2×n格子图的弱罗马控制数

图G弱罗马控制数是图G的所有弱罗马控制数(WRDF)的最小权.本文运用指标函数法和比较函数法确定了2×n 格子图的弱罗马控制数.

Abstract：

The weak Roman domination number of G is the minimum weight of a weak Roman dominating function (WRDF) in G. In this paper, we determine the weak Roman domination number of 2 × n grid graphs.     

Thermoelectric properties of p-type (Bi0.15Sb0.85)2Te3-PbTe graded thermoelectric materials with different barriers

The p-type (Bi_0.15Sb_0.85)₂Te₃ and PbTe are typical thermoelectric materials used for low and middle temperature range and functional graded materials (FGM) is an inevitable way to widen the working temperature range. Here two segments graded thermoelectric materials (GTM) consisting of (Bi_0.15Sb_0.85)₂Te₃, PbTe and different barriers were fabricated by the common hot pressure method. Metals Fe, Mg and Ni were used as barriers between the two segments. The diffusion of different barriers between the barriers and bases were analyzed by electron microprobe analysis (EMA). The phase and crystal structures were determined by X-ray diffraction analysis (XRD). The thermoelectric properties were measured at 303 K along the direction parallel to the pressing direction. The results show that the compositional diffusion occurs when there is no barrier at the interface of the two segments, and the diffusion of Pb is most obvious; as the barrier material, the diffusion of metals Fe, Mg and Ni between different bases is not very obvious, and the thermoelectric properties of GTM is much better than that of the original segment.     

Average widths and optimal recovery of multivariate Besov classes inL p (Rd)

Some weak asymptotic results for average σ-K width and average σ_L width of the isotropic Besov classes S r pθB(R d), S r pθb(R d) and the anisotropic Besov classes S r pθB(R d), S r pθb(R d) in L p(R d) (1≤p<∞) are obtained, and the corresponding weak asymptotic optimal subspaces are identified. Furthermore, the weak asymptotic behavior of optimal recovery is established for the isotropic Besov classes S r pθB(R d) in L p(R d) (1≤p≤∞).     

Large-scale synthesis of nickel sulfide micro/nanorods via a hydrothermal process

Rhombohedral-phase NiS micro/nanorods were synthesized on a large scale through a hydrothermal method using NiCl₂·6H₂O and thiourea crystals as starting precursors. Recrystallized thiourea was observed to play an important role in the formation of micro/nanosized rods and flower-like structures. The molar ratio and reaction temperature of the precursors influenced the morphology and phase of NiS products. Pure rhombohedral NiS micro/nanorods were obtained on a large scale when the molar ratio between NiCl₂·6H₂O and thiourea crystals was fixed at 2:1, and the mixture was heated at 250℃ for 5 h. Flower-like NiS nanostructures were formed when the molar ratio between NiCl₂·6H₂O and thiourea crystals was maintained at 1:1. The Raman and Fourier-transform infrared (FTIR) spectra of the as-prepared rhombohedral NiS micro/nanorods were collected, and their magnetic properties were investigated. The results showed that the FTIR absorption peaks of the as-prepared product are located at 634 cm-1 and their Raman peaks are located at 216 and 289 cm-1; the as-prepared NiS micro/nanorods exhibited weak ferromagnetic behavior due to the size effect.     

Photoactive Naphthalene Diimide Functionalized Titanium-Oxo Clusters with High Photoelectrochemical Responses

Photoactive functionalized titanium-oxo clusters(TOCs) are regarded as an important model compound for dye-sensitized titanium dioxide solar cells. However, the dyes used for sensitizing TOCs are still limited. Herein, two cyclic TOCs are reported, namely, [Ti₆(μ₃-O)₂(Oi-Pr)₈)(L_A)₂]·i-PrOH(S1) and [Ti₆(μ₃-O)₂(Oi-Pr)₈)(L_V)₂]·i-PrOH(S2), which are functionalized by ph...     

Impact analysis and control of weak intercalation on fly rock

The cause and mechanism of fly rock in geological condition of weak intercalation are analyzed. Ac- cording to the features of fly rock caused by weak intercalation, the differences of fly rock caused in weak inter- calation and general condition are distinguished. Specific to complicated circumstance of weak intercalation and town, the control measures of fly rock are given. With project examples, the control measures are scientific and rational, and have important project value.     

Inclusion variations and calcium treatment optimization in pipeline steel production

SiCa line and SiCaBaFe alloy were injected into liquid pipeline steel at the end of LF refining as calcium treatment, and samples were taken from the ladles, mould, and slabs. Analysis of Ca content and inclusions shows that Ca content in steel decreases obviously in the following process after calcium treatment; the compositions, morphology, and sizes of inclusions also vary much in the production; primary inclusions in the ladles prior to calcium treatment are mainly Al₂O₃ inclusions, but they turn to fine irregular CaS-CaO-Al₂O₃ compound inclusions after the treatment, then become fine globular CaO-Al₂O₃ inclusions in the mould, and finally change to a few larger irregular CaS-CaO-Al₂O₃ complex inclusions in the slabs. Thermodynamic study reveals that inclusion variations are related with the preferential reactions among Ca, Al₂O₃, and S and the precipitation of S in CaO-Al₂O₃ inclusions with high sulfur capacity. New evaluation standards for calcium treatment in high-grade pipeline steel were put forward according to the inclusion variations and requirements of pipeline steel on inclusion controlling, and the calcium process was studied and optimized.     

Structural diversity and reactivity of d^10 metal- （4-pyridylthio）acetate system

The hydrothermal synthesis and crystal structures of four coordination polymers, namely, 2D [Zn（μ3-ta）（pytaH）]n （1）, 2D [Zn（μ3-pyta）Cl]n （2）, 1D [Cd（μ-pyta）2（H2O）]n （3）, and 3D [Cd（μ3-pyta）（μ-Cl）]n （4） （pyta = （4-pyridylthio）acetate, ta = thioglycolate）, are reported. They are based on （4-pyridylthio）acetate and its derived ligand. The ta^2- ligand present in 1 was generated from an in situ C（sp^2）-S bond cleavage of the pyta ligand. In these compounds, versatile intermolecular interactions, such as close S…S interactions and strong （O-H…O/N/S） or weak （C-H…O/S, C-H…Cl） hydrogen bonding interactions, play an important role in the formation of three-dimensional supramolecular networks in the solid state.     

Atomic Decompositions of Weak Hardy Spaces of B-Valued Martingales

The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.     

Reinforcing effect of graphene on the mechanical properties of Al<Subscript>2</Subscript>O<Subscript>3</Subscript>/TiC ceramics

Multilayer graphene (MLG)-reinforced Al₂O₃/TiC ceramics were fabricated through hot pressing sintering, and the reinforcing effect of MLG on the microstructure and mechanical properties of the composites was investigated by experiment and simulation. The simulation of dynamic crack initiation and propagation was investigated based on the cohesive zone method. The results show that the composite added with 0.2wt% MLG has excellent flexural strength and high fracture toughness. The major reinforcing mechanisms are the synergistic effect by strong and weak bonding interfaces, MLG pull-out, and grain refinement resulting from the addition of MLG. In addition, the aggravating of crack deflection, branching, blunting, and bridging have indispensable contribution to the improvement of the as-designed materials.