一类函数空间的刻画

在Ｏｒｌｉｃｚ空间Ｌ_p（Ｒ^ｎ）中给出一类于空间Ｃ_p^a（Ｒ^ｎ）,利用一标准算子序列的逼近,得到 其等价刻画．     

四个对激波与涡旋有高分辨率的计算格式的比较*

近十年来,计算非定常无粘可压气体力学Euler方程组的高分辨率差分格式有显着进展.本文选择四个近年受到重视的格式,用一较复杂的二维不定常问题作进一步的考验.所选算例为平面激波遇矩形障碍物初始阶段的绕射与反射.在挡板头部有两个尖角点,角点附近流场参量变化剧烈,会有中心稀疏波和集中涡的出现,要模拟好它们,就要求格式有较好的适应性.本文选择特殊的激波马赫数M_s=2.068,使静止坐标系下激波后流速恰为声速,并沿中心稀疏波区从角点发出的一条曲线也有这一现象,以考察各格式在方程组某一特征值恰为零时的计算特点,因零特征值可以使某些格式局部受损.计算结果的图形显示可表明四个格式在激波分辨率,格式粘性、膨胀波的计算、模拟非定常集中涡产生过程的能力等方面的性质.     

A discontinuous Galerkin‐based sharp‐interface method to simulate three‐dimensional compressible two‐phase flow

A numerical method for the simulation of compressible two‐phase flows is presented in this paper. The sharp‐interface approach consists of several components: a discontinuous Galerkin solver for compressible fluid flow, a level‐set tracking algorithm to follow the movement of the interface and a coupling of both by a ghost‐fluid approach with use of a local Riemann solver at the interface. There are several novel techniques used: the discontinuous Galerkin scheme allows locally a subcell resolution to enhance the interface resolution and an interior finite volume Total Variation Diminishing (TVD) approximation at the interface. The level‐set equation is solved by the same discontinuous Galerkin scheme. To obtain a very good approximation of the interface curvature, the accuracy of the level‐set field is improved and smoothed by an additional P_NP_M‐reconstruction. The capabilities of the method for the simulation of compressible two‐phase flow are demonstrated for a droplet at equilibrium, an oscillating ellipsoidal droplet, and a shock‐droplet interaction problem at Mach 3. Copyright © 2015 John Wiley & Sons, Ltd.     

奇异积分算子q-变差的定量最优加权估计

本文将定量最优A_p权理论推广到联系于ω-Calderón-Zygmund算子的q-变差情形.这些结果利用了Lerner最新给出的稀疏控制方法来控制q-变差,和Hyt?nen等关于q-变差的最优加权成果相比,本文涉及的ω仅需满足Dini条件,并且其截断是非光滑的.     

Vertices of degree k in random unlabeled trees

Let ??_n be the class of unlabeled trees with n vertices, and denote by H _n a tree that is drawn uniformly at random from this set. The asymptotic behavior of the random variable deg_k(H _n) that counts vertices of degree k in H _n was studied, among others, by Drmota and Gittenberger in [J Graph Theory 31(3) (1999), 227–253], who showed that this quantity satisfies a central limit theorem. This result provides a very precise characterization of the “central region” of the distribution, but does not give any non‐trivial information about its tails. In this work, we study further the number of vertices of degree k in H _n. In particular, for k = ??((logn/(loglogn))^1/2) we show exponential‐type bounds for the probability that deg_k(H _n) deviates from its expectation. On the technical side, our proofs are based on the analysis of a randomized algorithm that generates unlabeled trees in the so‐called Boltzmann model. The analysis of such algorithms is quite well‐understood for classes of labeled graphs, see e.g. the work [Bernasconi et al., SODA '08: Proceedings of the 19th Annual ACM‐SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2008, pp. 132–141; Bernasconi et al., Proceedings of the 11th International Workshop, APPROX 2008, and 12th International Workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization, Springer, Berlin, 2008, pp. 303–316] by Bernasconi, the first author, and Steger. Comparable algorithms for unlabeled classes are unfortunately much more complex. We demonstrate in this work that they can be analyzed very precisely for classes of unlabeled graphs as well. © 2011 Wiley Periodicals, Inc. J Graph Theory. 69:114‐130, 2012     

Endpoint estimates for n-dimensional Hardy operators and their commutators

In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed.     

The property of having a k ‐regular subgraph has a sharp threshold

In this paper it is proved that in the random graph model G(n,p), the property of containing a k ‐regular subgraph, has a sharp threshold for k ≥ 3. It is also shown how to use similar methods to prove, quite easily, the (known fact of) sharpness of having a non empty k ‐core for k ≥ 3. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 42, 509–519, 2013     

Core inverse of matrices

This article introduces the notion of the Core inverse as an alternative to the group inverse. Several of its properties are derived with a perspective towards possible applications. Furthermore, a matrix partial ordering based on the Core inverse is introduced and extensively investigated.     

2011年春夏季长江中下游地区旱涝急转特征分析

本文选用美国环境预报中心/国家大气研究中心提供的全球再分析资料, 中国气象局国家气候中心提供的中国740站降水资料及中国气象信息中心提供的中国区域 2011年降水格点资料,对2011年长江中下游地区6月初旱涝急转现象及环流背景特征进行简要分析, 结论如下: 1) 2011年1-5月长江中下游地区降水较气候平均值偏少且降水变率较小, 6月长江中下游地区降水量急剧增多,发生旱涝急转现象,其转折点为第31候(6月第1候); 2)旱涝急转前后,水汽通量及其经验正交函数分解的第1, 2模态的时间和空间演变均表现出弱水汽输送向强水汽输送转变的特征; 3)转折前后大气环流场差异显著. 急转前,北半球冬季风偏强,南半球夏季风偏弱,在春季,东亚大槽偏强导致季风的转换延迟, 不利于南方暖湿气流的北上,南方降水偏少,并发生大范围持续性的严重干旱. 6月初(急转期)环流迅速调整,西太平洋副高突然西伸北跳,东亚大槽异常偏西偏强、 鄂海阻高减弱,使冷暖空气在长江中下游地区汇合,有利于该地区的降水发生并持续, 是长江中下游地区由严重干旱向洪涝急转的主要原因.