Side chain liquid crystal poly(fumarate)s bearing tolane‐based mesogens

Cyanotolane or fluorotolane mesogens were for the first time introduced into the fumarate monomer under basic conditions. All fumarate monomers undergo radical polymerization in benzene in the presence of dimethyl 2,2′‐azobis(isobutyrate) as an initiator at 60 °C, affording the corresponding poly(fumarate)s with a molecular weight (M_n) of ～ 10⁴ and an exceptionally narrow polydispersity. The phase behaviors of the fumarate monomers and the correspoding poly(fumarate)s were comprehensively investigated by differential scanning calorimetry (DSC), polarized optical microscopy (POM), and X‐ray diffraction (XRD) analysis. For the fumarate monomers, fluorotolane derivatives were prone to form higher‐order liquid crystal phases such as a smectic phase, while cyanotolane derivatives tended to show a wide mesophase temperature range, depending on the alkyl chain spacer length. Very surprisingly, these features dramatically weakened when they were polymerized. The mesophase temperature ranges became narrow and completely disappeared for the poly(fumarate)s with a shorter alkyl chain spacer. A nematic phase representing lower‐order arrangements became a predominant liquid crystal phase for the poly(fumarate) carrying cyanotolane mesogens. Only the poly(fumarate) carrying fluorotolane mesogens with a longer alkyl chain spacer displayed the characteristic XRD patterns of the smectic B phase. The transient photocurrent measurements of the fumarate monomer with cyanotolane mesogens displayed a hole mobility of the order of 10^?4–10^?5 cm² V^?1 s^?1 at room temperature. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5101–5114, 2008     

Kolmogorov’s 1954 paper on nearly-integrable Hamiltonian systems

Following closely Kolmogorov’s original paper [1], we give a complete proof of his celebrated Theorem on perturbations of integrable Hamiltonian systems by including few “straightforward” estimates.      

Structured replacement policies for a Markov-modulated shock model

We establish the optimality of structured replacement policies for a periodically inspected system that fails silently whenever the cumulative number of shocks, or the magnitude of a single shock it has received, exceeds a corresponding threshold. Shocks arrive according to a Markov-modulated Poisson process which represents the (controllable or uncontrollable) environment.     

反向Chrystal不等式

利用控制不等式理论建立了三个反向Chrysta l不等式,并给出了若干应用.     

A crystal field investigation of the properties of RCuAs2 (R=Pr, Nd, Sm, Tb, Dy, Ho, Er and Yb)

A crystal field (CF) investigation of the magnetic properties and heat capacities of RCuAs₂ (R=Pr, Nd, Sm, Tb, Dy, Ho, Er and Yb) has been carried out using the observed average magnetic susceptibilities (1.8-300 K) of the title compounds. The CF parameters proposed for the systems show a systematic variation throughout the rare-earth series. Other physical properties dependent on the CF are also computed and compared with available experimental data. The experimental heat capacity data reported for a limited range of temperature agree well with computed heat capacity for all the compounds (except SmCuAs₂ and YbCuAs₂). CF J mixing was found to be appreciable for all the samples except YbCuAs₂.     

Large deviations: An introduction to 2007 Abel prize

2007 Abel prize has been awarded to S R S Varadhan for creating a unified theory of large deviations. We attempt to give a flavour of this branch of probability theory, highlighting the role of Varadhan.     

Convergence of series of dependent φ-subgaussian random variables

The almost sure convergence of weighted sums of φ-subgaussian m-acceptable random variables is investigated. As corollaries, the main results are applied to the case of negatively dependent and m-dependent subgaussian random variables. Finally, an application to random Fourier series is presented.     

On generalized Erd?s spaces

During the last years both Erd?s space and complete Erd?s space were topologically characterized by Dijkstra and van Mill. Applications include results about Erd?s type spaces in ?p-spaces as well as results about Polishable ideals on ω. We present an unifying theorem in terms of sets with a reflexive relation that among other things contains these apparently dissimilar results as special cases.     

An illustrated theory of hyperbolic virtual polytopes

The paper gives an illustrated introduction to the theory of hyperbolic virtual polytopes and related counterexamples to A.D. Alexandrov’s conjecture.      

Points of Bounded Height on Equivariant Compactifications of Vector Groups, I

We prove asymptotic formulas for the number of rational points of bounded height on certain equivariant compactifications of the affine plane.