实局部p-凸空间l^p,L^p(μ)(0＜p＜1)的共轭锥的次表示定理

该文属于非局部凸分析的范畴,研究实局部p-凸空间l^p与L^p(μ)(0<p<1)的共轭锥(l^p)_p~*与[L^p(μ)]_p~*的表示问题,得到(l^p)p~*■m^+×m^+,[L^p(μ)]_p~*■M^+(μ)×M^+(μ),称为(l^p))p~*与(l^p))p~*的次表示定理.

Ultrafast Dynamics Through Conical Intersections in 2,6-dimethylpyridine Studied with Time-resolved Photoelectron Imaging

The ultrafast dynamics through conical intersections in 2,6-dimethylpyridine has been studied by femtosecond time-resolved photoelectron imaging coupled with time-resolved mass spectroscopy. Upon absorption of 266 nm pump laser, 2,6-dimethylpyridine is excited to the S2 state with a ππ character from So state. The time evolution of the parent ion signals consists of two exponential decays. One is a fast component on a timescale of 635 fs and the other is a slow component with a timescale of 4.37 ps. Time-dependent photo- electron angular distributions and energy-resolved photoelectron spectroscopy are extracted from time-resolved photoelectron imaging and provide the evolutive information of S2 state. In brief, the ultrafast component is a population transfer from S2 to S1 through the S2/S1 conical intersections, the slow component is attributed to simultaneous IC from the S2 state and the higher vibrational levels of S1 state to So state, which involves the coupling of S2/S0 and S1/So conical intersections. Additionally, the observed ultrafast S2--＋S1 transition occurs only with an 18% branching ratio.

l^p(X)的共轭锥的次表示定理(0＜p＜1)(英文)

众所周知,对于Banach空间X,l^1(X)的共轭空间可以表示为l~∞(X*).当0<p<1时l^p(X)非局部凸,但却是局部p-凸的,其共轭锥[l^p(X)]_p~*充分大足以分离空间l^p(X)中点.本文探究0<p<1时l^p(X)的共轭锥[l^p(X)]_p~*的表示问题,对于任意Banach空间X,得到次表示定理[l^p(X)]_p~*■l~∞(X_p~*).对于数域X=R或C,次表示定理简化为[lp(R)]_p~*■m^+×m^+与[l^p(C)]_p~*■mM_p^+(T).

(l^(β_1))_(β_2)~*的次表示定理与l^(β_1)的非局部β_2-凸性(0＜β_1＜β_2≤1)(英文)

对0<β_1<β_2≤1,本文得到l^(β_1)的β_2-共轭锥的次表示定理(l^(β_1))_(β_2)~*■m^+×m^+,证明l^(β_1)不是局部β_2-凸空间.