树和单圈图的斜谱矩

给定图$G$,对图$G$的每条边确定一个方向,称为$G$的定向图$G^\sigma$, $G$称为$G^\sigma$的基础图. $G^\sigma$的斜邻接矩阵$S(G^\sigma)$是反对称矩阵,其特征值是0或纯虚数. $S(G^\sigma)$所有特征值的$k$次幂之和称为$G^\sigma$的$k$阶斜谱矩,其中$k$是非负整数.斜谱矩序列可用于对图进行排序.本文主要研究定向树和定向单圈图的斜谱矩,并对这两类图的斜谱矩序列依照字典序进行排序.首先确定了直径为$d$的树作为基础图的所有定向树中,斜谱矩序最大的$2\lfloor\frac{d}{4}\rfloor$个图; 然后确定以围长为$g$的单圈图作为基础图的所有定向单圈图中, 斜谱矩序最大的$2\lfloor\frac{g}{4}\rfloor+1$个图.     

面向对象有限元程序的类设计

传统有限元程序设计中的许多问题可以通过面向对象程序设计方法加以解决。本文介绍了我们尝试采用ＢｏｒｌａｎｄＣ＋＋２．０进行的一种面向对象有限元程序设计，着重进行有限元程序的类划分与定义，并将几个典型的类设计成类等级。面向对象语言的继承性、封装性、多态性等特性在我们的程序设计中均得到了运用。与传统的有限元程序（通常采用Ｆｏｒｔｒａｎ）相比，面向对象有限元程序更加结构化、更易于编写、更易于维护和扩充，程序代码的可重用成分更大，它为开发大型有限元分析软件提供了一条新途径     

电流变液体黏性变化趋势的试验研究

以微观试验和流变性能试验为手段，分别研究零电场下和在电场作用下的电流变液体黏性变化规律．研究结果表明：零电场下电流变液体的黏性与Krieger-Dougherty公式具有很好的拟合效果，其中逾渗临界值强依赖于悬浮液体中固体颗粒的性质并随工作温度变化．在电场作用下，电流变悬浮液体的黏度随剪切速率的变化规律分为3个阶段：即呈线性的启动段、非线性的幂定律模型流动段和宾汉模型流动段．研究结果为电流变效应工程应用提供依据．     

Biology‐Oriented Synthesis of a Withanolide‐Inspired Compound Collection Reveals Novel Modulators of Hedgehog Signaling

Biology‐oriented synthesis employs the structural information encoded in complex natural products to guide the synthesis of compound collections enriched in bioactivity. The trans‐hydrindane dehydro‐δ‐lactone motif defines the characteristic scaffold of the steroid‐like withanolides, a plant‐derived natural product class with a diverse pattern of bioactivity. A withanolide‐inspired compound collection was synthesized by making use of three key intermediates that contain this characteristic framework derivatized with different reactive functional groups. Biological evaluation of the compound collection in cell‐based assays that monitored biological signal‐transduction processes revealed a novel class of Hedgehog signaling inhibitors that target the protein Smoothened.     

Highly Stereoselective Synthesis of Natural‐Product‐Like Hybrids by an Organocatalytic/Multicomponent Reaction Sequence

In an endeavor to provide an efficient route to natural product hybrids, described herein is an efficient, highly stereoselective, one‐pot process comprising an organocatalytic conjugate addition of 1,3‐dicarbonyls to α,β‐unsaturated aldehydes followed by an intramolecular isocyanide‐based multicomponent reaction. This approach enables the rapid assembly of complex natural product hybrids including up to four different molecular fragments, such as hydroquinolinone, chromene, piperidine, peptide, lipid, and glycoside moieties. The strategy combines the stereocontrol of organocatalysis with the diversity‐generating character of multicomponent reactions, thus leading to structurally unique peptidomimetics integrating heterocyclic, lipidic, and sugar moieties.     

Near‐forward/high‐pressure‐backward Raman study of Zn1 − xBexSe (x ~ 0.5) – evidence for percolation behavior of the long (Zn―Se) bond

The apparently universal 1‐bond → 2‐mode percolation behavior in the Raman spectra of zincblende semiconductor alloys is generally observed for the short bond only, and not for the long one. In this work we perform a combined high‐pressure‐backward/near‐forward Raman study of the leading percolation‐type (Zn,Be)Se alloy (~50 at.% Be), which exhibits a distinct percolation doublet in the spectral range of its short Be―Se bond, in search of a Zn―Se analogue. The high‐pressure‐backward insight is not conclusive per se, but clarifies the perspective behind the near‐forward Raman study. The latter reveals an unique Zn―Se phonon–polariton. Its fair contour modeling depending on the scattering angle is achieved within the linear dielectric approach, based on ellipsometry measurement of the ZnBeSe refractive index. Somewhat surprisingly this reveals that the phonon–polariton in question is a ‘fractional’ one in that it carries only half of the available Zn―Se oscillator strength, as ideally expected in case of a BeSe‐like bimodal Raman behavior of the long Zn―Se bond. Copyright © 2015 John Wiley & Sons, Ltd.     

类似花状结构介晶钴的大规模控制合成及磁性能

以二乙烯三胺(DETA)作为配位剂,快速合成了纳米粒子定向组装构成的类似花状的介晶钴。通过控制反应的速率和配位剂的种类,依次获得了精美的钴花、差形貌的枝晶、由纳米粒子或纳米片构成的微球。配位剂在介晶钴的形成过程中起了很重要的作用。探讨了介晶钴花的形成机理。介晶钴不但具有钴纳米晶的性能(在300 K时矫顽力260 Oe),而且拥有块体钴的性能(饱和磁化强度168 emu·g-1)。合成方法简便、有效且具有较高的产率。     

The cut‐tree of large trees with small heights

We destroy a finite tree of size n by cutting its edges one after the other and in uniform random order. Informally, the associated cut‐tree describes the genealogy of the connected components created by this destruction process. We provide a general criterion for the convergence of the rescaled cut‐tree in the Gromov‐Prohorov topology to an interval endowed with the Euclidean distance and a certain probability measure, when the underlying tree has branching points close to the root and height of order . In particular, we consider uniform random recursive trees, binary search trees, scale‐free random trees and a mixture of regular trees. This yields extensions of a result in Bertoin (Probab Stat 5 (2015), 478–488) for the cut‐tree of uniform random recursive trees and also allows us to generalize some results of Kuba and Panholzer (Online J Anal Combin (2014), 26) on the multiple isolation of vertices. The approach relies in the close relationship between the destruction process and Bernoulli bond percolation, which may be useful for studying the cut‐tree of other classes of trees. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 404–427, 2017     

The effect of pore-structure on hysteresis in relative permeability and capillary pressure: Pore-level modeling

The effect of pore-structure upon two-phase relative permeability and capillary pressure of strongly-wetting systems at low capillary number is simulated. A pore-level model consisting of a network of pore-bodies interconnected by pore-throats is used to calculate scanning loops of hysteresis between primary drainage, imbibition and secondary drainage. The pore-body to pore-throat aspect ratio strongly influences the pattern of hysteresis. Changes in the patterns of hysteresis often attributed to consolidation can be understood in terms of changes in aspect ratio. Correlation between the sizes of neighboring pore-throats affects the shape of the relative permeability curves, while the width and shape of the pore-size distribution have only a minor influence.     

Multiscale Structures to Describe Porous Media Part I: Theoretical Background and Invasion by Fluids

A porous medium with a broad pore-size distribution is described on the basis of the Multiscale Percolation System concept. The representative structure is the superposition of several constitutive elementary networks, of which mesh sizes are proportional to the diameter of the class of pores considered. To account for the contribution of each class to the connection of the medium, a recurrent building process, involving rescaling and superposition, is defined. This process leads to an equivalent monoscale network, involving elements representative of the various classes. Mercury intrusion at increasing pressure into a finite-size sample of this equivalent network is modelled. The inverse problem is solved, leading to the identification of the representative multiscale structure of a given material from the experimental intrusion curve.