The number of symmetric colorings of the dihedral group D3

We compute the number of symmetric r-colorings and the number of equivalence classes of symmetric r-colorings of the dihedral group D₃.     

Association of biotin with silver (I) in solution: a circular dichroism study

A strong polymeric helical complex of Ag(I) with biotin, a water-soluble vitamin also called vitamin H or B₇, has been described in the crystal phase, yet with missing spatial characteristic of its solution structure. In this work, the complexation of d-(+)-biotin with Ag⁺ in aqueous solution has been studied by means of circular dichroism spectroscopy and mass spectrometry with electrospray ionization in positive mode (MS-ESI+). For comparison, the spectra of the Nujol suspension of studied systems in the solid state were also measured. The results indicate that the Ag(I)–biotin complex has a helical arrangement of the biotin molecules in solution. Our results show that the binding process involves the thioether sulfur atom and ureido carbonyl oxygen atom, while the carboxylate side group is not coordinated with the silver. The MS-ESI experiments have revealed the composite structures of Ag⁺ with biotin of various constitutions, which represent the products of the polymeric helical Ag(I)–biotin complex.     

Verbal ordinal classification with multicriteria decision aiding

Professionals in neuropsychology usually perform diagnoses of patients’ behaviour in a verbal rather than in a numerical form. This fact generates interest in decision support systems that process verbal data. It also motivates us to develop methods for the classification of such data. In this paper, we describe ways of aiding classification of a discrete set of objects, evaluated on set of criteria that may have verbal estimations, into ordered decision classes. In some situations, there is no explicit additional information available, while in others it is possible to order the criteria lexicographically. We consider both of these cases. The proposed Dichotomic Classification (DC) method is based on the principles of Verbal Decision Analysis (VDA). Verbal Decision Analysis methods are especially helpful when verbal data, in criteria values, are to be handled. When compared to the previously developed Verbal Decision Analysis classification methods, Dichotomic Classification method performs better on the same data sets and is able to cope with larger sizes of the object sets to be classified. We present an interactive classification procedure, estimate the effectiveness and computational complexity of the new method and compare it to one of the previously developed Verbal Decision Analysis methods. The developed and studied methods are implemented in the framework of a decision support system, and the results of testing on artificial sets of data are reported.     

ChemInform Abstract: Unique Seven-Node Rare-Earth Octacyanomolybdate(IV) Three-Dimensional Molecular Frameworks: {[Er(H2O)5(Er (H2O)4)3] [Mo(CN)8]3·11H2O}n and {[Eu(H2O)5(Eu (H2O)4)3] [Mo(CN)8]3·11H2O}n.

Good quality single crystals of the title compound are obtained by reaction of H₄[Mo(CN)₈] with the rare earth carbonates.     

Ab Initio structure determination of vaterite by automated electron diffraction

"This is a mineral about which there has been much discussion" is a typical statement about vaterite in older standard textbooks of inorganic chemistry. This polymorph of CaCO(3) was first mentioned by H. Vater in 1897, plays key roles in weathering and biomineralization processes, but occurs only in the form of nanosized crystals, unsuitable for structure determination. Its structure could now be solved by automated electron diffraction tomography from 50 nm sized nanocrystals.     

On topological Clifford semigroups embeddable into products of cones over topological groups

In this paper we give characterizations of topological Clifford semigroups which are embeddable into Tychonoff products of topological semilattices and cones over topological groups. Also we characterize topological Clifford semigroups which embed into compact topological Clifford semigroups.     

Spectral asymptotics for an elliptic operator in a locally periodic perforated domain

We consider the homogenization of an elliptic spectral problem with a large potential stated in a thin cylinder with a locally periodic perforation. The size of the perforation gradually varies from point to point. We impose homogeneous Neumann boundary conditions on the boundary of perforation and on the lateral boundary of the cylinder. The presence of a large parameter 1/ε in front of the potential and the dependence of the perforation on the slow variable give rise to the effect of localization of the eigenfunctions. We show that the jth eigenfunction can be approximated by a scaled exponentially decaying function that is constructed in terms of the jth eigenfunction of a one-dimensional harmonic oscillator operator.     

Acoustic wave velocities and elastic properties of Sn2P2(Se0.28S0.72)6 solid solutions

An experimental study and analysis is presented of the acoustic properties of Sn₂P₂(Se_0.28S_0.72)₆ ferroelectric crystals. Complete matrices of elastic stiffness and compliance as well as characteristic acoustic slowness surfaces have been obtained. The directions of propagation and polarisation of the slowest acoustic waves were determined. It was found that the elastic properties and the acoustic wave velocities for Sn₂P₂(Se_0.28S_0.72)₆ and Sn₂P₂S₆ crystals are almost the same at room temperature.     

Verma type modules for toroidal lie algebras

We study the structure of imaginary Verma modules induced from the"natural"Borel subalgebra of a toroidal Lie algebra. In particular, we establish a criterion of irreducibility for imaginary Verma modules and describe their submodules and irreducible quotients. We also describe the structure of Verma type modules in the case of sl(2)-toroidal Lie algebra over two variables.