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.     

Algebraic cycles and EPW cubes

Let X be a hyperkähler variety with an anti‐symplectic involution ι. According to Beauville's conjectural “splitting property”, the Chow groups of X should split in a finite number of pieces such that the Chow ring has a bigrading. The Bloch–Beilinson conjectures predict how ι should act on certain of these pieces of the Chow groups. We verify part of this conjecture for a 19‐dimensional family of hyperkähler sixfolds that are “double EPW cubes” (in the sense of Iliev–Kapustka–Kapustka–Ranestad). This has interesting consequences for the Chow ring of the quotient , which is an “EPW cube” (in the sense of Iliev–Kapustka–Kapustka–Ranestad).     

Research on the composition center of a class of rigid differential systems

In this paper, we answer the question: under what conditions a class of rigid differential systems have a composition center. We give the sufficient and necessary conditions for these systems to have a center at origin point. At the same time, we give the formula of focal values and the highest order of fine focus.     

Yau's uniformization conjecture for manifolds with non-maximal volume growth

The well-known Yau's uniformization conjecture states that any complete noncompact K¨ahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal volume growth has been recently confirmed by G. Liu in [23]. In the first part, we will give a survey on the progress.In the second part, we will consider Yau's conjecture for manifolds with non-maximal volume growth. We will show that the finiteness of the first Chern number C_1~n is an essential condition to solve Yau's conjecture by using algebraic embedding method. Moreover, we prove that,under bounded curvature conditions, C_1~n is automatically finite provided that there exists a positive line bundle with finite Chern number. In particular, we obtain a partial answer to Yau's uniformization conjecture on K¨ahler manifolds with minimal volume growth.     

多复变数一类α次星形映射齐次展开式各项的精细估计

本文首先给出复Banach空间单位球上一类α次星形映射齐次展开式各项的精细估计,特别当这些映射又是k折对称映射时,估计还是精确的.其次建立C~n中单位多圆柱上上述推广映射齐次展开式各项的精细估计,同样当这些映射又是k折对称映射时,估计仍是精确的.由此证明了多复变数中关于α次星形映射的弱Bieberbach猜想,且所得到的估计都能回到单复变数的情形.     

Persistence Approximation Property for Maximal Roe Algebras

Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coarse embedding into Hilbert space and X is coarsely uniformly contractible, then C_(max)~*(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.     

The Bateman–Horn conjecture: Heuristic,history, and applications

The Bateman–Horn conjecture is a far-reaching statement about the distribution of the prime numbers. It implies many known results, such as the prime number theorem and the Green–Tao theorem, along with many famous conjectures, such the twin prime conjecture and Landau’s conjecture. We discuss the Bateman–Horn conjecture, its applications, and its origins.     

Almost sure convergence of the multiple ergodic average for certain weakly mixing systems

The family of pairwise independently determined(PID) systems, i.e., those for which the independent joining is the only self joining with independent 2-marginals, is a class of systems for which the long standing open question by Rokhlin, of whether mixing implies mixing of all orders, has a positive answer. We show that in the class of weakly mixing PID one finds a positive answer for another long-standing open problem, whether the multiple ergodic averages 1/N N-1∑n=0 f_1(T~nx)···f_d(T~(dnx)),N→∞,almost surely converge.