Perfect matchings extend to two or more hamiltonian cycles in hypercubes

Kreweras conjectured that every perfect matching of a hypercube $Q_n$ for $n\ge 2$ can be extended to a hamiltonian cycle of $Q_n$. Fink confirmed the conjecture to be true. It is more general to ask whether every perfect matching of $Q_n$ for $n\ge 2$ can be extended to two or more hamiltonian cycles of $Q_n$. In this paper, we prove that every perfect matching of $Q_n$ for $n\ge 4$ can be extended to at least $2^{2^{n?4}}$ different hamiltonian cycles of $Q_n$.     

Characterization of the Insoluble Sludge from the Dissolution of Irradiated Fast Breeder Reactor Fuel

Insoluble sludge is generated in the reprocessing of spent fuel. The sludge obtained from the dissolution of irradiated fuel from the “Joyo” experimental fast reactor was analyzed to evaluate its chemical form. The sludge was collected by the filtration of the dissolved fuel solution, and then washed in nitric acid. The yields of the sludge weight were less than 1% of the total fuel weight. The chemical composition of the sludge was analyzed after decomposition by alkaline fusion. Molybdenum, technetium, ruthenium, rhodium, and palladium were found to be the main constituent elements of the sludge. X-ray diffraction patterns of the sludge were attributable to Mo₄Ru₄RhPd, regardless of the experimental conditions. The concentrations of molybdenum and zirconium in the dissolved fast reactor fuel solutions were low, indicating that zirconium molybdate hydrate is produced in negligible amounts in the process.     

On tight 6-cycle decompositions of complete 3-uniform hypergraphs

The complete 3-uniform hypergraph of order v has a vertex set V of size v and the set of all 3-element subsets of V as its edge set. A tight 6-cycle is a hypergraph with vertex set $\{a,b,c,d,e,f\}$ and edge set $\{\{a,b,c\},\{b,c,d\},\{c,d,e\},\{d,e,f\},\{e,f,a\},\{f,a,b\}\}$. We show that there exists a decomposition of the complete 3-uniform hypergraph of order v into isomorphic copies of a tight 6-cycle if and only if $v\equiv 1$, 2, 10, 20, 28, or $29(\mathrm{mod}36)$.     

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 .     

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).     

Phase Systems and Post-Column Dithizone Reaction Detection for the Analysis of Organo-Mercurials by HPLC

Abstract

The suitability of HPLC (normal and reversed phase adsorption) with UV or post-column reaction detection for the analysis of organomercurials was investigated systematically. The separation of organomercurials is best carried out on a reversed phase system with a C-8 bonded phase material as the stationary phase and acetonitrile-aqueous sodium bromide mixtures as the mobile phase.

The precision and detection limit of the method and the efficiency of the extraction procedure were established. For the alkylmercury compounds the lowest limit of detection (80ppb) was obtained with the dithizone reaction detection and for the phenylmercury compounds with UV detection (60ppb). A chromatogram of a spiked fish (2ppmHg) and a river water sample (50ppbHg) is shown.     

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.