Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas

The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviors. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.     

A note on Hadwiger’s conjecture for W5-free graphs with independence number two

The Hadwiger number of a graph $G$, denoted $h\left(G\right)$, is the largest integer $t$ such that $G$ contains $K_t$ as a minor. A famous conjecture due to Hadwiger in 1943 states that for every graph $G$, $h\left(G\right)\ge \chi \left(G\right)$, where $\chi \left(G\right)$ denotes the chromatic number of $G$. Let $\alpha \left(G\right)$ denote the independence number of $G$. A graph is $H$-free if it does not contain the graph $H$ as an induced subgraph. In 2003, Plummer, Stiebitz and Toft proved that $h\left(G\right)\ge \chi \left(G\right)$ for all $H$-free graphs $G$ with $\alpha \left(G\right)\le 2$, where $H$ is any graph on four vertices with $\alpha \left(H\right)\le 2$, $H=C_5$, or $H$ is a particular graph on seven vertices. In 2010, Kriesell subsequently generalized the statement to include all forbidden subgraphs $H$ on five vertices with $\alpha \left(H\right)\le 2$. In this note, we prove that $h\left(G\right)\ge \chi \left(G\right)$ for all $W_5$-free graphs $G$ with $\alpha \left(G\right)\le 2$, where $W_5$ denotes the wheel on six vertices.     

Unlocking the Drug Potential of the Bryostatin Family: Recent Advances in Product Synthesis and Biomedical Applications

Bryostatins are a class of naturally occurring macrocyclic lactones with a unique fast developing portfolio of clinical applications, including treatment of AIDS, Alzheimer's disease, and cancer. This comprehensive account summarizes the recent progress (2014–present) in the development of bryostatins, including their total synthesis and biomedical applications. An emphasis is placed on the discussion of bryostatin 1 , the most-studied analogue to date. This review highlights the synthetic and biological challenges of bryostatins and provides an outlook on their future development.     

Studies on metabolism of total glucosides of paeony from Paeoniae Radix Alba in rats by UPLC‐Q‐TOF‐MS/MS

Total glucosides of paeony are the active constituents of Paeoniae Radix Alba. In this study, a novel strategy was proposed to find more metabolites and the differences between paeoniflorin, albiflorin and total glucosides of paeony (TGP). This strategy was characterized as follows: firstly, the animals were divided into three groups (paeoniflorin, albiflorin and TGP) to identify the source of TGP metabolites from paeoniflorin or albiflorin; secondly, a generic information‐dependent acquisition scan for the low‐level metabolites was triggered by the multiple mass defect filter and dynamic background subtraction; thirdly, the metabolites were identified with a combination of data‐processing methods including mass defect filtering, neutral loss filtering and product ion filtering; finally, a comparative study was used in the metabolism of paeoniflorin, albiflorin and TGP. Based on the strategy, 18 metabolites of TGP, 10 metabolites of paeoniflorin and 13 metabolites of albiflorin were identified respectively. The results indicated that the hydrolysis, conjugation reaction and oxidization were the major metabolic pathways, and the metabolic sites were the glycosidic linkage, the ester bond and the benzene ring. This study is first to explore the metabolism of TGP, and these findings enhance our understanding of the metabolism and the interactions of paeoniflrin and albiflorin in TGP. Copyright © 2015 John Wiley & Sons, Ltd.     

C^n中子空间之间极端主角的一些应用

本文给出了Ｃ＾ｎ中子空间之间最大和最小主角在矩阵逼近，投影算子的扰动分析，群逆以及Ｏｒａｘｉｎ逆的扰动估计，条件数理论，Ｂｏｔｔ－Ｄｕｆｆｉｎ系统扰动分析中一些应用。     

Total Variation and Multisymplectic Structure for CNLS System

The relation between the total variation of classical field theory and the multisymplectic structure is shown. Then the multisymplectic structure and the corresponding multisymplectic conservation of the coupled nonlinear Schrodinger system are obtained directly from the variational principle.     

Proof of a conjecture on irredundance perfect graphs

Let ir(G) and γ(G) be the irredundance number and the domination number of a graph G, respectively. A graph G is called irredundance perfect if ir(H)=γ(H), for every induced subgraph H of G. In this article we present a result which immediately implies three known conjectures on irredundance perfect graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 292–306, 2002     

猜想M(2k,k+1)=3k-1+[(k-1)/2]的反例

Brualdi与Jung在[1]中研究了一类具有固定线和k的n×n矩阵上的最大跳跃数M(n,k),并提出猜想M(2k, k + 1) = 3k - 1 + [(k-1)/2].本文给出了这一猜想的两个反例．     

若干图类的邻强边染色

研究了若干图类的邻强边染色 .利用在图中添加辅助点和边的方法 ,构造性的证明了对于完全图 Kn和路 Lm 的笛卡尔积图 Kn× Lm,有χ′as(Kn× Lm) =△ (Kn× Lm) +1 ,其中△ (Kn× Lm)和χ′as(Kn× Lm)分别表示图 Kn× Lm的最大度和邻强边色数 .同理验证了 n阶完全图 Kn的广义图 K(n,m)满足邻强边染色猜想 .     

新颖外燃式湿空气燃气轮机循环及性能研究

本文首先提出一种新型的高效燃煤燃气轮机循环一外燃式湿空气透平循环动力系统。由于外燃的特点，作功工质为洁净湿空气，从而可以实现水的回收，是对常规ＨＡＴ循环的突破；另外洁净湿空气排放不受通常烟气露点限制，从而可回收利用湿空气降温时的低温凝结潜热，提高了加湿能力，从而提高系统性能。揭示了新型循环的基本规律；推导出具有湿化特点的约束方程和系统性能简明表达式，指明影响系统性能的关键因素。在透平初温为８５０℃的工况下，系统热效率高达４８．１１％。基于能量品位梯级利用原理和系统集成方法论，通过探索充分而合理利用中低温余热的有效途径，开拓洁净煤燃气轮机总能系统的新方向。