Partitioning series-parallel multigraphs into ν *-excluding edge covers

We prove that, for any given vertex ν* in a series-parallel graph G, its edge set can be partitioned into κ = min{κ′(G) + 1, δ(G)} subsets such that each subset covers all the vertices of G possibly except for ν*, where δ(G) is the minimum degree of G and κ′(G) is the edge-connectivity of G. In addition, we show that the results in this paper are best possible and a polynomial time algorithm can be obtained for actually finding such a partition by our proof.     

硼砂与氯化铵合成hBN反应机理的研究

 研究了以硼砂、氯化铵为原料在氨气气氛下合成hBN 的反应机理。指出氯化铵在反应中的主要作用是与硼砂反应形成可阻止硼砂颗粒团聚的高熔点膜层；而氨气的主要作用就是提供大量参与反应的NH₃分子，增加了反应几率；新生成的hBN则进一步隔离高度熔融的硼砂团粒，防止玻璃相的生成。     

Sizes of Critical Graphs with Small Maximum Degrees

In this paper, we give new lower bounds for the size of Δ-critical graphs with Δ=8,9 which improve the partial results of Luo [6] and Y. Zhao [12].     

Investigation of chemical decomposition of CCl4 on TiO2 near room temperature

Dissociative adsorption of CCl₄ on TiO₂ at 35 °C has been studied by Fourier-transform infrared spectroscopy, X-ray photoelectron spectroscopy, and electron spin resonance. CCl₄ decompose to form CO, CO₂, and CO₃ on the surface, at such a low temperature, in which CO₂ formation is not from CO oxidation on TiO₂, but CO₃ can be produced by CO and CO₂ adsorption. The Cl generated from CCl₄ decomposition is left on the surface and bonded to titanium ions. Mineralization of CCl₄ on TiO₂ involves the lattice oxygens. Thermodynamical driving force and possible reaction routes for CO and CO₂ formation in the CCl₄ decomposition on TiO₂ are discussed.     

Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².     

Necessary conditions for multistationarity in discrete dynamical systems

R. Thomas conjectured, 20 years ago, that the presence of a positive circuit in the interaction graph of a dynamical system is a necessary condition for the presence of several stable states. Recently, E. Remy et al. stated and proved the conjecture for Boolean dynamical systems. Using a similar approach, we generalize the result to discrete dynamical systems, and by focusing on the asynchronous dynamics that R. Thomas used in the course of his analysis of genetic networks, we obtain a more general variant of R. Thomas’ conjecture. In this way, we get a necessary condition for genetic networks to lead to differentiation.     

Dielectric and conduction mechanism studies of PVA-orthophosphoric acid polymer electrolyte

Polyvinyl alcohol (PVA)-based proton conducting polymer electrolytes have been prepared by the solution cast technique. The conductivity is observed to increase from 10⁻⁹ to 10⁻⁴ S cm⁻¹ as a result of orthophosphoric acid (H₃PO₄) addition. The plot of conductivity vs temperature shows that a phase transition occurred at 343 K in the sample PVA-33 wt% H₃PO₄. The β-relaxation peak is observed at 313 K. The glass transition temperature of PVA-33 wt% H₃PO₄ is 343 K. Orthophosphoric acid seems to play a dual role, i.e., as a proton source and as a plasticizer. The ac conductivity σ _ac = Aω ^s was also calculated in the temperature range from 303 to 353 K. The conduction mechanism was inferred by plotting the graph of s vs T from which the conduction mechanism for sample PVA-17 wt% H₃PO₄ was inferred to occur by way of the overlapping large polaron tunneling (OLPT) model and the conduction mechanism for the sample PVA-33 wt% H₃PO₄ by way of the correlated barrier height (CBH) model.