2-Resonant fullerenes

A fullerene graph $F$ is a planar cubic graph with exactly 12 pentagonal faces and other hexagonal faces. A set $\mathcal{H}$ of disjoint hexagons of $F$ is called a resonant pattern (or sextet pattern) if $F$ has a perfect matching $M$ such that every hexagon in $\mathcal{H}$ is $M$-alternating. $F$ is said to be $k$-resonant if any $i$ ($0\leq i\leq k$) disjoint hexagons of $F$ form a resonant pattern. It was known that each fullerene graph is 1-resonant and all 3-resonant fullerenes are only the nine graphs. In this paper, we show that the fullerene graphs which do not contain the subgraph $L$ or $R$ as illustrated in Fig. 1 are 2-resonant except for the specific eleven graphs. This result implies that each IPR fullerene is 2-resonant.Comment: 34 pages, 25 figure

Fullerenes with the maximum Clar number

The Clar number of a fullerene is the maximum number of independent resonant hexagons in the fullerene. It is known that the Clar number of a fullerene with n vertices is bounded above by [n/6]-2. We find that there are no fullerenes whose order n is congruent to 2 modulo 6 attaining this bound. In other words, the Clar number for a fullerene whose order n is congruent to 2 modulo 6 is bounded above by [n/6]-3. Moreover, we show that two experimentally produced fullerenes C80:1 (D5d) and C80:2 (D2) attain this bound. Finally, we present a graph-theoretical characterization for fullerenes, whose order n is congruent to 2 (respectively, 4) modulo 6, achieving the maximum Clar number [n/6]-3 (respectively, [n/6]-2)

Fractal model and Lattice Boltzmann Method for Characterization of Non-Darcy Flow in Rough Fractures.

The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass-Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures

The Management of Current Traffic Congestion Status During the Urbanization Development in Guiyang

With the development of urbanization and motorization, the imbalanced contradiction of urban traffic between supply and demand becomes increasingly sharp. Traffic congestion has become a serious “urban illness” in China, and it results in problems such as travel time delay, increase of traffic accidents, rise of fuel depletion, survival environmental degradation and so on. It severely affects the city’s normal function and its sustainable development. This paper first leads to important impact of traffic on urbanization development from the concept of urbanization, it then states the current traffic congestion status in the process of urbanization in Guiyang after introducing the research of domestic and overseas traffic status, finally, it puts forward some suggestions of countermeasures of traffic management in Guiyang. These aim to improve the traffic congestion problem in the city, and make Guiyang’s urbanization development to be more perfect.Key words: Urbanization; Traffic congestion; Sustainable development; Traffic managemen

Tetra­ethyl­ammonium bicarbonate trihydrate

In the title compound, C8H20N+·CHO3 −·3H2O, the bicarbon­ate anion, which has a small mean deviation from the plane of 0.0014 Å, fully utilises its three O and one H atom to form various O—H⋯O hydrogen bonds with the three water mol­ecules in the asymmetric unit, generating a hydrogen-bonded layer, which extends along (10). The tetra­ethyl­ammonium cations, as the guest species, are accommodated between every two neighboring layers, constructing a sandwich-like structure with an inter­layer distance of 7.28 Å

Kirchhoff index of composite graphs

AbstractLet G1+G2, G1∘G2 and G1{G2} be the join, corona and cluster of graphs G1 and G2, respectively. In this paper, Kirchhoff index formulae of these composite graphs are given

Tetra­ethyl­ammonium 4-hy­droxy­benzoate monohydrate

In the title compound, C8H20N+·C7H5O3 −·H2O, the carboxyl­ate group is slightly out of the plane of the parent benzene ring, the C—C—C—O torsion angles being 2.3 (2) and 2.0 (2)°. The carboxyl­ate group and the hy­droxy group form O—H⋯O hydrogen bonds, generating a head-to-tail chain along the b axis. Neighbouring hydrogen-bonded chains are linked by the water mol­ecule, generating two independent O—H⋯O donor hydrogen bonds. The carboxyl­ate group thus constructs a hydrogen-bonded host layer parallel to (10). The tetra­ethyl­ammonium cation is contained between these layers, forming a sandwich-like structure with an approximate inter­layer distance of 10.03 Å