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.     

Covalent attachment of a nickel nitrilotriacetic acid group to a germanium attenuated total reflectance element

The surface of a germanium internal reflectance element (IRE) was modified to bind 6X-histidine (his)-tagged biomolecules. The step-by-step surface modification was monitored via single-pass attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FT-IR). Initially an adlayer of 7-octenyltrimethoxysilane (7-OTMS) was formed on the Ge crystal through the surface hydroxyl groups, which were produced via ozonolysis of the Ge surface. The vinyl moiety of 7-OTMS was oxidized to a carboxylic acid, which was activated by 1,1'-carbonydiimidazole (CDI) to produce a labile imidazole. The labile imidazole that resulted from the CDI coupling was then displaced by the primary amine of nitrilotriacetic acid (NTA). Nickel sulfate was added to the system, and it coordinated with the three carbonyl groups and the nitrogen on NTA, thus leaving the ability of Ni to coordinate with two adjacent histidine residues. Binding of his-tagged biotin to nickel nitrilotriacetic acid (Ni-NTA) was observed by ATR-FT-IR spectroscopy. The surface modification method presented in this paper had minimal nonspecific binding, the Ni-NTA surface was reusable if stored properly, and complete removal of the organic surface was achievable.     

The first structurally characterized nonorganometallic titanium(III) alkoxo-bridged dinuclear complexes

The reaction of [Ti4(OMe)14Cl2] (1) with an excess of AlMe3 gave the cocrystallite [Ti2(mu-OMe)2(mu-Cl)Cl3(thf)3].[Ti2(mu-OMe)3Cl3(thf)3] (2.3) species in a 1:1 ratio. Similar to 2, [Ti2(mu-OEt)2(mu-Cl)Cl3-(thf)3] (4) was obtained in the reaction of an equimolar mixture of TiCl4 and Ti(OEt)4 with Al/AlMe3. The short distance [2.543(1)av A in 2.3 and 2.599(1) A in 4] between "Ti(+3)" atoms, their diamagnetism, and ELF analysis indicate the presence of a Ti-Ti bond.     

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     

Synthesis and evaluation of the catalytic properties of semicarbazides derived from N-triphenylmethyl-aziridine-2-carbohydrazides

A straightforward synthesis of a series of new catalysts derived from N-triphenylmethyl-aziridine-2-carbohydrazides is described. The new compounds have been tested for the enantioselective addition of diethyl- and phenylethynylzinc to aryl and alkyl aldehydes, which afforded the corresponding chiral alcohols in high chemical yields (up to 92%) and with excellent ee’s of approximately 90%.