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.     

K-theory for the maximal Roe algebra of certain expanders

We study in this paper the maximal version of the coarse Baum-Connes assembly map for families of expanding graphs arising from residually finite groups. Unlike for the usual Roe algebra, we show that this assembly map is closely related to the (maximal) Baum-Connes assembly map for the group and is an isomorphism for a class of expanders. We also introduce a quantitative Baum-Connes assembly map and discuss its connections to K-theory of (maximal) Roe algebras.     

On the energy of inviscid singular flows

It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space . When the singular set of the solution is (or belongs to) a smooth manifold, we derive various Lp-space regularity criteria dimensionally equivalent to the critical one. In particular, if the singular set is a hypersurface the energy of u is conserved provided the one-sided non-tangential limits to the surface exist and the non-tangential maximal function is L³ integrable, while the maximal function of the pressure is L3/2 integrable. The results directly apply to prove energy conservation of the classical vortex sheets in both 2D and 3D at least in those cases where the energy is finite.     

Ring semigroups whose subsemigroups form a chain

A multiplicative semigroup S is called a ring semigroup if an addition may be defined on S so that (S,+,⋅) is a ring. Such semigroups have been well-studied in the literature (see Bell in Words, Languages and Combinatorics, pp. 24–31, World Scientific, Singapore, 1994; Jones in Semigroup Forum 47(1):1–6, 1993; Jones and Ligh in Semigroup Forum 17(2):163–173, 1979). In this note, we use Mihăilescu’s Theorem (formerly Catalan’s Conjecture) to characterize the ring semigroups whose subsemigroups containing 0 form a chain with respect to set inclusion.     

ZrB2粒径对Si3N4-ZrB2陶瓷相组成、显微结构及电阻率的影响

以20vol; ZrB2粗粉和细粉为导电相,以3vol; MgO-2vol; YB2O3烧结助剂,通过热压烧结在1500℃制备了Si13N4-ZrB2复相陶瓷,研究了ZrB2粒径对致密度、相组成、显微结构以及电阻率的影响.结果表明,不依赖于Zrl2粒径,通过引入MgO-YB2O3烧结助剂,均可以获得高致密Si3N4-ZrB2陶瓷.以Zrl2粗粉为原料时,Si3N4-ZrB2陶瓷包含主要的αt-Si3N4 、β-Si3N4和ZrB2相以及微弱的Yb4 Si2N2O7相,由于ZrB2晶粒保持孤立状态,样品电阻率较高,为9.5×103 Ω·m;而以ZrB2细粉为原料时,其与Si3N4发生轻微的高温反应,除了包含主要的d-Si3N4、β-Si3N4和ZrB2相及微弱的Yb4Si2N2O7相之外,Si3 N4-ZrB2陶瓷还含有新生成的微弱ZrSi2和ZrN导电相,由于ZrB2晶粒保持连通状态,样品电阻率显著降低,仅有6.8 Ω·m.     

ZrO2对热压AlN陶瓷的显微结构与力学性能的影响

通过添加纳米ZrO2粉体,并结合Y2O3烧结助剂,采用热压烧结制备了AlN陶瓷.结果表明,加入ZrO2后,热压AlN陶瓷的物相包含AlN主相、Al5Y3O12晶界相以及ZrN新相.随着ZrO2的加入,热压AlN陶瓷的维氏硬度基本没有变化,然而其断裂韧性逐渐提高.这主要是由于添加的ZrO2与AlN发生高温反应生成了ZrN,导致AlN陶瓷从单一的沿晶断裂模式转变为包含沿晶和穿晶的混合断裂模式,强化了晶界,进而改善了断裂韧性.     

干旱区区域土壤盐渍化监测研究进展及其未来热点

土壤盐渍化是干旱区农业生产的重要障碍,威胁着绿洲生态环境的稳定。监测土壤盐渍化动态,掌握盐渍化土壤的分布规律,探索盐渍化的发生发展机理,总结土壤盐渍化的研究方法,对干旱区农业生产活动和生态安全稳定具有重要意义。盐渍化的发展变化不仅受到自然环境的强烈作用,同时也受到人类活动的深刻影响。随着人类活动的加剧,盐渍化问题日益突出,因此本文在中外关于土壤盐渍化研究的基础上,系统总结了我国干旱区区域土壤盐渍化监测的主要方法,为土壤盐渍化监测、预报和调控的方法与理论提供了补充,同时也提出了当前干旱区区域土壤盐渍化监测研究存在的问题,以及强调了今后面向区域农业生产迫切需要开展的四个领域的研究,为确保土地利用的可持续性,构建和谐的人地关系提供了决策参考。     

Vertex disjoint 4-cycles in bipartite tournaments

Let $k\ge 2$ be an integer. Bermond and Thomassen conjectured that every digraph with minimum out-degree at least $2k?1$ contains $k$ vertex-disjoint cycles. Recently Bai, Li and Li proved this conjecture for bipartite digraphs. In this paper we prove that every bipartite tournament with minimum out-degree at least $2k?2$, minimum in-degree at least $1$ and partite sets of cardinality at least $2k$ contains $k$ vertex-disjoint 4-cycles whenever $k\ge 3$. Finally, we show that every bipartite tournament with minimum degree $\delta =min\{{\delta }^{+},{\delta }^{?}\}$ at least $1.5k?1$ contains at least $k$ vertex-disjoint 4-cycles.