Mixed principal eigenvalues in dimension one

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the $L^{2}$-Poincar\'e inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.Comment: 45 pages; Front. Math. China, 201

Statistical Mechanics of Three-dimensional Kerr-de Sitter Space

The statistical computation of the (2+1)-dimensional Kerr-de Sitter space in the context of the {\it classical} Virasoro algebra for an asymptotic isometry group has been a mystery since first, the degeneracy of the states has the right value only at the infinite boundary which is casually disconnected from our universe, second, the analyses were based on the unproven Cardy's formula for complex central charge and conformal weight. In this paper, I consider the entropy in Carlip's "would-be gauge" degrees of freedom approach instead. I find that it agree with the Bekenstein-Hawking entropy but there are no the above problems. Implications to the dS/CFT are noted.Comment: Added comments about diffeomorphism generators and Wheeler-de Witt equation; Added references; Accpected in CQ

Cellular trafficking of thymosin beta-4 in HEPG2 cells following serum starvation

Thymosin beta-4 (Tβ4) is an ubiquitous multi-functional regenerative peptide, related to many critical biological processes, with a dynamic and flexible conformation which may influence its functions and its subcellular distribution. For these reasons, the intracellular localization and trafficking of Tβ4 is still not completely defined and is still under investigation in in vivo as well as in vitro studies. In the current study we used HepG2 cells, a human hepatoma cell line; cells growing in normal conditions with fetal bovine serum expressed high levels of Tβ4, restricted to the cytoplasm until 72 h. At 84 h, a diffuse Tβ4 cytoplasmic immunostaining shifted to a focal perinuclear and nuclear reactivity. In the absence of serum, nuclear reactivity was localized in small granules, evenly dispersed throughout the entire nuclear envelop, and was observed as earlier as at 48 h. Cytoplasmic immunostaining for Tβ4 in HepG2 cells under starvation appeared significantly lower at 48 h and decreased progressively at 72 and at 84 h. At these time points, the decrease in cytoplasmic staining was associated with a progressive increase in nuclear reactivity, suggesting a possible translocation of the peptide from the cytoplasm to the nuclear membrane. The normal immunocytochemical pattern was restored when culture cells submitted to starvation for 84 h received a new complete medium for 48 h. Mass spectrometry analysis, performed on the nuclear and cytosolic fractions of HepG2 growing with and without serum, showed that Tβ4 was detectable only in the cytosolic and not in the intranuclear fraction. These data suggest that Tβ4 is able to translocate from different cytoplasmic domains to the nuclear membrane and back, based on different stress conditions within the cell. The punctuate pattern of nuclear Tβ4 immunostaining associated with Tβ4 absence in the nucleoplasm suggest that this peptide might be localized in the nuclear pores, where it could regulate the pore permeabilit

Extraordinary Redox Activities in Ladder-Type Conjugated Molecules Enabled by B ← N Coordination-Promoted Delocalization and Hyperconjugation.

The introduction of B ← N coordinate bond-isoelectronic to C-C single bond-into π-systems represents a promising strategy to impart exotic redox and electrochromic properties into conjugated organic molecules and macromolecules. To achieve both reductive and oxidative activities using this strategy, a cruciform ladder-type molecular constitution was designed to accommodate oxidation-active, reduction-active, and B ← N coordination units into a compact structure. Two such compounds (BN-F and BN-Ph) were synthesized via highly efficient N-directed borylation. These molecules demonstrated well-separated, two reductive and two oxidative electron-transfer processes, corresponding to five distinct yet stable oxidation states, including a rarely observed boron-containing radical cation. Spectroelectrochemical measurements revealed unique optical characteristics for each of these reduced/oxidized species, demonstrating multicolor electrochromism with excellent recyclability. Distinct color changes were observed between each redox state with clear isosbestic points on the absorption spectra. The underlying redox mechanism was elucidated by a combination of computational and experimental investigations. Single-crystal X-ray diffraction analysis on the neutral state, the oxidized radical cation, and the reduced dianion of BN-Ph revealed structural transformations into two distinct quinonoid constitutions during the oxidation and reduction processes, respectively. B ← N coordination played an important role in rendering the robust and reversible multistage redox properties, by extending the charge and spin delocalization, by modulating the π-electron density, and by a newly established hyperconjugation mechanism