Singular perturbation problems have been studied by many mathematicians. Since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. This paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

In the paper, we establish existence of steady boundary layer solution Boltzmann equation with specular condition in L 2 ∩L ∞ half-space. The uniqueness, continuity and exponential decay are obtained, such estimates important to prove Hilbert expansion for half-space problem condition.

We prove, for any state in a conformal field theory defined on a set of boundary manifolds with corresponding classical holographic bulk geometry, that for any bipartition of the boundary into two non-clopen sets, the density matrix cannot be a tensor product of the reduced density matrices on each region of the bipartition. In particular, there must be entanglement across the bipartition surfa...

abstract: since the field of micro electromechanical systems (mems) continues to grow, the flow in micro devices have become an area that receives a significant attention. the microscopic flows are usually characterized by the knudsen number (kn). when the characteristic size of the particle decreases down to a value comparable to the mean free path of the molecules, the continuum assumption fa...

the isogeometric analysis is increasingly used in various engineering problems. it is based on non-uniform rational b-splines (nurbs) basis function applied for the solution field approximation and the geometry description. one of the major concerns with this method is finding an efficient approach to impose essential boundary conditions, especially for inhomogeneous boundaries. the main contri...

Yan-Lei Zhang,1,2 Chang-Ling Zou,1,2,3,* Xu-Bo Zou,1,2,† Liang Jiang,3 and Guang-Can Guo1,2 1Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People’s Republic of China 2Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China 3Departm...

Chang-Ling Zou,1,2,3 Liang Jiang,2,* Xu-Bo Zou,1,3,† and Guang-Can Guo1,3 1Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026 2Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA 3Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, ...