Uncommon suffix tries

Common assumptions on the source producing the words inserted in a suffix trie with n leaves lead to a height and saturation level. We provide an example of a suffix trie whose height increases faster than a power of n and another one whose saturation level is negligible with respect to . Both are built from VLMC (Variable Length Markov Chain) probabilistic sources and are easily extended to families of tries having the same properties. The first example corresponds to a “logarithmic infinite comb” and enjoys a non uniform polynomial mixing. The second one corresponds to a “factorial infinite comb” for which mixing is uniform and exponential. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 117–141, 2015     

Stability criteria in terms of two measures for functional differential equation with variable‐time impulses

This paper focuses on the stability in terms of two measures for functional differential equation with variable‐time impulses. Being different from most of existing literatures, the impulses of functional differential equation are assumed to be closely associated to the current state. We propose a new comparison principle for the considered systems and establish several stability criteria in terms of two measures. Also, the theoretical results are applied in a class of delayed neural network systems with variable‐tine impulses, and numerical simulations are introduced to illustrate the effectiveness of our results. Copyright © 2014 John Wiley & Sons, Ltd.     

In situ single‐crystal to single‐crystal (SCSC) transformation of the one‐dimensional polymer catena‐poly[[diaqua(sulfato)copper(II)]‐μ2‐glycine] into the two‐dimensional polymer poly[μ2‐glycine‐μ4‐sulfato‐copper(II)]

The one‐dimensional coordination polymer catena‐poly[diaqua(sulfato‐κO)copper(II)]‐μ₂‐glycine‐κ²O:O′], [Cu(SO₄)(C₂H₅NO₂)(H₂O)₂]_n, (I), was synthesized by slow evaporation under vacuum of a saturated aqueous equimolar mixture of copper(II) sulfate and glycine. On heating the same blue crystal of this complex to 435 K in an oven, its aspect changed to a very pale blue and crystal structure analysis indicated that it had transformed into the two‐dimensional coordination polymer poly[(μ₂‐glycine‐κ²O:O′)(μ₄‐sulfato‐κ⁴O:O′:O′′:O′′)copper(II)], [Cu(SO₄)(C₂H₅NO₂)]_n, (II). In (I), the Cu^II cation has a pentacoordinate square‐pyramidal coordination environment. It is coordinated by two water molecules and two O atoms of bridging glycine carboxylate groups in the basal plane, and by a sulfate O atom in the apical position. In complex (II), the Cu^II cation has an octahedral coordination environment. It is coordinated by four sulfate O atoms, one of which bridges two Cu^II cations, and two O atoms of bridging glycine carboxylate groups. In the crystal structure of (I), the one‐dimensional polymers, extending along [001], are linked via N—H...O, O—H...O and bifurcated N—H...O,O hydrogen bonds, forming a three‐dimensional framework. In the crystal structure of (II), the two‐dimensional networks are linked via bifurcated N—H...O,O hydrogen bonds involving the sulfate O atoms, forming a three‐dimensional framework. In the crystal structures of both compounds, there are C—H...O hydrogen bonds present, which reinforce the three‐dimensional frameworks.     

苯酚(醌)与烯烃的不对称[3+2]环化反应: 手性二氢苯并呋喃的合成进展

二氢苯并呋喃结构单元广泛存在于具有良好生物活性和药用价值的天然产物之中, 因而引起了有机合成化学家和药物化学家们的关注. 针对该结构单元所包含的C2和C3邻二立体中心的对映选择性构建, 也是目前有机合成方法学研究的挑战性问题之一. 在众多解决方案中, 以苯酚(醌)与烯烃为底物, 具体采用催化不对称和手性辅剂诱导的[3+2]环化两种方式, 可以构建具有光学活性的二氢苯并呋喃结构单元. 本综述将不同类型的手性催化剂和手性辅剂进行分类梳理, 介绍了近年来不对称[3+2]环化反应的发展, 并重点剖析其中涉及的立体选择性控制. 同时, 简要介绍了该关键方法在二氢苯并呋喃天然产物合成中的应用. 为了启发更加高效和普适性的新催化体系出现, 最后总结和展望了不对称[3+2]环化反应的发展趋势.     

Development of variable‐magnification X‐ray Bragg optics

A novel X‐ray Bragg optics is proposed for variable‐magnification of an X‐ray beam. This X‐ray Bragg optics is composed of two magnifiers in a crossed arrangement, and the magnification factor, M, is controlled through the azimuth angle of each magnifier. The basic properties of the X‐ray optics such as the magnification factor, image transformation matrix and intrinsic acceptance angle are described based on the dynamical theory of X‐ray diffraction. The feasibility of the variable‐magnification X‐ray Bragg optics was verified at the vertical‐wiggler beamline BL‐14B of the Photon Factory. For X‐ray Bragg magnifiers, Si(220) crystals with an asymmetric angle of 14° were used. The magnification factor was calculated to be tunable between 0.1 and 10.0 at a wavelength of 0.112 nm. At various magnification factors (M≥ 1.0), X‐ray images of a nylon mesh were observed with an air‐cooled X‐ray CCD camera. Image deformation caused by the optics could be corrected by using a 2 × 2 transformation matrix and bilinear interpolation method. Not only absorption‐contrast but also edge‐contrast due to Fresnel diffraction was observed in the magnified images.     

一种宽能谱多球中子谱仪能量响应的MC模拟

利用蒙特卡罗程序FLUKA模拟计算了聚乙烯慢化球和辅助材料慢化球对低能中子到高能中子的响应函数曲线。结果表明,对纯聚乙烯球来说,随着聚乙烯层厚度的增加,响应曲线峰逐步右移,峰值在高能区有所下降,对20 Me V以上的中子,无论纯聚乙烯球的尺寸有多大,其响应均下降到很低的程度;对辅助材料慢化球来说,中子能量小于1 Me V时,辅助材料慢化球与聚乙烯慢化球的响应曲线相似,但当中子能量大于20 Me V时,中子与辅助材料层发生(n,xn)反应,慢化球的响应呈显著上升趋势。分析计算结果,最终能够确定宽能谱多球中子谱仪的尺寸组合。     

Nickel‐Catalyzed C?H Alkylations: Direct Secondary Alkylations and Trifluoroethylations of Arenes

A versatile nickel catalyst allowed for C H alkylations of unactivated arenes with challenging secondary alkyl bromides and chlorides. The high catalytic efficacy also set the stage for direct secondary alkylations of indoles as well as C H trifluoroethylations with ample substrate scope.     

NMR波谱仪集中优化管理模式

论述了核磁中心采用的相对集中管理模式.集中管理模式主要体现在上样辅助、中央供气、数据集中上传与下载3个方面.另外,还提出了未来可以从集中供高纯N2和LN22个方面进一步改善中心的集中管理模式,从而能够更好的优化测试效率和工作环境.     

n阶变系数线性差分微分方程的解

利用Mikusi'nski算符域中变系数算符概念和相应的算符系数移动算符幂级数的概念和结果,获得初值条件下n阶变系数线性差分微分方程的解.     

一类具有连续变量的二阶非线性阻尼差分方程的振动准则

考虑了一类具有连续变量的二阶非线性阻尼差分方程,利用积分变换和广义R iccati变换,给出了此类方程的振动准则.