Synthesis of thermally stable aromatic poly(spiroorthocarbonate)s having a Cardo or bent structure

Novel poly(spiroorthocarbonate)s [poly(SOC)]s having a Cardo or bent structure were synthesized by polycondensation of several bis‐catechols having fluorene (BCFL), spirobisindane (BCSPI), or spirobischromane (BCSPC) in the structure with 2,2,6,6‐tetrachlorobenzo[1,2‐d:4,5‐d’]bis[1,3]dioxole (4ClBD). Synthesis of poly(SOC)s was confirmed by NMR and IR spectrometry. The poly(SOC)s obtained from BCFL or BCSPC were soluble in common organic solvents. The glass transition temperature of the poly(SOC)s was not detected by differential scanning calorimetry (DSC) in the range of 50–300 °C. The 10 wt % decomposition temperature of the poly(SOC)s was found to be above 400 °C. These results indicated the high thermal stability of the poly(SOC)s. Soluble poly(SOC)s could be possessed to form a film on a glass plate by the spin coat method. The obtained polymer films were 0.2 μm in thickness with 95% light transmission in the optical wavelength range. These results suggested that the Cardo or bent structure may block the packing of the main‐chain of the structure, which improves the solubility of the polymers, increases transparency, and enhances the thermal stability of SOCs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1409‐1416     

On the minimal sum of Betti numbers of an almost complex manifold

We show that the only rational homology spheres which can admit almost complex structures occur in dimensions two and six. Moreover, we provide infinitely many examples of six-dimensional rational homology spheres which admit almost complex structures, and infinitely many which do not. We then show that if a closed almost complex manifold has sum of Betti numbers three, then its dimension must be a power of two.     

The B2–B7 phase transition in symmetrical bent‐shaped mesogens with methoxy substitution

New mesogens composed of achiral bent molecules with thermally stable ester linkages, and laterally substituted by a methoxy group symmetrically near the central benzene ring, were synthesized. Texture, calorimetric, electro‐optical, X‐ray and dielectric measurements were performed. In most of studied compounds the antiferroelectric B₂ phase was found on cooling from the isotropic phase, followed by the B₇ phase at lower temperatures. Undulation of layers in the B₇ phase was confirmed by precise synchrotron studies.     

Liquid crystalline banana‐shaped monomers derived from 2,7‐naphthalene: synthesis and properties

Three banana‐shaped monomers, i.e. 2,7‐naphthalene bis[4‐(4‐allyloxyphenylazo)‐benzoate], 2,7‐naphthalene bis[4‐(4‐allyloxy‐3‐fluorophenylazo)benzoate] and 2,7‐naphthalene bis{4‐[4‐(10‐undecenyloxy)phenylazo]benzoate}, containing azobenzene as side arms, 2,7‐dihydroxynaphthalene as central units and terminal double bonds as polymerisable functional groups, were synthesised and their mesophase behaviour investigated. Polarizing optical microscopy and DSC measurements reveal that all compounds exhibit nematic mesophases. The absorption spectrum of the trans‐azobenzene groups displays a high‐intensity π–π* transition at about 365 nm and a low‐intensity n–π* transition at around 450 nm for all compounds. Hence, photochromism can be achieved by the introduction of the azo linkage to banana‐shaped liquid crystals molecules.     

Lotka-Volterra型N-种群竞争系统的持久性和稳定性

本文研究一类具有无穷时滞的概周期Lotka-Volterra型N-种群竞争系统的持久性和全局渐近稳定性.一些新的充分条件被得到.     

Non-commutative complex differential geometry

This paper defines and examines the basic properties of non-commutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a differential structure on a non-commutative algebra defined in terms of a differential graded algebra. This is compared to current ideas on non-commutative algebraic geometry.     

On almost sure max-limit theorems of complete and incomplete samples from stationary sequences

Let M _n denote the partial maximum of a strictly stationary sequence (X _n ). Suppose that some of the random variables of (X _n ) can be observed and let [(M)\tilde]_n\tilde M_n stand for the maximum of observed random variables from the set {X ₁, ..., X _n }. In this paper, the almost sure limit theorems related to random vector ([(M)\tilde]_n\tilde M_n , M _n ) are considered in terms of i.i.d. case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.     

Generalized One-Sided Laws for the Larger Observations of a Triangular Array

Consider independent and identically distributed random variables {X,X _nj , 1jn,n1} with density f(x)=px ^–p–1 I(x1), where p>0. We show that there exist unusual generalized Laws of the Iterated Logarithm involving the larger order statistics from our array.