Symmetry specified enumeration of substituted derivatives: an easy solution to the complex problem

Several sophisticated methods to solution of symmetry specified enumeration problems are available in the modern literature. In this paper we propose a simple technique that allows one to manually compute the exact numbers of fixed-symmetry derivatives for a given structure either with inclusion or ignoring the substitution patterns. The basic idea of the method suggested consists in the derivation of Pólya-like cycle indices for the automorphism groups of specially constructed orbit partition graphs; the expansion of these indices and subsequent simple calculations result in the desired numbers of substituted derivatives with achiral substituents. Limitations of the new technique (and a method suggested earlier) depend on the relevance of the orbit partitions for particular subgroups of the point symmetry group. For illustration purposes, the results obtained for the prismane (D _3h ) and adamantane (T _d ) structures are discussed. In the former case the numbers of substituted derivatives can be found for all subgroups of the D _3h group, whereas in the latter case these numbers can be determined for eight out of eleven subgroups of the T _d point symmetry group. This work is based on the text of the lecture presented by the authors at the 5th All-Russia Conference on Molecular Modeling (Moscow, April 2007). The paper deals with the methodology and detailed treatment of applied aspects related to solution of enumeration problems for substituted derivatives with prescribed symmetry groups. Unlike the known methods of symmetry specified enumeration, the technique suggested is simple enough and may be regarded as generalization of the Pólya methodology, which is widely used by chemists. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 227–245, February, 2008.     

A Generalized Markov Sampler

A recent development of the Markov chain Monte Carlo (MCMC) technique is the emergence of MCMC samplers that allow transitions between different models. Such samplers make possible a range of computational tasks involving models, including model selection, model evaluation, model averaging and hypothesis testing. An example of this type of sampler is the reversible jump MCMC sampler, which is a generalization of the Metropolis–Hastings algorithm. Here, we present a new MCMC sampler of this type. The new sampler is a generalization of the Gibbs sampler, but somewhat surprisingly, it also turns out to encompass as particular cases all of the well-known MCMC samplers, including those of Metropolis, Barker, and Hastings. Moreover, the new sampler generalizes the reversible jump MCMC. It therefore appears to be a very general framework for MCMC sampling. This paper describes the new sampler and illustrates its use in three applications in Computational Biology, specifically determination of consensus sequences, phylogenetic inference and delineation of isochores via multiple change-point analysis.     

The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits

We investigate some basic questions concerning the relationship between the restricted Grassmannian and the theory of Banach Lie-Poisson spaces. By using universal central extensions of Lie algebras, we find that the restricted Grassmannian is symplectomorphic to symplectic leaves in certain Banach Lie-Poisson spaces, and the underlying Banach space can be chosen to be even a Hilbert space. Smoothness of numerous adjoint and coadjoint orbits of the restricted unitary group is also established. Several pathological properties of the restricted algebra are pointed out.     

丁基罗丹明B-Bi(Ⅲ)-SCN~--PVA-Tween-80体系荧光熄灭法测定痕量铋

本文研究了在PVA和Tween 80存在下,铋离子与硫氰酸钾和丁基罗丹明B形成缔合型三元配合物,使丁基罗丹明B的荧光熄灭,建立了痕量铋的荧光分析新方法。工作曲线线性范围为0～5.0μg/25mL。方法灵敏度高,ε_(588)为3.5×10~5L·mol~(-1)·cm~(-1),操作简便。用于铸铁中痕量铋的测定,结果满意。     

HPLC法测定阿奇霉素葡萄糖注射液中阿奇霉素的含量

利用高效液相色谱法，以VP-ODS型色谱柱，乙腈-异丙醇-水-氨水（60：25：15：0.1)为流动相，于210nm波长处测定了阿奇霉素葡萄糖注射液中阿奇霉素葡萄糖注射液中阿奇霉素的含量。阿奇霉素的浓度在0.75-1.75mg/mL线性关系良好，线性方程的A=881910.4c-16208.2，相关系数r=0.9999。阿奇霉素的平均回收率为99.59%，测定结果的相对标准偏差为1.31%。     

Coupling leads to chaos

The main goal of this paper is to prove analytically the existence of strange attractors in a family of vector fields consisting of two Brusselators linearly coupled by diffusion. We will show that such a family contains a generic unfolding of a 4-dimensional nilpotent singularity of codimension 4. On the other hand, we will prove that in any generic unfolding Xμ of an n-dimensional nilpotent singularity of codimension n there are bifurcation curves of (n−1)-dimensional nilpotent singularities of codimension n−1 which are in turn generically unfolded by Xμ. Arguments conclude recalling that any generic unfolding of the 3-dimensional nilpotent singularity of codimension 3 exhibits strange attractors.     

Structural characterisation of Sb-based heterostructures by X-ray scattering methods

Antimonide-based superlattices dedicated to the elaboration of opto-electronic devices have been studied by X-ray scattering techniques. In particular, specular and non-specular X-ray reflectometry experiments have been performed on two MBE-samples elaborated with different shutter sequences at the interfaces. The results have shown a limitation of the incorporation of Sb species in the subsequent InAs layer for one of the samples, as expected.Then, a study on a InGaAs-cap layer/(InGaAs/AlAsSb)_N superlattice grown on a InGaAs/InP buffer layer by both specular X-ray reflectometry and High resolution X-ray diffraction is reported. In particular, the results have revealed the presence of a highly disturbed thin-layer on top of the MOVPE-made GaInAs, whose presence has been explained by In-concentration modification during the desoxidation procedure at the surface of the MOVPE-made GaInAs.Beside the results on the Sb-based heterostructures, the use of X-ray scattering metrology as a routinely working non-destructive testing method has been emphasized.     

Simultaneous spectrophotometric determination of Zinc(II) and Nickel(II) with 1-(2-pyridylazo)-2-naphthol

A new procedure for the simultaneous spectrophotometric determination of Zn(II) and Ni(II) with 1-(2-pyridylazo)-2-naphthol as chromogenic reagent has been developed. It is based on resolution of the mixed spectrum over the wavelength range 530–590 nm by applying a least-squares fitting program to standard spectra from each component. The spectra are recorded at an apparent pH of 5.0, provided by an acetate buffer in a mixed 6040 v/v 2-ethoxyethanol/water medium. The relative standard deviations for determination of 13.7 g of Ni and 31.0 g of Zn were 1.9 and 1.0%, respectively (8 replications). The method has been applied to the analysis of iron surfaces coated with a Zn-Ni alloy. The results are compared with those obtained by atomic-absorption spectrophotometry.     

X射线荧光光谱滤纸片法测定矿石中的铜

我们用Ｘ射线荧光光谱滤纸片法分析了古今１３铜矿石样品中的铜含量，测量结果与化学法一致。此法不需要铜矿石的标样，而且手续简单，方便，检出限低，灵敏度高，测量结果正确可靠，是分析矿石中单一或几个元素的含量较好的方法之一。