Invariant ideals of twisted crossed products

We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on -algebras. Received: 25 January 2002; in final form: 22 May 2002/Published online: 2 December 2002 This work is partially supported by Hong Kong RGC Direct Grant.     

多小波子空间上的单小波表示

本文在较弱的条件下,建立了2重多小波子空间与单小波子空间的关系.即由2重多小波构造出单小波.一方面,这种单小波的平移伸缩与2重多小波的平移伸缩生成的子空间是完全相同的;另一方面,它具有插值性.因此通过构造出的单小波建立了多小波子空间上的Shannon型采样定理.     

匹配问题实例空间和解空间结构

本文通过研究匹配问题的实例空间，匈牙利算法和解空间三者之间的关系，指出S实例空间的数目与问题复杂度之间的关系既不是充分也不是必要的，而如何对问题的解空间进行合理的分解才能是问题的关键。     

剖析博彩弹子机的赢钱原理

介绍了博彩弹子机 ,运用数学建模法剖析了它的赢钱原理 ,强调了一般博彩业主永远是赢家的道理     

Influence of the sample orientation in Sn<Subscript>2</Subscript>P<Subscript>2</Subscript>S<Subscript>6</Subscript> crystals on the hydrostatic piezoelectric coefficients

The influence of the sample orientation on the effective value of the hydrostatic piezoelectric coefficients d _h ⁽ⁱ⁾ of Sn₂P₂S₆ crystals has been studied. The hydrostatic piezoelectric coefficients d _h ⁽¹⁾ and d′ _h ⁽³⁾ , were measured, d _h ⁽¹⁾ =(244±3) pC/N and d′ _h ⁽³⁾ =(92±1) pC/N. The hydrostatic piezoelectric coefficient d _h ⁽³⁾ for orthogonal axis system was calculated to be d _h ⁽³⁾ =(87±2) pC/N. The, optimal orientation of the sample has been found as (Xy l)−20°-cut. Maximal value of the effective hydrostatic piezoelectric coefficient d _h ⁽¹⁾ equals 260 pC/N. Double rotated samples were also studied. The orientation of the samples insensitive to the pressure has been found. The theoretical mean value of hydrostatic piezoelectric coefficient (d _h ) _mean corresponding to randomly oriented Sn₂P₂S₆ grains in a poled composite has been calculated to be (d _h ) _mean =136 pC/N.     

微模塑法制备PMMA/SiO2二氧化硅杂化材料微结构

以摩尔比为 1∶1的甲基丙烯酸甲酯 (MMA)、甲基丙烯酸 (3 三乙氧基硅烷基 )丙酯 (ESMA)单体、0 .2 %(单体总量的质量分数 )的偶氮二异丁腈AIBN引发剂和四氢呋喃 (THF)溶剂 ,及 2 0 % (总质量分数 )的正硅酸乙酯TEOS合成出PMMA/SiO2 有机 无机杂化的杂化溶胶 .将溶胶在洗净的普通光学玻璃基片表面甩膜 .利用软刻蚀中的微模塑法 ,把有机硅弹性印章复制有精细图纹一面轻放在杂化溶胶膜上进行微模塑 ,外加 1N压力于12 0℃下处理 2h使溶胶凝胶化 .印章剥离后在基片表面就形成了PMMA/SiO2 有机 无机杂化材料的微图纹结构 .从微图纹的光学显微镜照片可以看出微模塑方法制备杂化材料复制的图纹精细度高 ,操作简单易行 ,是一类比较理想的微细图纹结构加工的方法 .     

Degree-regular triangulations of torus and Klein bottle

A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In [8], Lutz has classified all the weakly regular triangulations on at most 15 vertices. In [5], Datta and Nilakantan have classified all the degree-regular triangulations of closed surfaces on at most 11 vertices. In this article, we have proved that any degree-regular triangulation of the torus is weakly regular. We have shown that there exists ann-vertex degree-regular triangulation of the Klein bottle if and only if n is a composite number ≥ 9. We have constructed two distinctn-vertex weakly regular triangulations of the torus for eachn ≥ 12 and a (4m + 2)-vertex weakly regular triangulation of the Klein bottle for eachm ≥ 2. For 12 ≤n ≤ 15, we have classified all then-vertex degree-regular triangulations of the torus and the Klein bottle. There are exactly 19 such triangulations, 12 of which are triangulations of the torus and remaining 7 are triangulations of the Klein bottle. Among the last 7, only one is weakly regular.     

Distribution results for lattices in SL(2,ℚ p )

In this paper we study the ergodic properties of the linear action of lattices Γ of SL(2,ℚ_p) on ℚ_p × ℚ_p and distribution results for orbits of Γ. Following Serre, one can define a “geodesic flow” for an associated tree (actually associated to GL(2,ℚ_p)). The approach we use is based on an extension of this approach to “frame flows” which are a natural compact group extension of the geodesic flow.     

Shell effects in the symmetric-modal fission of pre-actinide nuclei

Mass distributions of fragments in the low-energy fission of nuclei from ¹⁸⁷Ir to ²¹³At have been analysed. This analysis has shown that shell effects in symmetric-mode fragment mass yields from the fission of pre-actinide nuclei could be described if one assumes the existence of two strongly deformed neutron shells in the arising fragments with neutron numbers N₁ ≈ 52 and N₂ ≈ 68. A new method has been proposed for quantitatively describing the mass distributions of the symmetric fission mode for pre-actinides with A ≈ 180–220.