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.     

焊接过程的RBF神经网络建模

介绍了RBF神经网络的性能和算法结构 ,建立了RBF神经网络在船舶焊接过程中用于焊接变形预测分析的模型 ,并探讨了其应用和发展趋势     

关于Cauchy中值定理逆问题的渐近性

对Cauchy中值定理的逆问题作了进一步的研究,得到了Cauchy中值定理逆问题的渐近性.     

环状连续强激光下光学薄膜的瞬温和热畸变

详细研究了非冷却光学薄膜元件在环形激光光束辐照下的瞬态温度分布和随后的热畸变，并且用泰曼干涉仪实际测量了连续波氧碘激光辐照各种非冷却光学元件的热畸变量并与理论计算相比较，分析结果表明理论和实验相一致。