A scaling limit for the length of the longest cycle in a sparse random digraph

We discuss the length of the longest directed cycle in the sparse random digraph , constant. We show that for large there exists a function such that a.s. The function where is a polynomial in . We are only able to explicitly give the values , although we could in principle compute any .     

Separation of 1,3‐dimethylamylamine and other polar compounds in a dietary supplement formulation using aqueous normal phase chromatography with MS

Five ingredients (caffeine, l ‐arginine, creatine, β‐alanine, and 1,3‐dimethylamylamine) from a workout supplement were separated by HPLC with UV detection and LC–MS using an analytical column based on silica hydride operating in aqueous normal phase mode. While RP methods were observed to be inadequate for the analysis due to low retention, aqueous normal phase chromatography was able to readily retain and resolve the analytes. After method development on the HPLC–UV system, the conditions were successfully transferred to an LC–MS system for analysis. Based on calibration curve data, estimates of 63.5, 380.3, and 13.1 mg/serving (5.50 g) were obtained for creatine, l ‐arginine, and 1,3‐dimethylamylamine, respectively. Standard addition data results were compared to those of the calibration curve study, and the two values differed by less than 1% in the case of creatine. The conditions are suitable for further development as a reliable means of quantitating the analytes in workout supplement formulations.     

条件风险下的两基金分离定理

鉴于条件风险价值CVaR具有风险度量的合理性以及两基金分离定理对证券投资的重要意义,以CVaR作为风险度量研究两基金分离定理.在组合收益率服从正态分布的假设下,分别就投资组合含有或没有无风险资产的情形提出并证明了两基金分离定理;放开方差-协方差矩阵为非奇异这一通常假设,证明了CVaR风险度量下的两基金分离定理依然成立.     

Bifurcation analysis of a diffusive predator–prey system with a herd behavior and quadratic mortality

In this paper, a diffusive predator–prey system, in which the prey species exhibits herd behavior and the predator species with quadratic mortality, has been studied. The stability of positive constant equilibrium, Hopf bifurcations, and diffusion‐driven Turing instability are investigated under the Neumann boundary condition. The explicit condition for the occurrence of the diffusion‐driven Turing instability is derived, which is determined by the relationship of the diffusion rates of two species. The formulas determining the direction and the stability of Hopf bifurcations depending on the parameters of the system are derived. Finally, numerical simulations are carried out to verify and extend the theoretical results and show the existence of spatially homogeneous periodic solutions and nonconstant steady states. Copyright © 2014 John Wiley & Sons, Ltd.     

Brassinin inhibits proliferation and induces cell cycle arrest and apoptosis in nasopharyngeal cancer C666-1 cells

BackgroundNasopharyngeal cancer is a tumor that occurs in the mucous epithelium of the nasopharynx. Due to its rapid growth and early metastatic nature, the successful treatment of nasopharyngeal cancer is highly challenging.ObjectiveHere, we intended to assess the in vitro anticancer property of brassinin against the nasopharyngeal cancer C666-1 cells.MethodologyThe in vitro free radical scavenging property of the brassinin was assessed by various free radical scavenging activities such as FRAP, DPPH, chemiluminescence (CL), and ORAC assays. The cytotoxic level of the brassinin (1–50 µM) against the nasopharyngeal cancer C666-1 cells and normal Vero cells were assessed by the MTT cytotoxicity assay. The levels of TBARS, GSH, and the SOD activity was assessed using kits. The level of ROS generation, MMP, and apoptosis were investigated by the respective fluorescent staining techniques. The flow cytometry analysis was done to scrutinize the cell cycle arrest. The Bax/Bcl-2 level and caspase activities were examined using respective kits.ResultsThe brassinin treatment effectively scavenged the free radicals, which are assessed by the FRAP, DPPH, chemiluminescence (CL), and ORAC assays. The proliferation of brassinin treated C666-1 cells were decreased remarkably, while the same concentration of brassinin did not disturbed the Vero cell viability. The 30 µM of brassinin effectively increased the ROS production, depleted the MMP, and stimulated the apoptosis in the C666-1 cells. The brassinin increased the TBARS and depleted the GSH and SOD in the C666-1 cells. The flow cytometry analysis revealed that the brassinin administration improved the G0/G1 ratio and decreased the proportion of cells with ‘S’ and ‘G2/M’ phase. The Bax, caspase-3 and ?9 were elevated and Bcl-2 level was decreased in the brassinin administered C666-1 cells.ConclusionOur findings discovered that the brassinin has the capacity to prevent the proliferation and stimulate the apoptotic cell death C666‐1 cells via blocking cell cycle and increasing oxidative stress and apoptotic markers. Hence, it can be a talented therapeutic agent to treat the nasopharyngeal cancer in the future.     

Design,Synthesis and Anticancer Activity of a New Series of N-aryl-N′-[4-(pyridin-2-ylmethoxy)benzyl]urea Derivatives

The development of cancer treatments requires continuous exploration and improvement, in which the discovery of new drugs for the treatment of cancer is still an important pathway. In this study, based on the molecular hybridization strategy, a new structural framework with an N-aryl-N’-arylmethylurea scaffold was designed, and 16 new target compounds were synthesized and evaluated for their antiproliferative activities against four different cancer cell lines A549, MCF7, HCT116, PC3, and human liver normal cell line HL7702. The results have shown seven compounds with 1-methylpiperidin-4-yl groups having excellent activities against all four cancer cell lines, and they exhibited scarcely any activities against HL7702. Among them, compound 9b and 9d showed greatly excellent activity against the four kinds of cells, and the IC₅₀ for MCF7 and PC3 cell lines were even less than 3 μM.     

自支撑硫镍基电极材料制备及其赝电容性能

硫镍基赝电容超级电容器具有较高的比电容和功率密度等优点,是下一代理想的储能装置之一,但其实际应用受到其活性材料的制约,如导电性低和循环性能差等。研究者围绕增强硫镍基赝电容电极材料导电性和提升循环稳定性进行了大量的研究工作。其中,构建自支撑的电极材料被认为是一种降低活性材料和集流体之间界面电阻的有效方法。本文综述了制备自支撑硫镍基赝电容电极的常见方法,并就活性材料的形貌与性能关系进行了总结,主要着眼于集流体改性、离子掺杂、复合材料构建及形貌调控优化等。最后对自支撑硫镍基赝电容电极材料的研究方向进行了展望。     

Beddington-DeAngelis型捕食-食饵动力系统的正平衡点及其稳定性

A class of Beddington-DeAngelis' type predator-prey dynamic system with prey and predator both having linear density restriction is considered. By using the qualitative methods of ODE, the existence and uniqueness of positive equilibrium and its global asymptotic stability are analyzed. The direct criterions for local stability of positive equilibrium and existence of limit cycle are also established when inference parameter of predator is small.     

关于吸收式碳捕集热力学机制的探索

热再生吸收式碳捕集的传统认识难以揭示其热力学机制,一种新的认识是"热-化学能"转换中存在中间能量形式.本文从热力学碳泵概念出发,对吸收式碳捕集理想系统进行了解耦,其可视为"热机-碳泵"的热力学组合,探索了极限效率的表达,并采用第二定律效率作为评价参数对已有中试试验系统进行了性能水平探索.结果表明,理想循环性能系数仅取决...