一种基于多级查找表的高效Huffman编码算法

本文研究了适用于数字信号处理器的一种高效的Huffman编码算法的问题.利用多级查找表建立规则,并将Huffman树分割为若干子树且为分割后的所有子树建立一个统一的查找表的方法,获得了可用较小的查找表来存储Huffman树且能对比特流进行快速解码的结果.     

Zeros in tables of characters for the groups Sn and An

In the representation theory of symmetric groups, for each partition of a natural number n, the partition h() of n is defined so as to obtain a certain set of zeros in the table of characters for S_n. Namely, h() is the greatest (under the lexicographic ordering ) partition among P(n) such that (g) 0. Here, is an irreducible character of S_n, indexed by a partition , and g is a conjugacy class of elements in S_n, indexed by a partition . We point out an extra set of zeros in the table that we are dealing with. For every non self-associated partition P(n), the partition f() of n is defined so that f() is greatest among the partitions of n which are opposite in sign to h() and are such that (g) 0 (Thm. 1). Also, for any self-associated partition of n > 1, we construct a partition () P(n) such that () is greatest among the partitions of n which are distinct from h() and are such that (g) 0 (Thm. 2).Supported by RFBR grant No. 04-01-00463 and by RFBR-BRFBR grant No. 04-01-81001.Translated from Algebra i Logika, Vol. 44, No. 1, pp. 24–43, January–February, 2005.     

Full Non-rigid Group of Sponge and Pina

The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inversion and proved that the r-NRG of this molecule is a group of order 648, containing a subgroup of order 324 without inversions (see J. Math. Chem. 28(4) (2000) 377–388). In this work, a computational method is described, by means of which it is possible to calculate the symmetry group of molecules. We study the full non-rigid group (f-NRG) of Sponge and Pina molecules with C ₂ and C _i point groups, respectively. It proved that these are groups of order 162 and 13122 with 54 and 3240 conjugacy classes, respectively. The character tables of these groups are also computed.     

内蒙古地区沙生植物--沙枣对亚硝酸盐分解作用的研究

利用分光光度法研究了内蒙古地区沙生植物———沙枣对亚硝酸盐的分解作用。结果表明,沙枣中富含的维生素C、维生素E和脯氨酸等抗氧化剂可以作为还原剂与亚硝酸盐作用,从而降低亚硝酸盐的含量;加入的沙枣量愈多,随时间延长对亚硝酸盐的分解能力亦增强,但不呈线性关系。试验结果表明,沙枣不仅可以作水土保持、防沙造林的先锋树种,还由于它富含抗氧化物,可作为人体降低体内亚硝胺生成的良好补充源。     

Topological Space of the Chemical Elements and its Properties

We carried out a mathematical study of 72 chemical elements taking advantage of the chemotopological method. We selected 128 properties to define the elements (physico-chemical, geochemical and chemical properties). Then, we looked for correlated properties and we reduced the number of them to 90. In this way we defined each element as a 90-tuple. Afterwards, we applied principal component analysis and cluster analysis (4 similarity functions and 5 grouping methodologies). Then, we calculated a consensus tree for the 20 dendrograms generated by the CA. Afterwards, we extracted the similarity relationships from the consensus tree and built up a basis for a topology on the set of chemical elements. Finally, we calculated some topological properties (closures, derived sets, boundaries, interiors and exteriors) of several subsets of chemical elements. We found that alkali metals, alkaline earth metals and noble gases appear not related to the rest of the elements. Also, we found that the boundary of non-metals are the semimetals with a stair-shape on the periodic table     

一种基于线结构光的五轴扫描测量系统

提出了一种由线结构光测头、三坐标测量机和两个数控回转工作台组成的五轴线结构光扫描测量系统。该系统通过两个回转工作台带动被测物体旋转,使线结构光测头能够测量到物体四周和顶部的各个区域。为了把从不同角度测量的数据拼合到一起,建立了数据自动拼接的数学模型,并通过测量标准球实现了对系统的标定。实验结果表明,该系统能在一次装夹下完成对复杂物体的完整测量,测量数据能自动拼合在一起,拼接精度达到了0.008mm。