Topological Simplicity of a Certain LF-Algebra

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

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.     

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.     

Preparation and practical application of spinel pigment Co0.46Zn0.55(Ti0.064Cr0.91)2O4

Synthesis of the green spinel pigment Co_0.46Zn_0.55(Ti_0.064Cr_0.91)₂O₄ by a novel two-step method of preparation have been investigated. Inorganic pigments are almost always prepared by a solid state reaction. It is classical ceramic method which used oxides, hydroxides or carbonates as precursors. The reaction is performed at temperature higher than 1300°C and an agent of mineralization is usually present. The presented novel method of preparation decreases the calcining temperature necessary for reaching of bright and clear hue of the pigments prepared. Main attention was focused on the influence of two types of titanium raw materials on the temperature region of the spinel structure formation and on the colour properties of the pigments. The mixture of precursors with TiO₂ gives a one-phase system when calcining at 1100°C but the colour properties are more interesting at 1150°C. Thermal stability of this pigment is limited by temperature 1300°C. This temperature is connected with partial oxidation of Cr(III) to Cr(VI). Thermal analysis provided the first information about the temperature region of the pigment formation and determined the thermal stability of pigment.     

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