We discuss the Siciak-Zaharjuta extremal function of a real convex body in Cn, a solution of the homogeneous complex Monge-Ampère equation on the exterior of the convex body. We determine several conditions under which a foliation by holomorphic curves can be found in the complement of the convex body along which the extremal function is harmonic. We study a variational problem for holomorphic ...

In order to achieve the thermal structural integrity analysis of solid rocket motor nozzle accurately and efficiently, multifield (flow-thermal-mechanical) coupled numerical investigation was carried out based on mesh-based parallel code interface. The simulation process finite element model algorithm engineering were obtained, while physical simplified appropriately. interface parameters, inte...

It is proposed to establish a standard for Gateway to Gateway procedures that allow the Gateways to be mutually suspicious. This document is a DRAFT for that standard. Your comments are strongly encouraged.

It is shown how a recently proposed method of cloaking is effective over a broad range of frequencies. The method is based on three or more active devices. The devices, while not radiating significantly, create a "quiet zone" between the devices where the wave amplitude is small. Objects placed within this region are virtually invisible. The cloaking is demonstrated by simulations with a broadb...

We discuss quantum properties of the single-exterior, “geon”-type black (and white) holes that are obtained from the Kruskal spacetime and the spinless Bañados-Teitelboim-Zanelli hole via a quotient construction that identifies the two exterior regions. For the four-dimensional geon, the Hartle-Hawking type state of a massless scalar field is thermal in a limited sense, but there is a discrepan...

A new method of cloaking is presented. For two-dimensional quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is approximately one within one disk and zero within a second disk, and such a polynomial is constructed. For the tw...

We hybridize the methods of finite element exterior calculus for Hodge–Laplace problem on differential k k -forms in alttext="double-struck up...

<p style='text-indent:20px;'>We study properties of nonnegative functions satisfying (E)<inline-formula><tex-math id="M1">\begin{document}$ \;-{\Delta} u+u^p-M|\nabla u|^q = 0 $\end{document}</tex-math></inline-formula> in a domain <inline-formula><tex-math id="M2">\begin{document}$ {\mathbb R}^N when id="M3">\begin{document}$ p>1 $\end{docume...

We begin with a short presentation of the basic concepts related to Lie groupoids and Lie algebroids, but the main part of this paper deals with Lie algebroids. A Lie algebroid over a manifold is a vector bundle over that manifold whose properties are very similar to those of a tangent bundle. Its dual bundle has properties very similar to those of a cotangent bundle: in the graded algebra of s...

A discrete (finite-difference) analogue of differential forms is considered, defined on simplicial complexes, including triangulations of continuous manifolds. Various operations are explicitly defined on these forms, including exterior derivative and exterior product. The latter one is non-associative. Instead, as anticipated, it is a part of non-trivial A ∞ structure, involving a chain of pol...