Stability of Multiplier Ideal Sheaves

Chinese Annals of Mathematics, Series B - In the present article, the authors find and establish stability of multiplier ideal sheaves, which is more general than strong openness.     

三层流体中斜入射波作用下半无限板的水弹性响应

解析地研究了在三层流体中斜入射波浪与半无限弹性板的相互作用引起的波散射和板的水弹性响应. 三层流体在界面处的密度发生阶跃, 各层为一常数. 假设流体不可压缩、无黏、流体运动无旋. 在线性势流理论框架下, 使用本征函数展开法和内积式给出波板相互作用的半解析解. 根据色散关系分析, 得到了表面波模态和界面波模态入射时的临界入射角. 随着物理参数的变化, 临界角将随之发生变化. 临界角决定了当由开阔水域向板覆盖水域传播的表面波或界面波的存在性: (1)板覆盖水域入射界面上, 透射波能否存在; (2)入射界面之上界面中, 板覆盖水域中的透射波以及开阔水域中的反射波能否存在. 当下界面波入射时并且入射角足够大时, 开阔水域中的下界面波模态是整个流体域中唯一存在的模态.      

On the metabolites produced by Colletotrichum gloeosporioides a fungus proposed for the Ambrosia artemisiifolia biocontrol; spectroscopic data and absolute configuration assignment of colletochlorin A

Ambrosia artemisiifolia L. is responsible for serious allergies induced on humans. Different approaches for its control were proposed during the COST Action FA1203 “Sustainable management of Ambrosia artemisiifolia in Europe” (SMARTER). Fungal secondary metabolites often show potential herbicidal activity. Three phytotoxins were purified from the fungal culture filtrates of Colletotrichum gloeosporioides, isolated from infected leaves of A. artemisiifolia. They were identified by spectroscopic and chemical methods as colletochlorin A, orcinol and tyrosol (1, 2 and 3). The absolute configuration 6’R to colletochlorin A was assigned for the first time applying the advanced Mosher’s method. When assayed by leaf-puncture on A. artemisiifolia only 1 caused the appearance of large necrosis. The same symptoms were also induced by 1 on ambrosia plantlets associated with plant wilting. On Lemna minor, colletochlorin A caused a clear fronds browning, with a total reduction in chlorophyll content.     

Mixing time of an unaligned Gibbs sampler on the square

The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square ${[0,1]}^2$ to approach a stationary distribution with density proportional to $exp(?A^2{(u?v)}^2)$ for $(u,v)\in {[0,1]}^2$ with some large parameter $A$.Diaconis conjectured the mixing time of this process to be $O\left(A^2\right)$ which we confirm in this paper. This improves on the currently known $O(exp\left(A^2\right))$ estimate.     

Isomorphisms of spaces with large distortion

Let K and S be locally compact Hausdorff spaces and let X be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism T from onto satisfying then K and S are homeomorphic. Here denotes the Schäffer constant of X. Even for the classical cases , and , this result is the X‐valued Banach–Stone theorem via isomorphism with the largest distortion that is known so far, namely . On the other hand, it is well known that this result is not true for , even though K and S are compact Hausdorff spaces.     

A dynamic free-entry oligopoly with sluggish entry and exit adjustments

We study a dynamic free-entry oligopoly with sluggish entry and exit of firms under general demand and cost functions. We show that the number of firms in a steady-state open-loop solution for a dynamic free-entry oligopoly is smaller than that at static equilibrium and that the number of firms in a steady-state memoryless closed-loop solution is larger than that in an open-loop solution.     

Unconditionally Superclose Analysis of a New Mixed Finite Element Method for Nonlinear Parabolic Equation

This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example, a new mixed finite element method (FEM) is established and the $τ$ -independent superclose results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an error splitting technique, with which the time-discrete and the spatial-discrete systems are constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require certain time step conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.     

Weight enumerators of reducible cyclic codes and their dual codes

Let ${\mathbb{F}}_q$ be a finite field and $n$ a positive integer. In this paper, we find a new combinatorial method to determine weight enumerators of reducible cyclic codes and their dual codes of length $n$ over ${\mathbb{F}}_q$, which just generalize results of Zhu et al. (2015); especially, we also give the weight enumerator of a cyclic code, which is viewed as a partial Melas code. Furthermore, weight enumerators obtained in this paper are all in the form of power of a polynomial.