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。     

Decomposition of group rings and the converse of Schur’s lemma

In this work, we give necessary and su?cient conditions for a group ring (of finite group) to satisfy the converse of Schur’s lemma for group rings of finite groups. Rings considered here are commutative or noncommutative perfect. Some cases of twisted group rings are studied. Also we introduce the notion of semi-CSL ring.     

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.     

One-sided Hopf algebras and quantum quasigroups

We study the connections between one-sided Hopf algebras and one-sided quantum quasigroups, tracking the four possible invertibility conditions for the left and right composite morphisms that combine comultiplications and multiplications in these structures. The genuinely one-sided structures exhibit precisely two of the invertibilities, while it emerges that imposing one more condition often entails the validity of all four. A main result shows that under appropriate conditions, just one of the invertibility conditions is su?cient for the existence of a one-sided antipode. In the left Hopf algebra which is a variant of the quantum special linear group of two-dimensional matrices, it is shown explicitly that the right composite is not injective, and the left composite is not surjective.