl)-6,7-dimethylqinoxaline (2), 3-(hydroxyphenylmethyl)-6,7-dimethylquinoxalin-2-carboxylic-γ-lactone (5), 3-(hydroxyphenylmethyl)-6,7-dimethylquinoxalin-2-carboxylic acid phenylhydrazide (6), 3-[2-hydroxy-2-phenyl-1-(phenylhydrazono)ethyl]-6,7-dimethyl-2(1H)-quinoxalinone (7), 2,3-dihydro-6,7-dimethyl-3-phenylhydrazono-2-phenylfuro[2,3-b]auinoxaline (8), 3-(hydroxyphenylmethyl)-6,7-dimethyl-1-phenylflavazole (9), and 3-(acetoxyphenylmethyl)-6,7-dimethyl-1-phenylflavazole (10) have been studied.     

Polynomial expansions and generating functions

We study expansions in polynomials {P_n(x)}^∞_o generated by ∑^∞_{n = o}P_n(x)tⁿ = A(t) φ(xt^kθ(t)), θ(0) ≠ 0, and ∑^∞_{n = 0}P_n(x)tⁿ = ∑^k_{j = 1}A_j(t) φ(xt?_j), ?₁,…,?_k being the k roots of unity. The case k = 1 is contained in a recent work by Fields and Ismail. We also prove a new generalization of Vandermond's inverse relations.     

BEM for transient 2D elastodynamics using multiquadric functions

A new boundary element model for transient dynamic analysis of 2D structures is presented. The dual reciprocity method (DRM) is reformulated for the 2D elastodynamics by using the multiquadric radial basis functions (MQ). The required kernels for displacement and traction particular solutions are derived. Some terms of these kernels are found to be singular; therefore, a new smoothing technique is proposed to solve this problem. Hence, the limiting values of relevant kernels are computed. The validity and strength of the proposed formulation are demonstrated throughout several numerical applications. It is proven from the results that the present formulation is more stable than the traditional DRM, which uses the conical (1 + R) function, especially in predicting results in the far time zone.