Design,synthesis, and characterization of main‐chain,aromatic polyesters based on 3,4‐ethylenedioxythiophene

A series of new thermoplastic polyesters based on 3,4‐ethylenedioxythiophene (EDOT) with flexible aliphatic spacers have been synthesized and characterized for the first time. The thermal properties of these polyesters based on EDOT are comparable to those of conventional polyesters based on the 1,4‐phenyl unit, indicating that EDOT is a viable replacement for the phenyl units. The glass‐transition and melting‐transition temperatures decrease monotonically with an increase in the spacer length. Theoretical calculations have revealed that the core angle for EDOT is comparable to that of unsubstituted thiophene and hence should be compatible with the formation of the mesophase. This has been confirmed experimentally by the synthesis of a main‐chain, thermotropic, liquid‐crystalline polyester based on EDOT that exhibits fluid birefringence. In fact, this is the first report in which a main‐chain, liquid‐crystalline polymer based on 3,4‐disubstituted thiophene has been successfully designed and synthesized. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3479–3486, 2006     

Stable hysteretic reflection of light at a nonlinear interface

We have observed a hysteretic (bistable) reflection of a Gaussian laser beam at the interface between glass and a liquid solution of polystyrene microspheres as nonlinear medium with both branches of the hysteretic curve being stable, in contrast to the results of previous experiments.     

On hermitian polynomial optimization

We compare three levels of algebraic certificates for evaluating the maximum modulus of a complex analytic polynomial, on a compact semi-algebraic set. They are obtained as translations of some recently discovered inequalities in operator theory. Although they can be stated in purely algebraic terms, the only known proofs for these decompositions have a transcendental character. Received: 27 June 2005     

Formation and magnetic properties of Co–Fe-based bulk metallic glasses with supercooled liquid region

A new Co–Fe-based ferromagnetic bulk metallic glass (BMG) was synthesized by copper mould casting method. The thermal stability and crystallization processes were investigated by differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The soft magnetic behavior was studied by DC magnetic measurements. The high glass formation ability was interpreted in terms of the effective suppression of nucleation and growth of the intermetallic compounds which appear in the multicomponent system during solidification. The high thermal stability indicates that the new Co–Fe-based BMG could be used as high-temperature magnetic material. The low coercivity which was as low as 8 A/m for the as-cast sample was found in the Co–Fe-based metallic glass cylinder with a diameter of 1.5 mm.     

The condition on the stability of stationary lines in a curvature flow in the whole plane

The long time behavior of a curve in the whole plane moving by a curvature flow is studied. Studying the Cauchy problem, we deal with moving curves represented by entire graphs on the x-axis. Here the initial curves are given by bounded functions on the x-axis. It is proved that the solution converges uniformly to the solution of the Cauchy problem of the heat equation with the same initial value. The difference is of order O(t−1/2) as time goes to infinity. The proof is based on the decay estimates for the derivatives of the solution. By virtue of the stability results for the heat equation, our result gives the sufficient and necessary condition on the stability of constant solutions that represent stationary lines of the curvature flow in the whole plane.     

800nm激光泵浦掺Nd^3＋的氟化物玻璃光纤正向双程超荧光分析

从实验上探讨了掺Ｎｄ＾３＋的氟化物玻璃光纤正向双程超荧光基本特性，包括输入－输出特性、输出－带宽特性以及输出－波长（激发）特性。并给出了理论上的拟合公式，实验表明利用氟化物玻璃光纤有望获得性能优异的有应用前景的低相干度集成化光源。     

Thermal Analysis of the Conformational Disorder in SCLC Polymers with Rigid Backbone Glass transition studies

Bis [(ω-(4′-cyanobiphenyl)-4-yl)oxy-n-alkyl]norborn-5-ene-2,3-dicarboxylate was polymerised via ring opening metathesis polymerisation (ROMP). Two disubstituted polynorbornene derivatives both of cis configuration with different length of the side-chain were studied. Differential scanning calorimetry (DSC) was used to study the effect of thermal history on the assignment of the glass transition event associated with the biaxial orientation of a smectic phase. Glass transition temperatures, the change of isobaric specific heats at T_g and the enthalpies of isotropisation were calculated. The DSC traces only show the classic step-wise change in T_g in some cases, giving the evidence that the amorphous domains are constrained and highly restricted in movement due to the morphology developed as a result of the biaxial stretching. Based on the literature data of mono- and disubstituted polynorbornene derivatives and our calorimetric experiments, the shape of T_g dependence on number of (CH₂) units is interpreted. The origin of this shape is discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Heat “polynomials” for a singular differential operator on (0, ∞)

We generalize the theory of the heat polynomials introduced by P. V. Rosenbloom and D. V. Widder for a more general class of singular differential operator on (0, ). The heat polynomials associated with the Bessel operator and studied by D. T. Haimo appear as a particular case in this paper. In the special cases of second derivative and Bessel operators the heat polynomials are in fact polynomials inx andt, however, this property does not hold in general.Communicated by Tom. H. Koornwinder.     

Algorithms for non-linear huber estimation

The Huber criterion for data fitting is a combination of thel ₁ and thel ₂ criteria which is robust in the sense that the influence of wild data points can be reduced. We present a trust region and a Marquardt algorithm for Huber estimation in the case where the functions used in the fit are non-linear. It is demonstrated that the algorithms converge under the usual conditions.     

The absorption of pulsed CO2-laser radiation by ethylene at total pressures from 25 to 3000 Torr

The absorption of pulsed CO₂-laser radiation by ethylene has been measured at total pressures from 25 to 3000 Torr, using the P(12) and P(14) lines in the 10.6 m band, with incident fluences from 0.1 to 0.7 J/cm². Marked deviations from the Beer-Lambert absorption law were observed, with the effective absorption coefficient varying with pressure, fluence, absorption path-length and the addition of non-absorbing gas. Pressure broadening of the rotational lines of the ethylene absorption spectrum was shown to be the major cause of these deviations, together with lesser effects which can be attributed to the rise in temperature of the absorbing gas during the laser pulse.