A priori estimates, existence and non-existence of positive solutions of generalized mean curvature equations

This paper concerns a priori estimates and existence of solutions of generalized mean curvature equations with Dirichlet boundary value conditions in smooth domains. Using the blow-up method with the Liouville-type theorem of the p laplacian equation, we obtain a priori bounds and the estimates of interior gradient for all solutions. The existence of positive solutions is derived by the topological method. We also consider the non-existence of solutions by Pohozaev identities.     

Quantitative unique continuation of solutions to higher order elliptic equations with singular coefficients

We investigate the quantitative unique continuation of solutions to higher order elliptic equations with singular coefficients. Quantitative unique continuation described by the vanishing order is a quantitative form of strong unique continuation property. We characterize the vanishing order of solutions for higher order elliptic equations in terms of the norms of coefficient functions in their respective Lebesgue spaces. New versions of quantitative Carleman estimates are established.     

Grafted antimicrobial cotton fabrics with N-halamine groups via atom transfer radical polymerization

Cellulose - An N-halamine precursor 2-(3-(6-methyl-4-oxo-1,4-dihydropyrimidin-2-yl)ureido)ethyl methacrylate (SCMHBMA) was synthesized and grafted on cotton fabrics via atom transfer radical...     

Conductive,superhydrophobic, and microwave-absorbing cotton fabric by dip-coating of aqueous silk nanofibers stabilized MWCNTs and octadecanoyl chain bonding

Cellulose - Compared to previously reported methods, we developed a facile dip-coating method to endow cotton fabric (CF) with satisfactory conductivity, superhydrophobicity and microwave...     

Quantitative uniqueness of solutions to second order elliptic equations with singular potentials in two dimensions

In this article, we study the vanishing order of solutions to second order elliptic equations with singular lower order terms in the plane. In particular, we derive lower bounds for solutions on arbitrarily small balls in terms of the Lebesgue norms of the lower order terms for all admissible exponents. Then we show that a scaling argument allows us to pass from these vanishing order estimates to estimates for the rate of decay of solutions at infinity. Our proofs rely on a new \(L^p - L^q\) Carleman estimate for the Laplacian in \(\mathbb {R}^2\).     

Diode-end-Pumped Nd:YAG Ceramic and Crystal Operation at 1,123 nm

We present a high-power diode-end-pumped continuous-wave Nd:YAG laser operating at 1,123 nm. Laser operation was carried out and compared using high optical quality Nd:YAG ceramics fabricated in-house and commercial Nd:YAG single crystals. At the absorbed diode pump powers of 23.2 and 28.0 W, output powers of 10.7 and 12.5 W at 1,123 nm were achieved for the employed ceramics and crystals as the laser material, which correspond to conversion efficiencies of 46.1% and 44.6%. For high-power lasers, the Nd:YAG ceramic has the advantage of a higher destructive threshold than that of commercial crystals.