A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairs

After a careful consideration of some of the well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs, we were able to deduce a Frobenius formula for Gelfand pairs. For a given Gelfand pair, the structure coe?cients of its associated double-class algebra can be written in terms of zonal spherical functions. This is a generalization of the Frobenius formula which expresses the structure coe?cients of the center of a finite group algebra in terms of irreducible characters.     

Representation and approximation of convex dynamic risk measures with respect to strong–weak topologies

We provide a representation for strong-weak continuous dynamic risk measures from L^p into L^p_t spaces where these spaces are equipped respectively with strong and weak topologies and p is a finite number strictly larger than one. Conversely, we show that any such representation that admits a compact (with respect to the product of weak topologies) sub-differential generates a dynamic risk measure that is strong--weak continuous. Furthermore, we investigate sufficient conditions on the sub-differential for which the essential supremum of the representation is attained. Finally, the main purpose is to show that any convex dynamic risk measure that is strong-weak continuous can be approximated by a sequence of convex dynamic risk measures which are strong--weak continuous and admit compact sub-differentials with respect to the product of weak topologies. Throughout the arguments, no conditional translation invariance or monotonicity assumptions are applied.     

On the structure of quantum permutation groups

The quantum permutation group of the set corresponds to the Hopf algebra . This is an algebra constructed with generators and relations, known to be isomorphic to for , and to be infinite dimensional for . In this paper we find an explicit representation of the algebra , related to Clifford algebras. For the representation is faithful in the discrete quantum group sense.

     

<Emphasis Type="Italic">K</Emphasis>-finite matrix elements of irreducible Harish-Chandra modules are hypergeometric functions

We show that each K-finite matrix element of an irreducible infinite-dimensional representation of a semisimple Lie group can be obtained from spherical functions by a finite collection of operations. In particular, each matrix element admits a finite expression via the Heckman-Opdam hypergeometric functions.     

A simple approach to reduce dimensionality from comprehensive two-dimensional liquid chromatography coupled with a multichannel detector

Comprehensive two-dimensional liquid chromatographic (LC × LC) systems play an ever increasing role in separation and characterization of complex samples. When coupled with multichannel detectors, such as the diode array detector, these LC × LC systems become especially useful for non-target analysis and identification of patterns based on the information extracted from those complex samples. Nevertheless, due to the large amount of data generated by these systems, the extraction of useful information for the identification of patterns still is one of the major drawbacks for a wider application of this technique. As a preliminary step in data treatment, we have developed a simple and fast way to deal with this large amount of multi-dimensional data by identifying the three-dimensional (3D) regional maxima of each chromatographic peak generated in a LC × LC–DAD system: retention times at the peak maximum in the first- and second-dimensions and the wavelength of the maximum UV absorption. This dataset is then used to build a 3D fingerprinting of the given sample, which alongside the 3D fingerprinting of other samples, can be used to identify different patterns associated with the specific properties of every sample under study. The applicability of the developed methodology was further assessed by performing a non-target LC × LC–DAD analysis of four Portuguese red wine samples.     

Numerical Convergence of the Sinc Discrete Variable Representation for Solving Molecular Vibrational States with a Conical Intersection in Adiabatic Representation

Within the Born-Oppenheimer (BO) approximation, nuclear motions of a molecule are often envisioned to occur on an adiabatic potential energy surface (PES). However, this single PES picture should be reconsidered if a conical intersection (CI) is present, although the energy is well below the CI. The presence of the CI results in two additional terms in the nuclear Hamiltonian in the adiabatic presentation, i.e., the diagonal BO correction (DBOC) and the geometric phase (GP), which are divergent at the CI. At the same time, there are cusps in the adiabatic PESs. Thus usually it is regarded that there is numerical difficulty in a quantum dynamics calculation for treating CI in the adiabatic representation. A popular numerical method in nuclear quantum dynamics calculations is the Sinc discrete variable representation (DVR) method. We examine the numerical accuracy of the Sinc DVR method for solving the Schr?dinger equation of a two dimensional model of two electronic states with a CI in both the adiabatic and diabatic representation. The results suggest that the Sinc DVR method is capable of giving reliable results in the adiabatic representation with usual density of the grid points, without special treatment of the divergence of the DBOC and the GP. The numerical uncertainty is not worse than that after the introduction of an arbitrary vector potential for accounting the GP, whose accurate form usually is not easy to obtain.     

A visual representation for RNA secondary structure and its application

The graphical representation of biological sequences is an important subject in the area of genome studies. We propose a novel visual representation for RNA secondary structures. Some symmetric properties and information on the base distribution and compositions can be intuitively reflected by the projection graphs of the points corresponding to the RNA secondary structures. Then our method is applied to compute the similarity of 12 classical samples and 11 real RNA secondary structures. The results indicate that our method can not only effectively analyze the similarity between RNA secondary structures but also show a high consistency with other literatures. Moreover, our method only needs the geometrical center of the characteristic curve of the RNA secondary structure to compute the similarity matrix, which means a low computational complexity. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Using Huffman coding method to visualize and analyze DNA sequences

On the basis of the Huffman coding method, we propose a new graphical representation of DNA sequence. The representation can avoid degeneracy and loss of information in the transfer of data from a DNA sequence to its graphical representation. Then a multicomponent vector from the representation is introduced to characterize quantitatively DNA sequences. The components of the vector are derived from the graphical representation of DNA primary sequence. The examination of similarities and dissimilarities among the complete coding sequences of β-globin gene of 11 species and six ND6 proteins shows the utility of the scheme.     

Novel numerical and graphical representation of DNA sequences and proteins

We have introduced novel numerical and graphical representations of DNA, which offer a simple and unique characterization of DNA sequences. The numerical representation of a DNA sequence is given as a sequence of real numbers derived from a unique graphical representation of the standard genetic code. There is no loss of information on the primary structure of a DNA sequence associated with this numerical representation. The novel representations are illustrated with the coding sequences of the first exon of β-globin gene of half a dozen species in addition to human. The method can be extended to proteins as is exemplified by humanin, a 24-aa peptide that has recently been identified as a specific inhibitor of neuronal cell death induced by familial Alzheimer's disease mutant genes.     

视觉表征视角下中学化学教科书编排的“三序”结合*——以“物质结构”相关内容为例

教科书的编排有其内在的逻辑结构,视觉表征是教科书的重要组成部分,因此视觉表征的选用也应遵循一定的原则。研究借鉴Gkitzia等人的分析框架对人教版初、高中化学教科书中“物质结构”相关内容的视觉表征进行编码分析。在对表征类型及功能分布分析的基础上,结合教科书中物质结构相关知识内容的编排及学生认知、心理发展规律展开讨论。研究发现,人教版教科书中视觉表征的分布与教科书编排的“三序”原则较为契合,能够针对不同学段、学生特点选用视觉表征。最后,依据研究结论,针对教科书中视觉表征的编选和使用提出建议。