环状硅酸盐图的友好指数集

Let G be a graph with vertex set V(G) and edge set E(G). A labeling f : V(G) →Z2 induces an edge labeling f*: E(G) → Z2 defined by f*(xy) = f(x) + f(y), for each edge xy ∈ E(G). For i ∈ Z2, let vf(i) = |{v ∈ V(G) : f(v) = i}| and ef(i) = |{e ∈ E(G) : f*(e) =i}|. A labeling f of a graph G is said to be friendly if |vf(0)- vf(1)| ≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as {|ef(0)- ef(1)|: the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS(n, m).     

具有固定时滞的经济周期模型的动态分析

在经济活动中,投资行为和资本存量存在一定的时滞效应,这会影响经济周期模型的动态行为,进而使得投资政策对经济的稳定调整复杂化.考虑到资本存量的预期时间以及投资时滞对经济活动的影响,采用Hopf分岔理论,研究具有固定时滞的经济周期模型的均衡点的稳定性以及形成经济周期的条件.研究发现,投资过程中的投资时滞,以及投资决策中对于资本存量的预测时间构成经济周期产生的诱因;同时可通过政府投资政策调整达到预期均衡目标,这对保持经济周期稳定及经济政策制定有一定的指导作用.     

关于具有二次相关性收获率的捕食与被捕食系统极限环的存在性分析

讨论了一类两种群具有二次相关性收获率的捕食与被捕食系统,利用常微分定性方法和分支理论,得到了系统平衡点处的性态和极限环的存在性条件,并用Matlab软件对其进行数值模拟,推广了相关文献中两种群捕食模型定性分析的相应结论.     

Consequences of weak Allee effect on prey in the May–Holling–Tanner predator–prey model

In this work, a modified Holling–Tanner predator–prey model is analyzed, considering important aspects describing the interaction such as the predator growth function is of a logistic type; a weak Allee effect acting in the prey growth function, and the functional response is of hyperbolic type. Making a change of variables and time rescaling, we obtain a polynomial differential equations system topologically equivalent to the original one in which the non‐hyperbolic equilibrium point (0,0) is an attractor for all parameter values. An important consequence of this property is the existence of a separatrix curve dividing the behavior of trajectories in the phase plane, and the system exhibits the bistability phenomenon, because the trajectories can have different ω ? limit sets; as example, the origin (0,0) or a stable limit cycle surrounding an unstable positive equilibrium point. We show that, under certain parameter conditions, a positive equilibrium may undergo saddle‐node, Hopf, and Bogdanov–Takens bifurcations; the existence of a homoclinic curve on the phase plane is also proved, which breaks in an unstable limit cycle. Some simulations to reinforce our results are also shown. Copyright © 2015 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.     

Limit Cycles Bifurcating from a k-dimensional Isochronous Center Contained in ?n with k ? n

The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum periodic orbits of a k-dimensional isochronous center contained in ℝ ⁿ with n ⩾ k, when we perturb it in a class of differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree. As far as we know this is one of the first examples that this study can be made for a polynomial differential system having a center and a non-rational first integral. The first and third authors are partially supported by a MCYT/FEDER grant MTM2005-06098-C01, and by a CIRIT grant number 2005SGR-00550. The second author is partially supported by a FAPESP–BRAZIL grant 10246-2. The first two authors are also supported by the joint project CAPES–MECD grant HBP2003-0017.     

1‐Factor and Cycle Covers of Cubic Graphs

Let G be a bridgeless cubic graph. Consider a list of k 1‐factors of G. Let be the set of edges contained in precisely i members of the k 1‐factors. Let be the smallest over all lists of k 1‐factors of G. Any list of three 1‐factors induces a core of a cubic graph. We use results on the structure of cores to prove sufficient conditions for Berge‐covers and for the existence of three 1‐factors with empty intersection. Furthermore, if , then is an upper bound for the girth of G. We also prove some new upper bounds for the length of shortest cycle covers of bridgeless cubic graphs. Cubic graphs with have a 4‐cycle cover of length and a 5‐cycle double cover. These graphs also satisfy two conjectures of Zhang 18 . We also give a negative answer to a problem stated in 18 .     

Tailoring 3,3′‐Dihydroxyisorenieratene to Hydroxystilbene: Finding a Resveratrol Analogue with Increased Antiproliferation Activity and Cell Selectivity

Four novel compounds were designed by “tailoring” 3,3′‐dihydroxyisorenieratene (a natural carotenoid) based on an isoprene unit retention truncation strategy. Among them, the smallest molecule 1 (2,3,6,2′,3′,6′‐hexamethyl‐4,4′‐dihydroxy‐trans‐stilbene) was concisely synthesized in a one‐pot Stille–Heck tandem sequence, and surfaced as a promising lead molecule in terms of its selective antiproliferative activity mediated by blocking the NCI‐H460 cell cycle in G1 phase. Additionally, theoretical calculations and cell uptake experiments indicate that the unique polymethylation pattern of compound 1 significantly induces a conformational change shift out of planarity and increases its cell uptake and metabolic stability. The observation should be helpful to rationally design resveratrol‐inspired antiproliferative agents.     

涂碳铝箔对磷酸铁锂电池性能影响研究

本文研究了使用涂碳铝箔作为正极集流体磷酸铁锂电池的性能。研究对比了使用普通铝箔和涂层铝箔的10 Ah软包磷酸铁锂电池的主要性能。研究表明:使用涂层铝箔不但可以提高磷酸铁锂材料的粘结性,而且使用导电涂层可以有效降低正极材料和集流体的接触内阻,从而减小电池内阻,提高电池倍率性能。与使用普通铝箔作为集流体相比,通过使用涂碳铝箔可以使得电池的内阻降低65%左右,但是,磷酸铁锂正极材料的克容量却偏低约5~10 mAh·g-1,首次效率也偏低4%左右;在快速放电15C倍率下,使用涂碳铝箔的电芯比使用普通铝箔容量提高约15%左右,10C放电倍率下,平台增加0.3~0.4 V;使用涂碳铝箔电芯的常温自放电率较高,但容量恢复率也较高;550周循环下,使用涂碳铝箔可以使得电池的循环性能提高约1%。而在电池低温性能方面,使用涂碳铝箔对低温性能并无改善。