Volume Comparison of Conformally Compact Manifolds with Scalar Curvature <Emphasis Type="Italic">R</Emphasis> ≥ −<Emphasis Type="Italic">n</Emphasis> (<Emphasis Type="Italic">n</Emphasis> − 1)

In this paper, we use the normalized Ricci–DeTurk flow to prove a stability result for strictly stable conformally compact Einstein manifolds. As an application, we show a local volume comparison of conformally compact manifolds with scalar curvature R ≥ ?n (n ? 1) and also the rigidity result when certain relative volume is zero.     

A Topological Intersection Theorem with Applications in H-Spaces

In this paper, a topological intersection theorem of a family of sets with H-convex sections is established. As an application to this theorem, the Nash equilibrium of abstract economy, the Ky-Fan minimax theorem, and an existence problem of solution for quasi-variational inequality are studied. The results presented in this paper modify and extend the corresponding results given in the literature.AMS Subject Classification (2000) 47H10This work is supported by the Foundation of Yunnan Science Technology Commission, China.     

K(a)hler Manifolds with Almost Non-negative Ricci Curvature

Compact K(a)hler manifolds with semi-positive Ricci curvature have been investigated by various authors. From Peternell's work, if M is a compact K(a)hler n-manifold with semi-positive Ricci curvature and finite fundamental group, then the universal cover has a decomposition (M) ≌ X1 × … × Xm, where Xj is a Calabi-Yau manifold, or a hyperK(a)hler manifold, or Xj satisfies Ho(Xj,Ωp) = 0. The purpose of this paper is to generalize this theorem to almost non-negative Ricci curvature K(a)hler manifolds by using the Gromov-Hausdorff convergence. Let M be a compact complex n-manifold with non-vanishing Euler number. If for any ε ＞ 0, there exists a K(a)hler structure (Je,ge) on M such that the volume Volge(M) ＜ V, the sectional curvature |K(gε)| ＜ Λ2, and the Ricci-tensor Ric(gε)＞ -εgε, where ∨ and Λ are two constants independent of ε. Then the fundamental group of M is finite, and M is diffeomorphic to a complex manifold X such that the universal covering of X has a decomposition, (X) ≌ X1 × … × Xs, where Xi is a Calabi-Yau manifold, or a hyperK(a)hler manifold, or Xi satisfies Ho(Xi, Ωp) = {0}, p ＞ 0.     

Tightness and Convergence of Trimmed Lévy Processes to Normality at Small Times

For nonnegative integers r, s, let \(^{(r,s)}X_t\) be the Lévy process \(X_t\) with the r largest positive jumps and the s smallest negative jumps up till time t deleted, and let \(^{(r)}\widetilde{X}_t\) be \(X_t\) with the r largest jumps in modulus up till time t deleted. Let \(a_t \in \mathbb {R}\) and \(b_t>0\) be non-stochastic functions in t. We show that the tightness of \(({}^{(r,s)}X_t - a_t)/b_t\) or \(({}^{(r)}{\widetilde{X}}_t - a_t)/b_t\) as \(t\downarrow 0\) implies the tightness of all normed ordered jumps, and hence the tightness of the untrimmed process \((X_t -a_t)/b_t\) at 0. We use this to deduce that the trimmed process \(({}^{(r,s)}X_t - a_t)/b_t\) or \(({}^{(r)}{\widetilde{X}}_t - a_t)/b_t\) converges to N(0, 1) or to a degenerate distribution as \(t\downarrow 0\) if and only if \((X_t-a_t)/b_t \) converges to N(0, 1) or to the same degenerate distribution, as \(t \downarrow 0\).     

Determination of SYUIQ-F5, a Novel Telomerase Inhibitor and Anti-tumor Lead-Compound, in Tissues and Plasma Samples by LC�CMS�CMS: Application to a Tissue Distribution Study in Rat

A sensitive assay for determining SYUIQ-F5, a novel telomerase inhibitor and anti-tumor drug, in rat tissues and plasma was developed and validated by using liquid chromatography/tandem mass spectrometry (LC?CMS?CMS). After a single step liquid?Cliquid extraction with ethyl acetate-dichloromethane, SYUIQ-F5 and SUCL (internal standard) were subjected to LC?CMS?CMS analysis using positive electro-spray ionization under selected reaction monitoring mode. Chromatographic separation of SYUIQ-F5 and SUCL was achieved on a Zorbax Eclipse Plus C18 column (I.D. 4.6 mm × 150 mm, 3.5 ??m) with a mobile phase consisting of acetonitrile-2 mM ammonium formate (90:10, v/v) at a flow rate of 0.6 mL min^?1. The intra- and inter-batch precision of the method were <12.2 and 8.7%, respectively. The intra- and inter-batch accuracies ranged from 100.2 to 107.3%. The lowest limit of quantification for SYUIQ-F5 was 0.5 ng mL^?1. The method was applied to a SYUIQ-F5 tissue distribution study after an oral dose of 30 mg kg^?1 to rats. SYUIQ-F5 tissue concentrations decreased in the order of small intestine> liver> lung> spleen> stomach> kidneys> heart> brain> muscle> fat> testes> plasma. SYUIQ-F5 could still be detected in most of the tissues at 48-h post-dosing. These results indicated that the LC?CMS?CMS method was sensitive, reliable, and specific to quantify SYUIQ-F5 in different rat tissues.     

Hydration patterns and salting effects in sodium chloride solution

The salting effects of 2M sodium chloride electrolyte are studied based on a series of model solutes with properties ranging from hydrophobic to hydrophilic. Generally, hydrophobic solutes will be salted out and hydrophilic solutes will be salted in by NaCl solution. The solvation free energy changes are highly correlated with Kirkwood-Buff integrals. The underlying mechanism resorts to the preferential binding of ions and water to solutes. Our results demonstrate that the salting effect not only depends on the salt's position in Hofmeister series, but also on the solutes' specifics. Taking the hydration free energies of solutes and ions as independent variables, a schematic diagram of salting effects is suggested. The resolved multifaceted salting effects rely on the sensitive balance of the tripartite interaction among solutes, ions, and water.     

Comprehensive Comparison of Two Color Varieties of Perillae Folium by GC-MS-Based Metabolomic Approach

Perillae Folium (PF), the leaf of Perilla frutescens (L.) Britt, is extensively used as culinary vegetable in many countries. It can be divided into two major varietal forms based on leaf color variation, including purple PF (Perilla frutescens var. arguta) and green PF (P. frutescens var. frutescens). The aroma of purple and green PF is discrepant. To figure out the divergence of chemical composition in purple and green PF, gas chromatography–tandem mass spectrometry (GC-MS) was applied to analyze compounds in purple and green PF. A total of 54 compounds were identified and relatively quantified. Multivariate statistical methods, including principal component analysis (PCA), orthogonal partial least-squares discrimination analysis (OPLS-DA) and clustering analysis (CA), were used to screen the chemical markers for discrimination of purple and green PF. Seven compounds that accumulated discrepantly in green and purple PF were characterized as chemical markers for the discrimination of the purple and green PF. Among these 7 marker compounds, limonene, shisool and perillaldehyde that from the same branch of the terpenoid biosynthetic pathway were with relatively higher contents in purple PF, while perilla ketone, isoegomaketone, tocopheryl and squalene on other branch pathways were higher in green PF. The results of the present study are expected to provide theoretical support for the development and utilization of PF resources.     

Cruciform oligo(phenylenevinylene) with a bipyridine bridge: synthesis, its rhenium(I) complex and photovoltaic properties

A cruciform-shaped oligo(phenylenevinylene) (OPV) with a phosphorescent rhenium(I) chromophore incorporated at the centre and grafted triphenylamines around the periphery was designed as a new organic photovoltaic material, in which the chelation of rhenium(I) to the cruciform successfully constructs a three-dimensional intramolecular charge transfer system and extends the exciton lifetime; as a result, the rhenium-OPV complex shows a power conversion efficiency almost two times that of the metal ion-free parent compound.     

Metabolic Behaviors of Aconitum Alkaloids in Different Concentrations of Aconiti Lateralis Radix Praeparata and Effects of Aconitine in Healthy Human and Long QT Syndrome Cardiomyocytes

Aconiti Lateralis Radix Praeparata (Fu Zi) is the processed lateral root of Aconitum carmichaelii Debx, which is widely used in emergency clinics. Poisoning incidents and adverse reactions occur with the improper intake of Fu Zi. Metabolic characteristics of aconitum alkaloids of Fu Zi may vary, and the effects of Fu Zi in healthy and Long QT syndrome (LQTS) patients is unknown. In this experiment, 24 Sprague Dawley rats were randomly divided into three groups: 2.0, 1.0, and 0.5 g/kg dose groups, and blood samples were collected after the oral administration of Fu Zi extract. We used an ultra-high performance liquid chromatography-tandem mass spectrometry system to detect the concentrations of six aconitum alkaloids. Cell toxicity, calcium imaging, and patch-clamp recordings of human induced pluripotent stem cells-cardiomyocytes (hiPSC-CMs) of aconitine in healthy and LQTS were observed. We found that the AUC_(0–48h), C_max, and t_1/2 of the six compounds increased with the multiplicative dosages; those in the high group were significantly higher than those in the low group. Aconitine concentration-dependently decreased the amplitude, which has no significant effect on the cell index of normal hiPSC-CMs. Aconitine at 5.0 μM decreased the cell index between 5–30 min for LQTS hiPSC-CMs. Meanwhile, aconitine significantly increased the frequency of calcium transients in LQTS at 5 μM. Aconitine significantly shortened the action potential duration of human cardiomyocytes in both normal and LQTS groups. These results show metabolic behaviors of aconitum alkaloids in different concentrations of Fu Zi and effects of aconitine in healthy and LQTS patients.     

Rigidity of Asymptotically Hyperbolic Manifolds

In this paper, we prove a rigidity theorem of asymptotically hyperbolic manifolds only under the assumptions on curvature. Its proof is based on analyzing asymptotic structures of such manifolds at infinity and a volume comparison theorem.The first author’s research is partially supported by NSF grant of China.The second author’s research is partially supported by an NSF grant and a Simon fund.