Relations among eigenvalues of Sturm-Liouville problems with different types of leading coefficient functions

For any Sturm-Liouville problem with a separable boundary condition and whose leading coefficient function changes sign (exactly once), we first give a geometric characterization of its eigenvalues λn using the eigenvalues of some corresponding problems with a definite leading coefficient function. Consequences of this characterization include simple proofs of the existence of the λn's, their Prüfer angle characterization, and a way for determining their indices from the zeros of their eigenfunctions. Then, interlacing relations among the λn's and the eigenvalues of the corresponding problems are obtained. Using these relations, a simple proof of asymptotic formulas for the λn's is given.     

一类Lagrangian对偶问题的零对偶间隙性质及其最优路径的收敛性

针对一般的非线性规划问题,利用某些Lagrange型函数给出了一类Lagrangian对偶问题的一般模型,并证明它与原问题之间存在零对偶间隙．针对具体的一类增广La- grangian对偶问题以及几类由非线性卷积函数构成的Lagrangian对偶问题,详细讨论了零对偶间隙的存在性．进一步,讨论了在最优路径存在的前提下,最优路径的收敛性质．     

Synthesis and optoelectronic properties of silole‐containing polyfluorenes with binary structures

2,5‐Bis(2‐bromofluorene‐7‐yl)silole was prepared by a modified one‐pot synthesis with a reverse addition procedure, from which novel silole‐containing polyfluorenes with binary random and alternating structures (silole contents between 4.5 and 25% and high M_w up to 509 kDa were successfully synthesized. The well‐defined repeating unit of the alternating copolymer comprises a terfluorene and a silole ring. Optoelectronic properties including UV absorption, electrochemistry, photoluminescence (PL), and electroluminescence (EL) of the copolymers were examined. The different excitation energy transfers from fluorene to silole of the copolymers in solution and in the solid state were compared. The films of the copolymers showed silole‐dominant green emissions with high absolute PL quantum yields up to 83%. EL devices of the copolymers with a configuration of ITO/PEDOT/copolymer/Ba/Al displayed exclusive silole emissions peaked at around 543 nm and the highest EL efficiency was achieved with the alternating copolymer. Using the alternating copolymer and poly(9,9‐dioctylfluorene) as the blend‐type emissive layer, a maximum external quantum efficiency of 1.99% (four times to that of the neat film) was realized, which was a high efficiency so far reported for silole‐containing polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 756–767, 2007     

On Two Parallel Matched Gratings Demodulation Method of Fiber Grating Strain Sensor

The method of demodulation with two parallel matched fiber Bragg gratings( FBGs)system is introduced to enlarge the range of strain that can be detected by the FBG sensor system.     

Classification of real moduli spaces over genus 2 curves

We classify, in terms of simple algebraic equations, the fixed point sets of the moduli space of stable bundles over genus 2 curves with anti-holomorphic involutions.Research supported by SRF of University of Missouri.     

An algorithm for decomposing a polynomial system into normal ascending sets

We present an algorithm to decompose a polynomial system into a finite set of normal ascending sets such that the set of the zeros of the polynomial system is the union of the sets of the regular zeros of the normal ascending sets.If the polynomial system is zero dimensional,the set of the zeros of the polynomials is the union of the sets of the zeros of the normal ascending sets.     

Construct non-graded bi-Frobenius algebras via quivers

Using the quiver technique we construct a class of non-graded bi-Frobenius algebras. We also classify a class of graded bi-Frobenius algebras via certain equations of structure coefficients.     

Kinetic behaviour of aluminum naphthenate/benzene system in process of gelation and degradation

The kinetic behaviour of aluminum naphthenate/benzene system in the process of gelation and degradation was systematically studied. The results obtained from the kinetic experiments indicated that the gelation stage was in accordance with a kinetic model of an auto-catalytic first-order reaction, and the degradation stage was a simple first-order reaction. The rate constants in these two stages at various temperaturs were measured. And the determined apparent activation energies for the gelation stage and for the degradation stage are 27.5±2.0 and 37.7±2.3 kJ/mol, respectively.     

四阶方程两点边值问题Hermite有限元解的渐近展式与外推

1引言有限元解的渐近展式是提高微分方程数值解精度的重要工具,比如亏量校正和外推就是建立在有限元解的渐近展式的基础之上．许多作者对此进行了大量的研究(见[1]-[4]),特别是文[1],提出了在研究有限元解的渐近展式中十分有用的能量嵌入技巧．本文利用能量嵌入定理得到了四阶方程两点边值问题Hermite有限元解及其二阶平均导数的渐近展式,进一步我们还讨论了它们的Richardson外推公式．考虑四阶方程两点边值问题     

Nanoparticle composites: FePt with wide-band-gap semiconductor

We present a simple way to synthesize FePt and ZnO (wide-band-gap semiconductor) nanoparticle composites. The FePt nanoparticles were fabricated using the method reported by Sun et al. By controlling the heating rate, 3 nm FePt nanoparticles were synthesized. Well-dispersed FePt and ZnO nanoparticle composites were prepared by further adding zinc acetate and oleyl amine into the 3 nm FePt nanoparticle dispersion. By controlling the molar ratio of the FePt and zinc acetate, FePt and ZnO nanoparticle composites with different FePt particle fractions were obtained. The intensity of photo luminescence spectra of the nanoparticle composites increases very much with decreasing FePt particle fraction, whereas the peak position shifts a little. After annealing at 550 °C for half an hour, the nanoparticle composites become magnetically hard or semi-hard with coercivity much dependent on the FePt particle volume fraction. The coercivity of the composites increases with annealing temperature. The composites hold the promise of applications in new generation recording and/or optical devices.