Gilch Synthesis of Poly(ortho‐Phenylene Vinylenes): A Powerful Access to High‐Molecular‐Weight Blue‐Emitting Polymers

For the first time, the successful Gilch synthesis of poly(ortho‐phenylene vinylenes) (ortho‐PPVs) is reported. The molar mass of the constitutionally homogeneous ortho‐PPVs reaches values as high as M_w ≈ 300 000 Da. The ortho‐connectivity of the repeating units forces the chains to assume closely packed conformations even in good solvents. Significant perturbation of the π–electron systems and considerable shortening of the conjugation lengths are the consequences. UV–vis absorption and photoluminescence maxima consequently are shifted clearly toward shorter wavelengths compared to, e.g., classic para‐PPVs.

     

Synthesis and characterization of poly(thioether ether sulfone imide)s derived from isomeric bis(chlorophthalimide)s and bis(4-mercaptophenyl) sulfone

A series of isomeric bis(chlorophthalimide)s (BCPIs) were conveniently prepared from 3-chlorophthalic anhydride, 4-chlorophthalic anhydride, and mixtures thereof. Polymerization of BCPIs with bis(4-mercaptophenyl) sulfone (BMPS) proceeded smoothly in the presence of tributylamine, from which a class of isomeric poly(thioether ether sulfone imide)s (PTESIs) with inherent viscosities of 0.45-0.82 dL/g were obtained. The solubility, thermal stability, and mechanical properties of these polymers were characterized. Compared to the PTESIs derived from single BCPIs, i.e., 3,3′-, 3,4′-, or 4,4′-BCPIs, the PTESIs derived from mixed BCPIs showed better solubility and higher storage modulus. These PTESIs also demonstrated good thermal stability, giving only 5% weight loss at temperature of 490 °C in nitrogen atmosphere. The glass transition temperatures (T_gs) of these isomeric PTESIs were between 242 and 265 °C, and were increased with increasing of the ratio of 3-chlorophthalimide unit in the polymer backbone.     

Synthesis and characterization of alternating copolymers containing triphenylamine as hole‐transporting units

A series of light‐emitting poly(p‐phenylene vinylene)s with triphenylamine units as hole‐transporting moieties in the main chain were synthesized via Wittig condensation in good yields. The newly formed vinylene double bonds possessed a trans configuration, which was confirmed by Fourier transform infrared and NMR spectroscopy. The high glass‐transition temperature (83–155 °C) and high decomposition temperature (>300 °C) suggested that the resulting copolymers possessed high thermal stability. These copolymers, especially TAAPV1, possessed a high weight‐average molecular weight (47,144) and a low polydispersity index (1.55). All the copolymers could be dissolved in common organic solvents, such as tetrahydrofuran (THF), CHCl₃, CH₂Cl₂, and toluene, and exhibited intense photoluminescence in THF (the emission maxima were located from 478 to 535 nm) and in film (from 478 to 578 nm). The low onsets of the oxidation potential (0.6–0.75 V) suggested that the alternating copolymers possessed a good hole‐transporting property due to the incorporation of triphenylamine moieties. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3278–3286, 2001     

两类广义Fibonacci数列的关系

本文将研究广义Fibonacci数列｛un=un-1 un-2｝和数列｛αn=αn-1 αn-3 αn-4｝的内在关系，得到：设αn=1，α2=(m↑∑↑i=1ui s)^2,α4=(m 1↑∑↑i=2ui s)^2,α6=(m 2↑∑、i=3ui s)^2且αn=αn-1 αn-3 αn-4，则（1）α2n=(m n-1↑∑↑i=nui s)^2,α2n 1 α2n-2 α2n-3=2(m n-2↑∑↑i=n-1ui s)(m n-1↑∑↑i=nui s)(2)α2n 1=(m n-1↑∑↑i=nui s)(m n↑∑↑i=n 1ui s) (-1)^n 1X(m,s)，其中X（m,s)=(um s 1-us 1)(um s 2-us 2)-1。     

关于具有正系数的某一类解析函数

目的讨论在单位圆内具有正系数的一个解析函数类。方法介绍在单位圆内具有正系数的一个解析函数类B（n,m,α,β）,利用解析函数的性质和不等式技巧进行讨论。结果和结论得到B（n,m,α,β）中函数的系数不等式、偏差定理、包含关系、凸的线性关系、Hadamard乘积等。     

叶轮机械中考虑气体粘性的激波关系

叶轮机械中考虑气体粘性的激波关系黄修乾，徐建中（中国科学院工程热物理研究所北京１０００８０）关键词激波关系，叶轮机械，粘性流动，三维流动１引言随着叶轮机械叶尖速度和负荷的提高，其内部空间激波及激波／边界层相互作用对性能的影响更加显著。就激波／边界层相...     

Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field

The motion of a particle in the field of an electromagnetic monopole (in the Coulomb–Dirac field) perturbed by an axially symmetric potential after quantum averaging is described by an integrable system. Its Hamiltonian can be written in terms of the generators of an algebra with quadratic commutation relations. We construct the irreducible representations of this algebra in terms of second-order differential operators; we also construct its hypergeometric coherent states. We use these states in the first-order approximation with respect to the perturbing field to obtain the integral representation of the eigenfunctions of the original problem in terms of solutions of the model Heun-type second-order ordinary differential equation and present the asymptotic approximation of the corresponding eigenvalues.     

Ecological optimization for an irreversible magnetic Ericsson refrigeration cycle

An irreversible Ericsson refrigeration cycle model is established, in which multi-irreversibilities such as finite-rate heat transfer, regenerative loss, heat leakage, and the efficiency of the regenerator are taken into account. Expressions for several important performance parameters, such as the cooling rate, coefficient of performance （COP）, power input, exergy output rate, entropy generation rate, and ecological function are derived. The influences of the heat leakage and the time of the regenerative processes on the ecological performance of the refrigerator are analyzed. The optimal regions of the ecological function, cooling rate, and COP are determined and evaluated. Furthermore, some important parameter relations of the refrigerator are revealed and discussed in detail. The results obtained here have general significance and will be helpful in gaining a deep understanding of the magnetic Ericsson refrigeration cycle.     

Dimer Coverings on the Sierpinski Gasket

We present the number of dimer coverings N _d (n) on the Sierpinski gasket SG _d (n) at stage n with dimension d equal to two, three, four or five. When the number of vertices, denoted as v(n), of the Sierpinski gasket is an even number, N _d (n) is the number of close-packed dimers. When the number of vertices is an odd number, no close-packed configurations are possible and we allow one of the outmost vertices uncovered. The entropy of absorption of diatomic molecules per site, defined as , is calculated to be ln (2)/3 exactly for SG ₂. The numbers of dimers on the generalized Sierpinski gasket SG _d,b (n) with d=2 and b=3,4,5 are also obtained exactly with entropies equal to ln (6)/7, ln (28)/12, ln (200)/18, respectively. The number of dimer coverings for SG ₃ is given by an exact product expression, such that its entropy is given by an exact summation expression. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for SG _d (n) with d=3,4,5. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of with d=3,4,5 can be evaluated with more than a hundred significant figures accurate. This paper is written during the Lung-Chi Chen visit to PIMS, University of British Columbia. The author thanks the institute for the hospitality.     

The Ternary System Li2O-Al2O3-B2O3: Compounds and Phase Relations

The ternary system Li₂O-Al₂O₃-B₂O₃ is reinvestigated with solid-state reaction and X-ray powder diffraction technique to clarify some long-standing uncertainties. The phase relations are constructed based on the phase identifications of 51 ternary samples. Six ternary compounds, Li₂AlB₅O₁₀, LiAlB₂O₅, Li₃AlB₂O₆, Li₂AlBO₄, LiAl₇B₄O₁₇ and a compound with a composition close to 0.66Li₂O·0.06Al₂O₃·0.28B₂O₃, are observed or confirmed in this system, and the thermal stability of these ternary compounds is also discussed on the basis of DTA experimental results.