Formal orthogonal polynomials revisited. Applications

From some results concerning the formal orthogonal polynomials, already proved in [5], we develop new properties of generalized adjacent polynomials which correspond to a change in the weight function. A new structure of the singular blocks is given. These results have a direct application to Lanczos methods, theG and -algorithms.     

The zeros of Faber polynomials generated by an -star

It is shown that the zeros of the Faber polynomials generated by a regular -star are located on the -star. This proves a recent conjecture of J. Bartolomeo and M. He. The proof uses the connection between zeros of Faber polynomials and Chebyshev quadrature formulas.

     

Degenerate polynomial patches of degree 11 for almostGC 2 interpolation over triangles

We consider the problem of interpolating scattered data in ³ by analmost geometrically smoothGC ² surface, where almostGC ² meansGC ² except in a finite number of points (the vertices), where the surface isGC ¹. A local method is proposed, based on employing so-called degenerate triangular Bernstein-Bézier patches. We give an analysis of quintic patches forGC ¹ and patches of degree eleven for almostGC ² interpolation.     

Analyzing electrochemical noise with Chebyshev’s discrete polynomials

The principles underlying a novel method intended for analyzing experimental data obtained when studying fluctuation processes are considered. The method in question is Chebyshev’s spectroscopy. The application of this method allows one to determine statistic characteristics of steady-state electrochemical noise against the background of severe deterministic interference without invoking the procedure of the fitting of the initial data. The potentialities of this novel method, which is intended for treating noise experiment, are demonstrated by examining model examples and analyzing the electrochemical noise generated by a lithium electrode placed in an aprotic organic electrolyte.     

选相原位法合成立方氮化硼的关键影响因素

利用选相原位法在水溶液中成功制备出了立方氮化硼晶体，对反应条件进行了优化。结果表明，利用选相原位法合成立方氮化硼的最佳实验条件是：反应压力为10.0 MPa，在氯离子加入下利用混合氮源进行反应。在该条件下得到了纯相的立方氮化硼晶体。     

不同光滑度立方体氧化铁对液晶电光性能的改善

向列相液晶被广泛应用于液晶显示中,但是由于杂质的存在,会导致液晶的驱动电压变大,增加能耗。 为了降低阈值电压和饱和电压,通常向液晶中添加纳米颗粒来提高电光性能。 本文利用水热法制备了表面粗糙和光滑的两种立方体Fe₂O₃纳米颗粒,其形貌均匀,尺寸约550 nm。 将二者分别掺杂到向列相液晶E7中,结果表明,粗糙立方体Fe₂O₃/E7复合体系具有比光滑立方体Fe₂O₃/E7复合体系和向列相液晶E7更优的电光性能,且在掺杂质量分数为0.4%时,其电光性能达到最优,阈值电压和饱和电压分别降低9.9%和11.6%,对比度增大80%,响应时间降低至6.0 ms。 这归因于粗糙立方体Fe₂O₃具有足够的表面积和表面所带电荷更多,所以会更易吸附体系中的杂质离子和减弱杂质离子的屏蔽作用,从而提高了电光性能。     

Closed‐form rectangular atomic wave functions of an N‐dimensional atom

A closed‐form expression has been derived to obtain the N‐dimensional rectangular atomic wave functions. The wave functions can be obtained straightforwardly with the knowledge of the angular momentum quantum numbers and the dimension and there is no need to employ recursive methods as in previous works. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 263–274, 2002     

鞘磷脂和神经节苷脂对磷脂酰乙醇胺混合脂超分子体系液晶态立方相Im3m和Pn3m结构影响的研究

用磷脂酰乙醇胺(DEPE)、鞘磷脂(Sphingomyeline, Sph)、神经节苷脂(Gm1)和胆固醇(Chol)模拟了生物膜超分子体系液晶态结构, 通过用小角X射线衍射(SAXD)对混合脂体系液晶态结构进行了研究, 鉴定出了两种立方相: 即Im3m(Q²²⁹)和Pn3m(Q²²⁴)结构. 实验发现, 鞘磷脂的含量对DEPE膜的结构有一定的影响, 随着鞘磷脂浓度的增加, 混合脂体系的液晶态结构发生了由Im3m(Q²²⁹)到Pn3m(Q²²⁴)的变化. 神经节苷脂(Gm1)的含量对混合脂体系的液晶态结构也有一定的影响, 当神经节苷脂(Gm1)含量达到某一临界值时, 混合脂体系的液晶态结构发生了从Im3m(Q²²⁹)到Pn3m(Q²²⁴) 的变化. 当DEPE-Shp-Gm1超分子聚集体中含有胆固醇时, 胆固醇的极性头部(—OH)与磷脂酰乙醇胺(DEPE)、鞘磷脂(Shp)、神经节苷脂(Gm1)的极性头部通过氢键相互作用形成液晶态立方相Im3m(Q²²⁹)结构, 再通过疏水/亲水相互作用形成稳定的Pn3m (Q²²⁴)结构.