Kurzweil-Henstock type integral on zero-dimensional group and some of its applications

A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case. Supported by RFFI-08-01-00669.     

Andrews–Gordon type identities from combinations of Virasoro characters

For p∈{3,4} and all p′>p, with p′ coprime to p, we obtain fermionic expressions for the combination χ _1,s ^p,p′+q ^Δ χ _p−1,s ^p,p′ of Virasoro (W ₂) characters for various values of s, and particular choices of Δ. Equating these expressions with known product expressions, we obtain q-series identities which are akin to the Andrews–Gordon identities. For p=3, these identities were conjectured by Bytsko. For p=4, we obtain identities whose form is a variation on that of the p=3 cases. These identities appear to be new. The case (p,p′)=(3,14) is particularly interesting because it relates not only to W ₂, but also to W ₃ characters, and offers W ₃ analogues of the original Andrews–Gordon identities. Our fermionic expressions for these characters differ from those of Andrews et al. which involve Gaussian polynomials. BF is partially supported by grant number RFBR 05-01-01007, and OF by the Australian Research Council (ARC).     

Projective Brauer Theory

In this article, we define and study a new concept of projective Brauer characters. Following the direct approach as taken in Navarro (1998 Navarro , G. ( 1998 ). Characters and Blocks of Finite Groups. Cambridge , UK : Cambridge University Press . [Google Scholar]) and Isaacs (1975 Isaacs , I. M. ( 1975 ). Character Theory of Finite Groups . New York : Academic Press . [Google Scholar]), we study the resulting projective blocks of projective Frobenius characters and projective Brauer characters of a given group determined by certain linkage condition as an introduction to a projective extension of classic Brauer theory.     

On the Character Degrees of Suzuki p-Groups of Type A and C

In this note, we construct the irreducible characters of Suzuki p-groups of types A _p (m, θ) and C _p (m, θ, ?).     

Self‐assembly: An intriguing relationship between structures of metal complexes and shapes of ancient Chinese characters

Self‐assembly is a fundamental principle, which generates structural organization on all scales from molecules to galaxies. In the field of chemistry and materials science, the self‐assembly process driven by noncovalent interactions offers considerable advantages over the stepwise bond formation in the construction of large supramolecular assemblies with different sizes and shapes. The structures of metal clusters are mainly constructed from the assembly of mononuclear metal center to dinuclear, trinuclear species, and so on. It is of interest that Chinese ancient people also used this concept to create and encrypt characters. Herein, we report on an intriguing relationship between structures of metal complexes and the shapes of ancient Chinese characters, in which the self‐assembly principle is clearly demonstrated.     

An Improved Chinese String Comparator for Bloom Filter Based Privacy-Preserving Record Linkage

With the development of information technology, it has become a popular topic to share data from multiple sources without privacy disclosure problems. Privacy-preserving record linkage (PPRL) can link the data that truly matches and does not disclose personal information. In the existing studies, the techniques of PPRL have mostly been studied based on the alphabetic language, which is much different from the Chinese language environment. In this paper, Chinese characters (identification fields in record pairs) are encoded into strings composed of letters and numbers by using the SoundShape code according to their shapes and pronunciations. Then, the SoundShape codes are encrypted by Bloom filter, and the similarity of encrypted fields is calculated by Dice similarity. In this method, the false positive rate of Bloom filter and different proportions of sound code and shape code are considered. Finally, we performed the above methods on the synthetic datasets, and compared the precision, recall, F1-score and computational time with different values of false positive rate and proportion. The results showed that our method for PPRL in Chinese language environment improved the quality of the classification results and outperformed others with a relatively low additional cost of computation.     

Dirichlet characters,Gauss sums and arithmetic Fourier transforms

In this paper, a general algorithm for the computation of the Fourier coefficients of 2π-periodic(continuous) functions is developed based on Dirichlet characters, Gauss sums and the generalized M¨obius transform. It permits the direct extraction of the Fourier cosine and sine coefficients. Three special cases of our algorithm are presented. A VLSI architecture is presented and the error estimates are given.     

互素作用下的不变块(英文)

令A,G为有限群且(|A|,|G|)=1.设A通过自同构作用在G上.令B是G的A-不变块.若B的每一个指标都是A-不变的,且B的亏群是循环群,则A中心化B的某一亏群.     

Three pure inorganic materials based on Strandberg-type phosphomolybdate and different transition metal linkers

Abstract

Three inorganic materials based on Strandberg polyoxoanion, Na₁₀[Ag(P₂Mo₅O₂₃)]₂·8H₂O (1), Na₈[{Cu(H₂O)₄}(HP₂Mo₅O₂₃)₂]·8H₂O (2), and Na₈[{Co(H₂O)₄}(HP₂Mo₅O₂₃)₂]·6H₂O (3), were hydrothermally synthesized and characterized by elemental analyses, IR, TG, and single crystal X-ray diffraction analyses. The compounds are based on the [P₂Mo₅O₂₃]^6? cluster and transition metal linkers. Compound 1 is a 1-D wave-like chain connected by Ag⁺ bridges. Compounds 2 and 3 are isostructural dimers bonded by {Cu(H₂O)₄} or {Co(H₂O)₄} linkers. The 1-D chain and dimeric clusters of 1-3 are further extended to 3-D supramolecular networks via hydrogen bonds and supramolecular interactions. Channels with different sizes are observed in 1-3, in which isolated Na⁺ and lattice water molecule fill the channels via intermolecular interactions. Weak interactions play important roles in stabilizing the three 3-D networks. Electrochemical and electrocatalytic properties of 1-3 have been investigated.