Renormalization group approach to lattice gauge field theories

We study four-dimensional pure gauge field theories by the renormalization group approach. The analysis is restricted to small field approximation. In this region we construct a sequence of localized effective actions by cluster expansions in one step renormalization transformations. We construct also -functions and we define a coupling constant renormalization by a recursive system of renormalization group equations.     

Synthesis of block copolymers by atom transfer radical polymerization of tert‐butyl acrylate with poly(oxyethylene) macroinitiators

Poly(oxyethylene)s terminated at both ends with 2‐bromopropionate end‐groups were prepared and characterized by means of MALDI TOF mass spectrometry. It was shown, that atom transfer radical polymerization (ATRP) of methyl methacrylate with a poly(oxyethylene) macroinitiator in bulk proceeds with low initiation efficiency while polymerization of tert‐butyl acrylate proceeds with practically quantitative initiation, leading to ABA block copolymers. Originally formed tert‐butyl acrylate blocks contain terminal bromine, as expected for the ATRP mechanism. MALDI TOF analysis indicates, however, that in the later stages of polymerization side reactions lead to elimination of terminal bromine.     

Dilithium tetrabromonickelate (II) as a source of soft nucleophilic bromide : Reaction with epoxides

Dilithium tetrabromonickelate (II) in THF serves as a source of “soft” nucleophilic bromide and reacts regioselectively with epoxides to give bromohydrins in high yield.     

Preparation, Structure, and Thermal Decomposition of Co(II) Complexeswith 2,3- and 2,5-Dichlorobenzoic Acid and Imidazole

 The reaction products of Co(II)-2,3- and -2,5-dichlorobenzoate with imidazole (1, 2; CoL ₂⋯2imdċ2H₂O, L=C₇H₃Cl₂O, imd=imidazole) were characterized by their spectroscopic and thermochemical properties. The compounds crystallize in the monoclonic system with space group = P2₁/c, a=13.848(3), b=12.841(3) ?, c= 7.064(2) ?, β=98.12 °, V=1243.5(4) ?³, Z=2 for 1 and space group =P2₁/n, a=13.293(3), b= 6.964(2), c=13.800(3) ?, β=108.92(3) °, V=1208.6(4) ?³, Z=2 for 2. The complexes lose their crystal water in one step at 333 K and subsequently decompose to CoO with intermediate formation of Co₃O₄.     

Bicyclic [b]‐heteroannulated pyridazine derivatives. 9. cyclization reactions of 4,4‐dimethyl‐ and 4‐phenyltetrahydropyridazine‐3,6‐dione 3‐hydrazones with esters of keto dicarboxylic acids

Bis(ethoxycarbonyl)alkylidene derivatives 4 and 5 of the respective title hydrazones were obtained in the reactions with diethyl oxomalonate, diethyl oxosuccinate, diethyl 2‐oxoglutarate, and diethyl oxalo‐propionate as mixtures of geometric isomers with high predominance of one of them. On heating at 160‐200° without any solvent or on refluxing in ethanol 4 cyclized to yield the corresponding pyri‐dazino[6, 1‐c]triazines 6 , whereas heating of 5 gave, depending on the chain length, the corresponding pyra‐zolylpyridazines 8b and 8d or the pyridazinylpyridazine 8c . X‐ray analysis was used to determine the structures of 6 and 8 ; the unit cell of 6c was found to accommodate 16 molecules representing four conforma‐tional varieties. The different behavior of 4 and 5 in the cyclization reactions was interpreted in terms of the tautomeric equilibrium which was shifted towards the enamine form in 4 , and towards the imine form, in 5 . Transmission of a long‐range chirality effect in 4d and 5a‐d manifested itself in the ¹H nmr spectra as the magnetic non‐equivalence of the CH₂ protons in one or both ester ethyl groups.     

Electrical properties of TiO<Subscript>2</Subscript>: equilibrium vs dynamic electrical conductivity

The present work reports semiconducting properties of high purity TiO₂ determined in the gas/solid equilibrium, as well as during controlled heating and cooling in the range 300–1,273 K. The activation energy of the electrical conductivity is considered in terms of the activation enthalpy of the formation of ionic defects and the activation enthalpy of the mobility of electronic defects. These data, determined from the dynamic electrical conductivity experiments, are compared to the electrical conductivity data determined in equilibrium. It is shown that only the equilibrium electrical conductivity data for high-purity TiO₂ are well defined. It is shown that the activation energy of the electrical conductivity determined in equilibrium differs substantially from that for the dynamic electrical conductivity data during cooling and heating. It is concluded that the formation enthalpy term determined from the dynamic conductivity data is determined by the heating/cooling rate rather than materials’ properties.     

Small shower CORSIKA simulations

Extensive Air Showers (EAS) induced by cosmic ray particles of very low energies, owing to the significantly steep cosmic ray energy spectrum, dominate the secondary particle flux measured by single detectors and small shower arrays. Such arrays connected in extended networks can be used to determine potentially interesting spatial correlations between showers, which may shed new light on the nature of ultra high-energy cosmic rays. The quantitative interpretation of showers recorded by small local arrays requires a methodology that differs from that used by ordinary large EAS arrays operating in the "knee" region and above. We present "small EAS generator," a semi-analytical method for integrating cosmic ray spectra over energies of interest and summing over the mass spectra of primary nuclei in arbitrary detector configurations. Furthermore, we provide results on the EAS electron and muon fluxes and particle density spectra.     

Solvent extraction of Cu,Mo, V,and U from leach solutions of copper ore and flotation tailings

A micro-cloud point extraction method was discussed for preconcentration and spectrophotometric quantification of U(VI). The method depends on complex formation between U(VI) and 2-(4-sulphophenyloazo)-1,8-dihydroxy-3,6-naphtalenedisulphonic acid (SPADNS) at pH 7.0 and subsequent extraction of the complex in a mixed surfactant medium (cethyltrimethyl ammonium bromide and Triton X-114). The separation was carried out in the presence of 1% Na₂SO₄ at room temperature. The calibration curve was linear up to 3000 µg L^?1. The enrichment factor, detection limit and precision were 16.0, 1.05 µg L^?1, and 2.3%, respectively. The method was employed for the determination of U(VI) in real samples with different matrices.