Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

直接碳燃料电池燃料的研究进展

直接碳燃料电池(DCFC)是一种清洁高效利用碳资源发电的装置。其因能量转换率高,对环境污染小,燃料选择范围广等优点获得了越来越多的关注。DCFC的性能与使用的燃料密切相关,为了探究燃料对DCFC的影响,本文分别阐述了石墨、炭黑、中密度纤维板、生物质、煤、活性炭的特性及改性方法,分析讨论了燃料表面含氧官能团以及燃料中的金属催化剂对阳极电化学反应的促进作用,发现燃料表面化学性质要比比表面积更加重要。同时,本文也提出了对生物质这一优良的可再生资源的期待,为未来DCFC燃料的发展提供参考。     

Classical solution for a nonlinear hybrid system modeling combustion in a multilayer porous medium

Combustion processes in porous media have been used by the petroleum engineering industry to extract heavy oil from reservoirs. This study focuses on a one-dimensional nonlinear hybrid system consisting of $n$ reaction–diffusion–convection equations coupled with $n$ ordinary differential equations, which models a combustion front moving through a porous medium with $n$ parallel layers. The state variables are the temperature and fuel concentration in each layer. Coupling occurs in both the reaction function and differential operator coefficients. We prove the existence of a classical solution, first locally and then globally over time, to an initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. The local solution is obtained by defining an operator in a set of Hölder continuous functions and using Schauder’s fixed-point theorem to find a fixed point as the desired solution. Using Zorn’s lemma, we extend the local solution to a global solution, proving that the first-order spatial derivative of the temperature in each layer is a bounded function.     

On amenability of two-generator groups

A discrete group G is amenable if there exists a finitely additive probability measure on G which is invariant under left translations and is defined on all subsets of G. It is proved that if the group is generated by two elements and is amenable then there are words being relators whose most of the consecutive pairs of the letters belong to a certain four-element set of pairs. This fact is applied to reproving non-amenability of a braid group. The same group provides an example showing that such type of condition is not su?cient for amenabilty.