Differentiable spaces that are subcartesian

We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows.     

The full basis theorem does not imply analytic wellordering

A finite support product of ${\omega }_1$ clones of Jensen's minimal ${\Pi }_2^1$ singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals.     

Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

In this paper, let $(M^n,g,d\mu )$ be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation

${△}_{p,f}v+c{v}^{\sigma }=0,$

where $c\le 0,m>n\ge 1,1<p<\frac{m?1+\sqrt{(m?1)(m+3)}}{2},\sigma \le p?1$ are real constants.     

Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

焦炉上升管内壁结焦炭层的光谱学分析及结焦机理研究

以焦炉上升管内壁结焦炭层块为研究对象，采用X射线荧光光谱仪（XRF）、X射线衍射仪（XRD）、傅里叶红外光谱仪（FTIR）和激光共聚焦拉曼光谱仪（Raman）对结焦炭层的元素组成，以及各结焦炭层的矿物组成、组成结构和分子结构进行测试。分析从结焦炭层块外表面向内表面过渡的各结焦炭层的差异性，揭示焦炉上升管内壁结焦机理。结果表明焦炉上升管内粉尘中Fe，S和Cr极易催化荒煤气中蒽、萘等稠环芳烃化合物成炭，在焦炉上升管内壁形成炭颗粒沉积，为焦油凝结挂壁提供载体，在荒煤气温度降至结焦温度时易结焦积碳。结焦炭层均含有芳香层结构，随着结焦炭层从外表面向内表面过渡，各结焦炭层的面层间距(d₀₀₂)逐渐降低、层片直径(L_a)先降低后增加、层片堆砌高度(Lc)和芳香层数(N)先稳定后增加。结焦炭层石墨化过程是由结焦炭层内表面向外表面进行，主要包括其片层外缘的羧基和部分C-O结构的降解剥离，从而形成高度规整的共轭结构。结焦炭层块中C元素是以结晶碳与无定型碳的混合物形式存在。以上研究为解决焦炉上升管内壁结焦及腐蚀问题，提高换热器换热效率，有效回收焦炉荒煤气显热，降低焦化企业能耗提供实验基础和理论依据。     

Algebra matrix and similarity classification of operators

In this paper, by the Gelfand representation theory and the Silov idempotents theorem, we first obtain a central decomposition theorem related to a unital semi-simple n-homogeneous Banach algebra, and then give a similarity classification of two strongly irreducible Cowen-Douglas operators using this theorem.     

The Chang-Łoś-Suszko theorem in a topological setting

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.