Hausdorff dimension of some kind of alternating Oppenheim series expansion

For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.     

Finite generation of symmetric ideals

Let be a commutative Noetherian ring, and let be the polynomial ring in an infinite collection of indeterminates over . Let be the group of permutations of . The group acts on in a natural way, and this in turn gives the structure of a left module over the group ring . We prove that all ideals of invariant under the action of are finitely generated as -modules. The proof involves introducing a certain well-quasi-ordering on monomials and developing a theory of Gröbner bases and reduction in this setting. We also consider the concept of an invariant chain of ideals for finite-dimensional polynomial rings and relate it to the finite generation result mentioned above. Finally, a motivating question from chemistry is presented, with the above framework providing a suitable context in which to study it.

     

The association of octadecyl-end-capped poly-(sodium 2-acrylamido-2-methylpropanesulfonates) in water and salt solutions: A study by fluorescence spectroscopy and isothermal titration calorimetry

Steady-state fluorescence spectroscopy and isothermal titration calorimetry (ITC) have been used to study the aggregation in aqueous solutions of poly-(2-acrylamido)-2-methylpropanesulfonic acids, sodium salt mono-endcapped with either N,N-di-n-octadecyl or N-4-[(1-pyrenyl)butyl]-N-n-octadecyl which were prepared by free radical polymerization of 2-(acrylamido)-2-methylpropane sulfonic acid (AMPS) initiated with the azo compounds, 4,4'-azobis{cyano-N,N-di-n-octadecyl}pentanamide and 4,4'-azobis{cyano-N,N-[4-(1-pyrenyl)butyl]-n-octadecyl}pentanamide, respectively. Both techniques indicate the occurrence of multimolecular aggregates in solutions of the polymers in water and in 0.2 M NaCl. The concentration range for aggregation is about 1-14 mmol AMPS l^-1 (0.5-2.7 g l^-1) in 0.2 M NaCl and the enthalpy of micellization, estimated from ITC data, is ∼100 J [mol AMPS]^-1. The accessibility of the chromophores to neutral molecules and to cationic species was assessed by quenching of fluorescence with nitromethane and thallium nitrate, respectively. The association of the mono-endcapped polymers is compared to that of PAMPS derivatives carrying hydrophobic groups randomly attached along the chain. Received 7 August 2000 and Received in final form 26 October 2000     

Photoinduced transformations and holographic recording in nanolayered a-Se/As2S3 and AsSe/As2S3 films

Received: 13 October 1998 / Accepted: 9 December 1998 / Published online: 24 February 1999     

等离子体效应对碳的类氢离子能级的影响

通过在狄拉克方程中考虑德拜休克尔(Debye-Hückel)屏蔽势,研究了类氢离子C5 低能级能量1s(2S1/2),2s(2S1/2),2p(2P1/2和2P3/2)随等离子体电子温度及电子密度的变化规律,计算得到类氢离子C5 能级能量及能级电离势随等离子体环境的变化关系。同时,拟合得到了基于德拜休克尔屏蔽势下相当好的束缚态能级能量随等离子体环境变化的解析公式,利用该公式得到了类氢离子C5 相应各能级发生压致电离的临界电子密度,其结果与其它文献比有很好的可比性。结果表明:束缚态能级能量随等离子体电子温度的升高而减小,随等离子体电子密度的增大而增大。能级能量百分漂移量的对数值与等离子体电子密度的对数值以及等离子体电子温度的对数值之间均呈现出近似线性关系。对计算等离子体电离态分布及光谱模拟具有一定的意义。     

荒漠-绿洲交错地带典型植被光谱特征研究

植被对区域生态环境保护具有重要意义,尤其是在荒漠-绿洲交错地带,植被对土壤保持、提高土地的抗剪切性能有重要意义,对土壤风蚀和荒漠化防治的影响作用较大,利用高光谱技术测定并分析荒漠-绿洲交错带典型植被的光谱特性,不仅能够指导区域的植被遥感分类,还能够对植被实行远程监控提供依据。研究借助美国Field Spec 4高分辨率地物光谱仪,在研究区采集棉花、柽柳、梭梭和盐穗木等四种典型植被不同条件下的光谱数据,在对数据进行归类、筛选及综合处理后,分别对原始数据进行FDR(一阶导数反射率)和RLR(倒数取对数反射率)变换。利用原始数据、FDR和RLR分别分析不同植物的光谱敏感波段和表达方式。结果表明：植物的光谱曲线具有类似的变化特征,植被种类不同在“红边”区和近红外780～1 260 nm波段的表达方式区别较大;植物对可见光的吸收非常强烈,对不同波长的光吸收强弱变化会形成波峰和波谷;植物红边特征具有特殊性,蕴含植物自身的特有信息,三种方式的处理结果显示,光谱特征在经FDR计算后,植物光谱红边特征区差异性非常明显;利用三种不同方式处理后的光谱数据,分别来计算改进的植物NDVI值,经RLR变换后重新计算得到的NDVI值在植物不同种之间表现出较大差别,用于植物种类区分的效果明显。     

一种基于HLLC算法的Mie-Grüneisen多介质混合模型

建立一种修正的HLLC （Harten-Lax-Van Leer-Contact）格式下稳定的Mie-Grüneisen多介质混合计算模型.Mie-Grüneisen混合模型中的通量包括守恒和非守恒两个部分,原始的HLLC格式对守恒部分适用,但是原始的HLLC格式直接用于非守恒部分,很难控制住数值振荡的产生.在原始格式中,间断面的移动速度为间断网格的左侧或右侧速度,修正后替换为网格中的平均速度,经过修正后,对HLLC格式重新进行推导,并随之扩展到二维问题.数值实验表明,利用修改后的HLLC格式,Mie-Grüneisen混合模型可以取得较好的稳定性和准确性.     

压缩变形对C20富勒烯分子电子传输特性的影响

The geometry,electronic structure and electronic transmission of Au electrode-compressed C20 fullerene Au electrode systems are investigated systemically,and some interesting results are obtained by use of molecular dynamics,Extend Hückel method of the first principle,and Green's function based method. The analytical results show that,due to intervention of Au electrodes,the electronic structure of compressed C20 fullerene is changed significantly,the coalescent between C20 fullerene and Au electrodes is intervenient of covalent bond and electrovalent bond,and the compressed C20 fullerenes are better conductors of electricity than those uncompressed or slightly compressed ones. The methods and the relative conclusions are beneficial to go further deep into electronic transmission of carbon fullerenes.     

贵金属金的状态方程

 提出了一个热压强的计算公式,从而获得金的状态方程。并结合实验数据与文献中常用的其它两个状态方程进行了比较。结果发现,修正后的状态方程与实验数据吻合很好,略优于其它两个状态方程。     

Grünwald插值算子的L2收敛性

证明了以Legendre多项式的极值点为插值结点组的Grünwald插值多项式在L2范数下是收敛的.