正规发散级数

本文推广了维数正规发散的古典概念，将幂级数的一个定理推广到很一般的情况，然后讨论其在各种复函数项级数中的应用．     

Solvability of the Inverse Problem of Finding Thermal Conductivity

We study the inverse problem of finding the coefficient of thermal conductivity of the heat equation (along with the solution). As the overdetermination condition we take the values of the solution at the final time. Existence of a regular solution is proven.     

On the Iterated Biclique Operator

A biclique of a graph G is a maximal induced complete bipartite subgraph of G. The biclique graph of G, denoted by , is the intersection graph of the bicliques of G. We say that a graph G diverges (or converges or is periodic) under an operator F whenever ( for some m, or for some k and , respectively). Given a graph G, the iterated biclique graph of G, denoted by , is the graph obtained by applying the biclique operator k successive times to G. In this article, we study the iterated biclique graph of G. In particular, we classify the different behaviors of when the number of iterations k grows to infinity. That is, we prove that a graph either diverges or converges under the biclique operator. We give a forbidden structure characterization of convergent graphs, which yield a polynomial time algorithm to decide if a given graph diverges or converges. This is in sharp contrast with the situsation for the better known clique operator, where it is not even known if the corresponding problem is decidable. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 181–190, 2013     

Total Syntheses of Xiamycins A,C, F,H and Oridamycin A and Preliminary Evaluation of their Anti‐Fungal Properties

Divergent and enantiospecific total syntheses of the indolosesquiterpenoids xiamycins A, C, F, H and oridamycin A have been accomplished. The syntheses, which commence from (R)‐carvone, employ a key photoinduced benzannulation sequence to forge the carbazole moiety characteristic of these natural products. Late‐stage diversification from a common intermediate enabled the first syntheses of xiamycins C and F, and an unexpected one‐pot oxidative decarboxylation, which may prove general, led to xiamycin H. All synthetic intermediates and the natural products were tested for anti‐fungal activity. Xiamycin H emerged as an inhibitor of three agriculturally relevant fungal pathogens.     

Divergent Total Syntheses of Enmein‐Type Natural Products: (−)‐Enmein, (−)‐Isodocarpin,and (−)‐Sculponin R

Divergent total syntheses of the enmein‐type natural products (?)‐enmein, (?)‐isodocarpin, and (?)‐sculponin R have been achieved in a concise fashion. Key features of the strategy include 1) an efficient early‐stage cage formation to control succeeding diastereoselectivity, 2) a one‐pot acylation/akylation/lactonization to construct the C‐ring and C8 quarternary center, 3) a reductive alkenylation approach to construct the enmain D/E rings and 4) a flexible route to allow divergent syntheses of three natural products.     

1,3-Sulfinate Migration Triggered by α-Imino Carbene and Divergent Zwitterion Cyclization: Synthesis of Cyclopropane,Dihydropyrrole, and Azepane Ring Systems

Cyclopropane, dihydropyrrole, and azepane ring systems were synthesized conveniently from sulfinate-tethered triazoles. The divergent synthetic strategy started with the unique 1,3-sulfinate migration of an α-imino carbene. The efficient reaction allowed control of the zwitterion bearing multiple reactive sites depending on the increased stability of the resulting carbocation and anion. The sulfinate was converted to a sulfone after the group migration, and a stable anion bearing two electron-withdrawing groups was thus formed. Catalytic amounts of iodide acted as a switch for the synthesis of cyclopropanes and dihydropyrroles. The reaction merits including readily available substrates, mild reaction conditions, and excellent functional group compatibility qualified this protocol a possible synthetic tool for cyclic compounds, especially for N-heterocycles.     

燃烧轻气炮多级渐扩型燃烧室流场特性数值研究

为了分析多级渐扩型燃烧室结构对燃烧轻气炮氢氧燃烧特性的影响, 通过计算流体力学方法, 分别对采用传统圆柱型燃烧室和多级渐扩型燃烧室的燃烧轻气炮氢氧燃烧发射过程进行数值模拟。对比结果表明, 多级渐扩型燃烧室结构能够明显地减小燃烧室压力波动幅度, 提高氢氧燃烧稳定性; 多级渐扩型燃烧室内形成回流区, 可以减小气流轴向运动速度; 火焰扩展形态与渐扩型结构相吻合, 燃烧反应区表面变化平稳; 多级渐扩型燃烧室结构对氢氧火焰传播过程和压力波动现象有着重要影响。     

On Taylor-like integral representations of analytic functions

Let f be an analytic function in a complex domain D and (without loss of generality) assume 0∈D. Then the paper’s aim is to derive a Taylor-like integral expression for f, i.e. an integral representation analogous to the corresponding power series, say, ∑ _k=0^∞ a _k t ^k /k!. We start from the simplest case f(t)=e ^t , which leads to the identity

新型二维发散波电磁粒子速度计的设计初探

为探索发散波作用下粒子速度二维电磁测试方法,研究了脉冲电流作用下Helmholtz线圈磁场特性,设计了新型二维发散波电磁粒子速度计构型.通过有机玻璃试验样品中粒子速度的一维和二维电磁测试对比实验,表明新型二维发散波电磁粒子速度计可以为具有分界面、沟槽或节理的非均匀分层介质中的发散波传播规律研究提供有效的测试手段.