Graphs are (1,Δ+1)-choosable

A graph $G$ is $(k,k^{\prime })$-choosable if the following holds: For any list assignment $L$ which assigns to each vertex $v$ a set $L\left(v\right)$ of $k$ real numbers, and assigns to each edge $e$ a set $L\left(e\right)$ of $k^{\prime }$ real numbers, there is a total weighting $?:V\left(G\right)\cup E\left(G\right)\to R$ such that $?\left(z\right)\in L\left(z\right)$ for $z\in V\cup E$, and ${\sum }_{e\in E\left(u\right)}?\left(e\right)+?\left(u\right)\ne {\sum }_{e\in E\left(v\right)}?\left(e\right)+?\left(v\right)$ for every edge $uv$. This paper proves that if $G$ is a connected graph of maximum degree $\Delta \ge 2$, then $G$ is $(1,\Delta +1)$-choosable.     

ChemInform Abstract: Explaining Stability of Transition Metal Carbides — and Why TcC Does Not Exist.

The formation of transition metal (M) carbides M_xC_y and trends of their stability are systematically investigated using the USPEX code within the DFT.     

Preparation of ZSM‐5 Coated on Monolithic Interconnected Macroporous Al2O3 Using Cheap n‐Butylamine as Template

Using cheap n‐butylamine as template, ZSM‐5 zeolites have been successfully synthesized and coated on monolithic interconnected macroporous Al₂O₃ by the secondary growth method. The use of cheap n‐butylamine could significantly reduce the synthesis cost. Hierarchical monolithic ZSM‐5 zeolites were prepared from synthetic mixtures with different H₂O/Na₂O or SiO₂/Al₂O₃ ratio. The synthesized samples were characterized by scanning electron microscopy (SEM), X‐ray diffraction (XRD), Fourier transform infrared spectroscopy (FT‐IR) and N₂ adsorption‐desorption. The results show that the hierarchical monolithic zeolites were obtained with cheap n‐butylamine template as template. During the hydrothermal reaction process, the morphology of the micrometer‐sized support was well maintained. The irregular crystals were formed in a wide range of the H₂O/Na₂O or SiO₂/Al₂O₃ ratio of synthetic mixtures and coated on monolithic Al₂O₃. The relative crystallinity of the zeolites was highest at H₂O/Na₂O=250 or SiO₂/Al₂O₃=160. This type of composites exhibited hierarchical porous structures and relatively high specific surface areas.     

Deoxygenation of methyl laurate to hydrocarbons on silica-supported Ni-Mo phosphides: Effect of calcination temperatures of precursor

SiO2-supported Ni-Mo bimetallic phosphides were prepared by temperature-programmed reduction(TPR) method from the phosphate precursors calcined at different temperatures. Their properties were characterized by means of ultraviolet-visible diffuse reflectance spectroscopy(UV-Vis DRS), H2temperature-programmed reduction(H2-TPR), X-ray diffraction(XRD), transmission electron microscopy(TEM), CO chemisorption, H2 and NH3temperature-programmed desorptions(H2-TPD and NH3-TPD). Their catalytic performances for the deoxygenation of methyl laurate were tested in a fixed-bed reactor. When the precursors were calcined at 400 and 500?C, respectively, Ni Mo P2 phase could be formed apart from Ni2 P and Mo P phases in the prepared C400 and C500 catalysts. However, when the precursors were calcined at600, 700 and 800°C, respectively, only Ni2 P and Mo P phases could be detected in the prepared C600, C700 and C800 catalysts. Also, in C400, C500 and C600 catalysts, Mo atoms were found to be entered in the lattice of Ni2 P phase, but the entering extent became less with the increase of calcination temperature. As the calcination temperature of the precursor increased, the interaction between Ni and Mo in the prepared catalysts decreased, and the phosphide crystallite size tended to increase, subsequently leading to the decrease in the surface metal site density and the acid amount. C600 catalyst showed the highest activity among the tested ones for the deoxygenation of methyl laurate. As the calcination temperature of the precursor increased, the selectivity to C12 hydrocarbons decreased while the selectivity to C11 hydrocarbons tended to increase. This can be mainly attributed to the decreased Ni-Mo interaction and the increased phosphide particle size. In sum, the structure and performance of Ni-Mo bimetallic phosphide catalyst can be tuned by the calcination temperature of precursor.