On the second boundary value problem for Monge-Ampere type equations and geometric optics

In this paper, we prove the existence of classical solutions to second boundary value prob- lems for generated prescribed Jacobian equations, as recently developed by the second author, thereby obtaining extensions of classical solvability of optimal transportation problems to problems arising in near field geometric optics. Our results depend in particular on a priori second derivative estimates recently established by the authors under weak co-dimension one convexity hypotheses on the associated matrix functions with respect to the gradient variables, (A3w). We also avoid domain deformations by using the convexity theory of generating functions to construct unique initial solutions for our homotopy family, thereby enabling application of the degree theory for nonlinear oblique boundary value problems.Comment: Final version to appear in Archive for Rational Mechanics and Analysi

Relation of SiO maser emission to IR radiation in evolved stars based on the MSX observation

Based on the space MSX observation in bands A(8$\mu$m), C(12$\mu$m), D(15$\mu$m) and E(21$\mu$m), and the ground SiO maser observation of evolved stars by the Nobeyama 45-m telescope in the v=1 and v=2 J=1-0 transitions, the relation between SiO maser emission and mid-IR continuum radiation is analyzed. The relation between SiO maser emission and the IR radiation in the MSX bands A, C, D and E is all clearly correlated. The SiO maser emission can be explained by a radiative pumping mechanism according to its correlation with infrared radiation in the MSX band A.Comment: 11 pages, 4 figures, to appear in ApJ

Oblique boundary value problems for augmented Hessian equations I

In this paper, we study global regularity for oblique boundary value problems of augmented Hessian equations for a class of general operators. By assuming a natural convexity condition of the domain together with appropriate convexity conditions on the matrix function in the augmented Hessian, we develop a global theory for classical elliptic solutions by establishing global a priori derivative estimates up to second order. Besides the known applications for Monge-Amp`ere type operators in optimal transportation and geometric optics, the general theory here embraces prescribed mean curvature problems in conformal geometry as well as oblique boundary value problems for augmented k-Hessian, Hessian quotient equations and certain degenerate equations.Comment: Revised version containing minor clarification

On the Dirichlet problem for general augmented Hessian equations

In this paper we apply various first and second derivative estimates and barrier constructions from our treatment of oblique boundary value problems for augmented Hessian equations, to the case of Dirichlet boundary conditions. As a result we extend our previous results on the Monge-Ampere and k-Hessian cases to general classes of augmented Hessian equations in Euclidean spaceComment: This paper is a spin-off from our treatment of oblique boundary value problems which was first posted on arXiv in 2015 and replaces earlier draft

Size dependence of second-order hyperpolarizability of finite periodic chain under Su-Schrieffer-Heeger model

The second hyperpolarizability $\gamma_N(-3\omega\omega,\omega,\omega)$ of $N$ double-bond finite chain of trans-polyactylene is analyzed using the Su-Schrieffer-Heeger model to explain qualitative features of the size-dependence behavior of $\gamma_N$. Our study shows that $\gamma_N/N$ is {\it nonmonotonic} with $N$ and that the nonmonotonicity is caused by the dominant contribution of the intraband transition to $\gamma_N$ in polyenes. Several important physical effects are discussed to reduce quantitative discrepancies between experimental and our resultsComment: 3 figures, 1 tabl