Topological Simplicity of a Certain LF-Algebra

We show that the LF-algebra considered by Akkar and Nacir in [1] is topologically simple.     

Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer n_M such that for all finitely generated Λ-modules N, if Ext_Λⁱ(M,N)=0 for all i?0, then Ext_Λⁱ(M,N)=0 for all i?n_M. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

The measure of a translated ball in uniformly convex spaces

Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r ^q , whereq depends on the properties of the norm. We specify it in the case ofL spaces, >1.     

FT IR ATR Study of Molecular Interactions in the Urea/Dimethyl Sulfoxide and Urea/Diethyl Sulfoxide Binary Systems

FT IR ATR spectra of urea/dimethyl sulfoxide and urea/diethyl sulfoxide mixtures in the S=O and N—H stretching vibration regions at different molar ratios have been measured. On the basis of the band deconvolution data, various types of intermolecular associated forms, including dimers and hydrogen-bonded urea–sulfoxide complexes, have been revealed. The latter has been confirmed also by ab initio calculations.     

Solution conformation of a nitrobenzoxadiazole derivative of the polyene antibiotic nystatin: a FRET study

Nystatin is a polyene antibiotic frequently applied in the treatment of topical fungal infections. In this work, a 7-nitrobenz-2-oxa-1,3-diazole (NBD) hexanoyl amide derivative of nystatin was synthesized and its detailed photophysical characterization is presented. The average conformation of the labelled antibiotic in tetrahydrofuran, ethanol and methanol was determined by intramolecular (tetraene to NBD) fluorescence resonance energy transfer measurements. At variance with the literature [Can. J. Chem. 63 (1985) 77-85], it was concluded that there is no need to invoke a solvent-dependent conformational equilibrium between extended and closed conformers of the antibiotic, because the mean tetraene-to-NBD separating distance was found to remain constant (approximately 18 A) in all the solvents studied. In addition, the large solvent dependence of the fluorescence anisotropy observed for the non-derivatized nystatin, was rationalized on the basis of the prolate ellipsoidal geometry of the molecule. It was concluded that the rod shaped and amphipathic antibiotic remains monomeric in different solvents within the concentration range studied (2-20 microM).     

The thermoelastic behaviour of the orientationally disordered ionic crystals in two dimensions

The anomalous temperature dependence of the elastic constantsc ₁₁ andc ₆₆ and the elastic instability temperatureT _c are obtained in the two-dimensional microscopic model of the alkali cyanides crystals. It has been found, by means of the Michel and Naudts' theory of the translation rotation coupling, that the orientational disorder in the high-temperature phase leads to the critical softening of the shear elastic constantc ₆₆.     

Citric acid production from raw glycerol by acetate mutants of Yarrowia lipolytica

Three acetate mutants of the yeast species Yarrowia lipolytica were screened using batch cultivation. The strain Y. lipolytica 1.31 was found to be the most suitable for citric acid production from raw glycerol, a by-product of biodiesel production from rapeseed oil. At the initial concentration of glycerol of 200 g dm⁻³, the citric acid production of 124.5 g dm⁻³, yield of 0.62 g g⁻¹, and productivity of 0.88 g dm⁻³ h⁻¹ were achieved. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Gamow-Teller beta decay of the very neutron-deficientN=50 nuclide98Cd

For the first time, detailed decay-spectroscopic investigations were performed for the very neutron-deficientN=50 nuclide⁹⁸Cd. The⁹⁸Cd activity was produced in spallation reactions between 600 MeV protons and a natural tin target, yielding a⁹⁸Cd beam intensity of 10 to 60 atoms/s at the collector of the ISOLDE massseparator. By means of-ray and conversion-electron spectroscopy, 19 transitions were found to follow the ⁺/EC decay⁹⁸Cd⁹⁸Ag. The transitions at 61 and 107 keV were shown to beM1(+E2) andE2, respectively, and the⁹⁸Cd half-life was measured as 9.2±0.3 s. TheQ _EC value of⁹⁸Cd is determined semiempirically and is compared to model predictions together with the measuredQ _EC values of the neighbouring cadmium isotopes^100,102Cd and theN=50 isotones⁹²Mo,⁹⁴Ru, and⁹⁶Pd, taken from the literature. The newly established decay scheme of⁹⁸Cd includes 9 excited states of⁹⁸Ag. Four states at 1691, 1861, 2164, and 2544 keV are directly fed by 0⁺ 1⁺ Gamow-Teller beta transitions with a summed strength of 3.5 _–0.7 ^+0.8 . This value corresponds to 25±5% of the strength predicted for the GT transformation of a g_9/2 proton (in⁹⁸Cd) into a g_7/2 neutron (in⁹⁸Ag) by the extreme single-particle shell model. The GT-strength splitting and quenching, observed for⁹⁸Cd, are compared with the corresponding data for lighter even-even N=50 isotones, and are discussed with reference to the predictions of more sophisticated nuclear models. We find that only in some cases it is possible to explain qualitatively the observed GT strength distribution and its total magnitude without renormalizing the free-neutron value of the axial-vector coupling constant.Dedicated to Prof. P. Armbruster on the occasion of his 60th birthday