Inequalities for the Moments and Distribution of the Ladder Height of a Random Walk

We obtain upper bounds for the tail distribution of the first nonnegative sum of a random walk and for the moments of the overshoot over an arbitrary nonnegative level if the expectation of jumps is positive and close to zero. In addition, we find an estimate for the expectation of the first ladder epoch.     

Cyclic and telechelic ladder polymers derived from tetrahydroxytetramethylspirobisindane and 1,4‐dicyanotetrafluorobenzene

5,5′,6,6′‐Tetrahydroxy‐3,3,3′,3′‐tetramethylspirobisindane was polycondensed with 1,4‐dicyanotetrafluorobenzene in four different solvents at 70 °C. In dimethylformamide, N‐methylpyrrolidone, and sulfolane exclusively, cyclic polymers were detectable by matrix‐assisted laser desorption/ionization time‐of‐flight (MALDI‐TOF) mass spectrometry up to masses around 13,000 Da. In dimethyl sulfoxide, linear byproducts were also found. Higher temperatures caused degradation reactions catalyzed by potassium carbonate. Polycondensations performed with the addition of 4‐tert‐butyl catechol or 2,2′‐dihydroxy binaphthyl yielded linear telechelic oligomers. Equimolar mixtures of linear and cyclic ladder polymers were examined by MALDI‐TOF mass spectra to determine how the end groups and the cyclic structure influenced the signal‐to‐noise ratio. The results suggested a preferential detection of the linear chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5344–5352, 2006     

New PIM-1 copolymers containing 2,3,6,7-anthracenetetrayl moiety and their use as gas separation membranes

1. Download : Download high-res image (198KB)
2. Download : Download full-size image

     

Two Polymorphs of (Anilinium)(18-Crown-6)[Ni(dmit)2]: Structure and Magnetic Properties

Two polymorphs of monovalent [Ni(dmit)₂]⁻ (dmit²⁻=2-thioxo-1,3-dithiole-4,5-dithiolate) crystals A and B, (anilinium)(18-crown-6)[Ni(dmit)₂], were prepared, and the structure and magnetic properties were investigated. In these crystals, the [Ni(dmit)₂]⁻ molecules form dimers, which arranged into chains between the supramolecular cation structure (anilinium)(18-crown-6). In crystal A, supramolecular cation formed a regular stack, inducing ladder structure of [Ni(dmit)₂], whose magnetism had been well fitted by spin ladder equation with the spin gap of Δ=190 K. Crystal B is ca. 3% more densely packed compared to crystal A. Due to the dense packing, supramolecular cation stack is distorted, which prevented the intermolecular interaction between [Ni(dmit)₂]⁻ dimers in direction corresponds to the ladder-leg direction in crystal A. Reflecting the [Ni(dmit)₂]⁻ arrangement, crystal B showed a temperature dependence of magnetic susceptibility well reproduced by the singlet-triplet thermal activation model, whose antiferromagnetic exchange interaction (2J) was 140 K.     

The double‐stranded ladder‐like structure of poly[[bis(μ2‐acetato‐κ2O:O′)bis(acetato‐κO)bis(μ‐4,4′‐bipyridine‐κ2N:N′)dicopper(II)] 4‐nitrophenol disolvate tetrahydrate]

The reaction of 4,4′‐bipyridine with copper acetate in the presence of 4‐nitrophenol led to the formation of the title compound, {[Cu(CH₃COO)₂(C₁₀H₈N₂)]·C₆H₅NO₃·2H₂O}_n. The complex forms a double‐stranded ladder‐like coordination polymer extending along the b axis. The double‐stranded polymers are separated by 4‐nitrophenol and water solvent molecules. The two Cu^II centres of the centrosymmetric Cu₂O₂ ladder rungs have square‐pyramidal coordination environments, which are formed by two acetate O atoms and two 4,4′‐bipyridine N atoms in the basal plane and another acetate O atom at the apex. The ladder‐like double strands are separated from each other by one unit‐cell length along the c axis, and are connected by the water and 4‐nitrophenol molecules through a series of O—H...O and C—H...O hydrogen‐bonding interactions and two unique intermolecular π–π interactions.     

飞秒激光参数对三态阶跃型分子Autler-Townes分裂的影响

利用三态模型和含时波包法, 研究了K₂分子在强飞秒泵浦-探测激光场中泵浦/探测场强、波长对光电子能谱Autler-Townes(AT)分裂的影响．通过分别改变两激光场的场强或者波长预测AT峰移和间距,并且首次量化了AT分裂的峰移和间距．光电子能谱在共振时显示为对称双峰,失谐时为非对称双峰。AT分裂间距随泵浦场强增大而增大,但不因探测场强改变而改变．     

Synthesis,Thermal Behavior,and Dehydrogenation Kinetics Study of Lithiated Ethylenediamine

The lithiation of ethylenediamine by LiH is a stepwise process to form the partially lithiated intermediates LiN(H)CH₂CH₂NH₂ and [LiN(H)CH₂CH₂NH₂][LiN(H)CH₂CH₂N(H)Li]₂ prior to the formation of dilithiated ethylenediamine LiN(H)CH₂CH₂N(H)Li. A reversible phase transformation between the partial and dilithiated species was observed. One dimensional {Li_nN_n} ladders and three‐dimensional network structures were found in the crystal structures of LiN(H)CH₂CH₂NH₂ and LiN(H)CH₂CH₂N(H)Li, respectively. LiN(H)CH₂CH₂N(H)Li undergoes dehydrogenation with an activation energy of 181±8 kJ mol^?1, whereas the partially lithiated ethylenediamine compounds were polymerized and released ammonia at elevated temperatures. The dynamical dehydrogenation mechanism of the dilithiated ethylenediamine compounds was investigated by using the Johnson‐Mehl‐Avrami equation.     

Three Octacyanometallate‐Based LnIII–MV (Ln = La,Ce; M = Mo,W) Bimetallic Assemblies with a One‐Dimensional Rope‐Ladder Chain Structure

Three octacyanometallate‐based hetero‐bimetallic complexes, [Ln(H₂O)₄(CH₃CN)₂][M(CN)₈] · CH₃CN [Ln = La, M = Mo( 1 ), W( 2 ); Ln = Ce, M = W( 3 )], were synthesized and characterized structurally. Single‐crystal X‐ray analysis reveals that 1 – 3 are isomorphous and consist of infinite one‐dimensional (1D) 3,3 rope‐ladder chains, in which the 12‐membered puckered square Ln₂M₂(CN)₄ is the basic building unit. The 1D chains are further linked through interchain hydrogen bonds, resulting in a three‐dimensional (3D) supramolecular network.