On simple modules over conformal Galilei algebras

We study irreducible representations of two classes of conformal Galilei algebras in 1-spatial dimension. We construct a functor which transforms simple modules with nonzero central charge over the Heisenberg subalgebra into simple modules over the conformal Galilei algebras. This can be viewed as an analogue of oscillator representations. We use oscillator representations to describe the structure of simple highest weight modules over conformal Galilei algebras. We classify simple weight modules with finite dimensional weight spaces over finite dimensional Heisenberg algebras and use this classification and properties of oscillator representations to classify simple weight modules with finite dimensional weight spaces over conformal Galilei algebras.     

On Cohen-Macaulay modules over non-commutative surface singularities

We generalize the results of Kahn about a correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities. As an application, we give examples of non-commutative surface singularities which are not Cohen-Macaulay finite, but are Cohen-Macaulay tame.     

Formation of Pyrogenic Silica: Spectroscopic and Quantum Chemical Insight

This article describes the genesis of amorphous silica under high-heat conditions from SiO₂ molecules through protoparticles, primary particles, and aggregates to agglomerates using vibrational spectra and quantum chemical simulations data. The impact of small molecules (water, HCl, CO₂) is also discussed. The article also explains the nature of the pyrogenic silica amorphism.     

On a problem of Eidelheit from The Scottish Book concerning absolutely continuous functions

A negative solution of Problem 188 posed by Max Eidelheit in the Scottish Book concerning superpositions of separately absolutely continuous functions is presented. We discuss here this and some related problems which have also negative solutions. Finally, we give an explanation of such negative answers from the “embeddings of Banach spaces” point of view.     

Aspects of Pre-quantum Description of Deformed Theories

We discuss deformations of the classical systems in the phase space and show that one can use non-canonical transformations to relate regular and deformed models. On the other hand some of the models can be obtained as a classical limit of the deformed quantum models, i.e. as the result of the dequantization procedure. Nonrelativistic deformations are described.     

Multigrid solver for the reference interaction site model of molecular liquids theory

In this article, we propose a new multigrid-based algorithm for solving integral equations of the reference interactions site model (RISM). We also investigate the relationship between the parameters of the algorithm and the numerical accuracy of the hydration free energy calculations by RISM. For this purpose, we analyzed the performance of the method for several numerical tests with polar and nonpolar compounds. The results of this analysis provide some guidelines for choosing an optimal set of parameters to minimize computational expenses. We compared the performance of the proposed multigrid-based method with the one-grid Picard iteration and nested Picard iteration methods. We show that the proposed method is over 30 times faster than the one-grid iteration method, and in the high accuracy regime, it is almost seven times faster than the nested Picard iteration method.     

Detailed investigations of ZnO photoelectrodes preparation for dye sensitized solar cells

Wurtzite ZnO hexagonal nanopyramids were successfully synthesized in the liquid phase from homogeneous methanolic solutions of zinc acetate and tetramethylammonium hydroxide at an excess of zinc ions. The formation and properties of the nanocrystals were examined as a function of synthesis conditions. No significant influence of the [Zn(2+)]/[OH(-)] ratio was noticed on the final particle size, in spite of increased amounts of OH(-) ions, which tend to accelerate the particle nucleation and growth. Nevertheless, the reactant concentration ratio influences the surface properties of the ZnO nanocrystals. Mesoporous ZnO films were prepared by doctor blading ethanolic pastes containing ZnO nanoparticles and ethyl cellulose onto FTO conductive glass substrate followed by calcination. Additionally, the influence of a plasticizer (triacetin)-used during the paste preparation-on the film quality was investigated. A higher content of ZnO nanoparticles and plasticizer in the pastes improved the film quality. Four different temperatures (i.e., 400, 425, 450, and 475 °C) were used for the film calcination and their influence on the structural properties of the films was characterized. In principle, increasing the calcination temperature goes hand in hand with an increase of particle size, as well as the pore diameter and reduction of the surface area. Suitable mesoporous films were employed as photoanodes in dye sensitized solar cells (DSSCs). In order to assess the effect of the varied parameters on complete DSSC devices-using cis-diisothiocyanato-bis(2,2'-bipyridyl-4,4'-dicarboxylato) ruthenium(II)bis(tetrabutylammonium (N719) as a sensitizer-incident photon to current efficiency (IPCE) and current voltage measurements were carried out. The IPCE measurements confirmed photoinduced electron injection from the dye, reaching IPCE values up to 76%. Furthermore, current-voltage characteristics of complete cells emphasized the importance of the proper preparation methods and temperatures. These features are important assets for the preparation of nanocrystalline ZnO based photoelectrodes and for improving the DSSC performance.     

Heterometallic Cu/Co and Cu/Co/Zn complexes bearing rare asymmetric tetranuclear cores: synthesis, structures, and magnetic and catalytic properties toward the peroxidative oxidation of cycloalkanes

The three novel heterometallic complexes [CuCo(III)Co(II)(2)(MeDea)(3)Cl(3)(CH(3)OH)(0.55)(H(2)O)(0.45)](H(2)O)(0.45) (1), [CuCo(III)Zn(2)(MeDea)(3)Cl(3)(CH(3)OH)(0.74)(H(2)O)(0.26)](H(2)O)(0.26) (2), and [CuCo(III)Zn(2)(MeDea)(3)Cl(3)(DMF)] (3) have been prepared using a one-pot reaction of copper powder with cobalt chloride (1) and zinc nitrate (2, 3) in a methanol (1, 2) or dimethylformamide (3) solution of N-methyldiethanolamine. A search of the Cambridge Structural Database shows that the tetranuclear asymmetric cores M(4)(μ(3)-X)(μ-X)(5) of 1-3 represent an extremely rare case of M(4)X(6) arrays. The magnetic investigations of 1 disclose antiferromagnetic coupling in a Co(II)-Cu(II)-Co(II) exchange fragment with J(Co-Cu)/hc = -4.76 cm(-1), J(Co-Co)/hc = -2.76 cm(-1), and D(Co)/hc = +34.3 cm(-1). Compounds 1-3 act as precursors for the mild peroxidative oxidation of cyclohexane to cyclohexanol and cyclohexanone with overall yields up to 23%. The synthetic and structural features as well as the thermogravimetric behavior and electrospray ionization mass spectrometry data are discussed.