On the solutions to a Liouville-type system involving singularity

In this paper, we consider a Liouville-type system with singularity in the plane. The existence and uniqueness of solutions to the Dirichlet problem are proved. In addition, the structure of solutions in terms of analogues of the so-called total curvature in geometry or total mass in physics will be offered as well.     

Vanishing coefficients and identities concerning Ramanujan’s parameters

The Ramanujan Journal - In this paper we investigate several infinite products with vanishing Taylor coefficients in arithmetic progressions. These infinite products are closely related to...     

Hydrolytic stability and high Tg of polyimides derived from the novel 4,9‐bis[4‐(3,4‐dicarboxyphenoxy)phenyl]‐diamantane dianhydride

This work reports the synthesis and characterization of diamantane‐based polyimides obtained from 4,9‐bis[4(3,4‐dicarboxyphenoxy)phenyl]diamantane dianhydride and various aromatic diamines. Interestingly, the diamantane‐based polyimides were very stable to hydrolysis. This novel polyimide exhibits a low dielectric constant (2.65–2.77), low moisture absorption (<0.67%), good solubility, high T_g and unusually high thermal stability. Dynamic mechanical analysis (DMA) reveals that the diamantane‐based polyimides have high T_g ranging from 281 to 379 °C. The high‐temperature β₁ subglass transition around 285 °C was observed in polyimide 6a derived from 2,2′‐bis(trifluoromethyl)benzidine. This class of novel diamantane‐based polyimide is very promising for electronic applications, because of its good mechanical properties, good thermal stability, low dielectric constant, excellent hydrolytic resistance, and low moisture absorption. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1673–1684, 2009     

Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws

We study the large-time behaviors of solutions of viscous conservation laws whose inviscid part is a nonstrictly hyperbolic system. The initial data considered here is a perturbation of a constant state. It is shown that the solutions converge to single-mode diffusion waves in directions of strictly hyperbolic fields, and to multiple-mode diffusion waves in directions of nonstrictly hyperbolic fields. The multiple-mode diffusion waves, which are the new elements here, are the self-similar solutions of the viscous conservation laws projected to the nonstrictly hyperbolic fields, with the nonlinear fluxes replaced by their quadratic parts. The convergence rate to these diffusion waves isO(t ^–3/4+1/2p+) inL ^p , 1p, with >0 being arbitrarily small.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38     

Nonreductive deiodination of ortho-iodo-hydroxylated arenes using tertiary amines

A convenient and nonreductive deiodination is reported for the ortho-iodo-hydroxylated arenes including derivatives of quinolinol, phenol, and naphthol. Tertiary amines pyridine, triethylamine, and N-methylmorpholine in the presence of water initiated deiodination of ortho-iodo-hydroxylated arenes without affecting para-iodine and other reduction-susceptible groups. This reported method also works efficiently for polyiodinated systems. Simplicity, short reaction times, and absence of reducing catalyst are features of this method.