多扇图的Pebbling数和Graham猜想

图G的pebbling数f(G)是最小的整数n,使得不论n个pebble如何放置在G的顶点上,总可以通过一系列的pebbling移动把1个pebble移到任意一个顶点上,其中一个pebbling移动是从一个顶点处移走两个pebble而把其中的一个移到与其相邻的一个顶点上。Graham猜想对于任意的连通图G和H有f(G×H)f(G)f(H)。多扇图F_n1,n2,…,nm是指阶为n₁+n₂+…+n_m+1的联图P₁∨(P_n1∪P_n2∪…∪P_nm)。本文首先给出了多扇图的pebbling数,然后证明了多扇图F_n1,n2,…,nm具有2-pebbling性质,最后论述了对于一个多扇图和一个具有2-pebbling性质的图的乘积来说,Graham猜想是成立的。作为一个推论,当G和H都是多扇图时,Graham猜想成立。     

圈的中间图pebbling数和Graham猜想

图G的一个pebbling移动是从一个顶点移走2个pebble, 而把其中的1个pebble移到与其相邻的一个顶点上. 图G 的pebbling数f(G)是最小的正整数n, 使得不论n个pebble 如何放置在G的顶点上, 总可以通过一系列的pebbling移动, 把1个pebble移到图G的任意一个顶点上. 图G 的中间图M(G) 就是在G 的每一条边上插入一个新点, 再把G 上相邻边上的新点用一条边连接起来的图. 对于任意两个连通图G和H, Graham猜测f(G\times H)\leq f(G)f(H). 首先研究了圈的中间图的pebbling 数, 然后讨论了一些圈的中间图满足Graham猜想.     

List edge and list total coloring of 1-planar graphs

A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that each 1-planar graph with maximum degree Δ is (Δ+1)-edge-choosable and (Δ+2)- total-choosable if Δ≥16, and is Δ-edge-choosable and (Δ+1)-total-choosable if Δ≥21. The second conclusion confirms the list coloring conjecture for the class of 1-planar graphs with large maximum degree.     

不锈钢/普碳钢爆炸焊接与轧制

以不锈钢/普碳钢为对象,对爆炸焊接+轧制联合技术进行了研究。爆炸焊接参数通过计算和优化设计,准确地预示了不锈钢/普碳钢大型厚板坯的爆炸焊接窗口;复合后的板坯在选定的轧制参数下进行热轧和冷轧;在保证复合质量的条件下,经过轧制可获得力学性能、尺寸精度完全合格的大面积薄复合板。     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

The effect of particle size on the thermal conductivity of alumina nanofluids

We present new data for the thermal conductivity enhancement in seven nanofluids containing 8–282 nm diameter alumina nanoparticles in water or ethylene glycol. Our results show that the thermal conductivity enhancement in these nanofluids decreases as the particle size decreases below about 50 nm. This finding is consistent with a decrease in the thermal conductivity of alumina nanoparticles with decreasing particle size, which can be attributed to phonon scattering at the solid–liquid interface. The limiting value of the enhancement for nanofluids containing large particles is greater than that predicted by the Maxwell equation, but is predicted well by the volume fraction weighted geometric mean of the bulk thermal conductivities of the solid and liquid. This observation was used to develop a simple relationship for the thermal conductivity of alumina nanofluids in both water and ethylene glycol.     

煤经气化制液体燃料及其高温煤气净化研究进展

煤炭是中国最重要的能源.煤炭的有效利用不仅要提高效率,而且要降低污染物和温室气体二氧化碳的排放.相对于传统的煤燃烧利用技术,煤经气化生产各种化学产品被认为是先进的煤洁净利用的重要途径.几乎所有的目前由日趋枯竭的石油资源生产的化学产品,都可经煤气化从合成气转化获得.本文介绍了中国科学院山西煤炭化学研究所近年来在煤经气化制液体燃料及其高温煤气净化方面的研究进展,主要包括煤的灰熔聚流化床气化、高温气体净化、浆态床反应器铁基催化剂费托合成、低碳醇合成以及一步法二甲醚合成等技术.     

The total chromatic number of regular graphs of high degree

The total chromatic number χT (G) of a graph G is the minimum number of colors needed to color the edges and the vertices of G so that incident or adjacent elements have distinct colors. We show that if G is a regular graph and d(G) 32 |V (G)| + 263 , where d(G) denotes the degree of a vertex in G, then χT (G) d(G) + 2.     

Determination of pyrrolizidine alkaloids in comfrey by liquid chromatography-electrospray ionization mass spectrometry

Symphytum officinale L. (comfrey) is a medicinal plant commonly used in decoctions and aliments. Besides therapeutic bioactive compounds present in the herb, it is found to contain hepatotoxic pyrrolizidine alkaloids (PAs), such as lycopsamine and others. In the present study, PAs such as lycopsamine, echimidine and lasiocarpine were determined using electrospray liquid chromatography-mass spectrometry (LC-MS) with the method precision (relative standard deviation, RSD) <10%. Detection of lycopsamine, symviridine and their N-oxides could be confirmed with a newly developed method based on HPLC ion-trap and orbitrap MS with electrospray ionization interface. With LC-MS, quantitative analysis of lycopsamine in the botanical extract was carried out. The effect of extraction solvent was optimized by sonication and methanol: H₂O (50:50) was selected. Then a rapid method based on pressurized hot water extraction (PHWE) was employed for the extraction of lycopsamine from comfrey followed by the comparison with heating under reflux with the RSD ranging from 2.49% to 19.32%. Our results showed a higher extraction efficiency for heating under reflux compared with PHWE. It was proposed that the lower extraction efficiency for PHWE was attributable to dissolved nitrogen from air which caused the reduction in the solubility of lycopsamine in the compressed hot solvent. In this study, quantitative analysis of PAs in comfrey was demonstrated. In addition, it was found that the use of subcritical water for extractions depended on the physical properties of the dissolved solutes and their tendency to degrade under the chosen extraction conditions.