The support designs of the triply even binary codes of length 48

In this paper, we present examples of codes all of whose weight classes support 1‐designs, with duals whose classes include two that support 2‐designs. We can find these examples in the triply even binary codes of length 48, which have been classified by Betsumiya and Munemasa.     

Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.     

Alkane isomers: presence in petroleum ether and complexity

The presence and absence of alkane isomers in petroleum and petroleum derivatives depend on the complexity of these structures. It was assumed that the more complex the structure is the less probable it is that that the molecule can be detected in any petroleum derivative. Complexity is a vague concept, which has not been defined in quantitative terms yet, and therefore there is no experimental method, which could be used to determine ‘complexity’. Mass spectrometry and infrared spectroscopy in combination with gas chromatography were used to identify the various structural isomers of alkanes in petroleum ether. The isomers were categorised in quantitative terms by using topological indices and linear discriminant analysis. It was found that alkanes possessing a more complex, highly branched structure are less probable to be detected in petroleum ether than isomers with a simpler backbone structure. It was proposed that the experimental ‘measure’ of the complexity of isomer_i should be proportional to 1/C_i , where C_i , denotes the concentration of isomer_i in a (primary) petroleum derivative.     

氢键准则在DMSO水溶液中应用的评价

利用分子动力学模拟方法, 分别采用几何准则和能量准则分析了不同浓度下的二甲基亚砜(DMSO)水溶液的氢键统计和动力学等特性. 结果显示, 两种氢键准则可以很好地反映出溶液的氢键性质随浓度的变化趋势. 通过分析比较发现, 由于几何准则不能有效地排除具有弱对势能的分子对, 因此其统计的氢键数量要大于能量准则的结果.此外, 能量准则对于分子间相对取向的区分存在不足, 进而引起氢键寿命的计算结果偏大.因此,为使氢键分析更加准确, 本文建议使用几何-能量混合型氢键准则.     

Weight distributions of a class of cyclic codes with arbitrary number of nonzeros in quadratic case

Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three nonzeros. Recently, the authors of [37] constructed a class of cyclic codes with arbitrary number of nonzeros, and computed the weight distribution for several cases. In this paper, we determine the weight distribution for a new family of such codes. This is achieved by introducing certain new methods, such as the theory of Jacobi sums over finite fields and subtle treatment of some complicated combinatorial identities.