Graph Automorphisms and Cells of Lattices

In this paper we apply the notion of cell of a lattice for dealing with graph automorphisms of lattices (in connection with a problem proposed by G. Birkhoff).     

Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations

A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH₂O, H₂O, HF, F₂, HCN, SiH₄ and H₂S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T)), with affordable pcS‐2 basis set and corresponding complete basis set results, estimated from calculations with the family of polarization‐consistent pcS‐n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and shieldings obtained with the significantly smaller basis sets pcS‐2 and aug‐cc‐pVTZ‐J for the selected set of 37 calculation methods. It was possible to formulate a practical approach of estimating the values of isotropic nuclear magnetic shielding constants at the CCSD(T)/CBS and MP2/CBS levels from affordable CCSD(T)/pcS‐2, MP2/pcS‐2 and DFT/CBS calculations with pcS‐n basis sets. The proposed method leads to a fairly accurate estimation of nuclear magnetic shieldings and considerable saving of computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.     

Direct summands and retract mappings of generalized <Emphasis Type="Italic">MV</Emphasis>-algebras

In the present paper we deal with generalized MV-algebras (GMV-algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, GMV-algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of GMV-algebras. The relations between GMV-algebras and lattice ordered groups are essential for this investigation. Supported by VEGA Agency grant 1/2002/05. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information, grant I/2/2005.     

Null sets and games in Banach spaces

The notion of Aronszajn-null sets generalizes the notion of Lebesgue measure zero in the Euclidean space to infinite dimensional Banach spaces. We present a game-theoretic approach to Aronszajn-null sets, establish its basic properties, and discuss some ensuing open problems.     

Long-term operation of a domestic wastewater treatment plant with membrane filtration

Possibilities of membrane technology and the use of membrane processes in wastewater treatment were investigated. The main focus was the monitoring of the starting phase of a domestic wastewater treatment plant. Experimental part of the study was realized at the municipal wastewater treatment plant (WWTP) Devínska Nová Ves — Bratislava during the period from February 2005 to September 2006. The system was stable without any external chemical treatment of the membrane modules and the permeate quality was very high. Observed decrease of COD and BOD₅ values ranged between 91 % and 98 %. The process of nitrification was very successful considering its high efficiency (> 95 %). Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.     

<Emphasis Type="Italic">G</Emphasis>-compactness and groups

Lascar described E _KP as a composition of E _L and the topological closure of E _L (Casanovas et al. in J Math Log 1(2):305–319). We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an affine copy of G and in M′ we have the structure of M and the action of G on X. We prove that the Lascar group of M′ is a semi-direct product of the Lascar group of M and G/G _L . We discuss the relationship between G-compactness of M and M′. This example may yield new examples of non-G-compact theories. The first author is supported by the Polish Goverment grant N N201 384134. The second author is supported by the Polish Goverment grant N201 032 32/2231.     

Effect of Two Different UVA Doses on the Rabbit Cornea and Lens

The aim of the present paper was to examine the irradiation effect of two doses of UVA rays (365 nm) on the rabbit cornea and lens. Corneas of anesthetized adult albino rabbits were irradiated with UVA rays for 5 days (daily dose 1.01 J cm⁻² in one group of rabbits and daily dose 2.02 J cm⁻² in the second group of animals). The third day after the last irradiation, the rabbits were killed, and their eyes were employed for spectrophotometrical, biochemical and immunohistochemical investigations. Normal eyes served as controls. Absorption spectra of the whole corneal centers were recorded over the UV–VIS (visible) spectral range. Levels of antioxidant and prooxidant enzymes, nitric oxide synthases and nitric oxide (indirectly measured as nitrate concentration) were investigated in the cornea. Malondialdehyde, a byproduct of lipid peroxidation, was examined in the cornea and lens. The results show that the staining for endothelial nitric oxide synthase was more pronounced in corneas irradiated with the higher UVA dose. Otherwise, UVA rays at either dose did not significantly change corneal light absorption properties and did not cause statistically significant metabolic changes in the cornea or lens. In conclusion, UVA rays at the employed doses did not evoke harmful effects in the cornea or lens.