Synthesis,characterization and biological activity of copper(II) complexes with ligands derived from β-amino acids

Transition Metal Chemistry - Two copper(II) complexes with ligands derived from β-amino acids, 2-(1-aminocyclohexyl)acetic acid L1 and 2-(1-amino-4-(tert-butyl)cyclohexyl)acetic acid L2, were...     

Bands of k-Archimedean semigroups

In this paper we define the radical ϱ _k (k∈Z ⁺) of a relation ϱ on an arbitrary semigroup. Also, we define various types of k-regularity of semigroups and various types of k-Archimedness of semigroups. Using these notions we describe the structure of semigroups in which ρ _k is a band (semilattice) congruence for some Green’s relation.     

On the Gabai-Eliashberg-Thurston Theorem

We present a new, completely three-dimensional proof of the fact, due to the combined work of Gabai and Eliashberg-Thurston, that every closed, oriented, connected, irreducible 3-manifold with nonzero second homology carries a universally tight contact structure.     

Dynamical combinatorics and torsion classes

For finite semidistributive lattices the map κ gives a bijection between the sets of completely join-irreducible elements and completely meet-irreducible elements.Here we study the κ-map in the context of torsion classes. It is well-known that the lattice of torsion classes for an artin algebra is semidistributive, but in general it is far from finite. We show the κ-map is well-defined on the set of completely join-irreducible elements, even when the lattice of torsion classes is infinite. We then extend κ to a map on torsion classes which have canonical join representations given by the special torsion classes associated to the minimal extending modules introduced by the first and third authors and A. Carroll in 2019.For hereditary algebras, we show that the extended κ-map on torsion classes is essentially the same as Ringel's ?-map on wide subcategories. Also in the hereditary case, we relate the square of κ to the Auslander-Reiten translation.     

The concentrations and exposure doses of radon and thoron in residences of the rural areas of Kosovo and Metohija

This paper deals with the results of indoor radon and thoron concentrations and exposure doses obtained for 63 dwellings out of the 14 rural communities of Central Kosovo, North Kosovo and Prizren region. These research activities are part of overall radiological research that has systematically been carried out since 1986, particularly in Kosovo and Metohija regions. Passive radon/thoron discriminative detectors, exposed for three months, were used. The arithmetic mean concentrations of indoor radon and thoron are C_Rn = 429 Bq m^?3 C_Tn = 85 Bq m^?3.     

High-pressure optical studies on R-line fluorescence lifetime in Al2O3:V2+

The effect of high hydrostatic pressure (up to 10.3?GPa) at room temperature on fluorescence lifetime τ for R line (²E→⁴A₂ transition) in ruby Al₂O₃:V²⁺ was studied. The performed studies show the linear increase of τ with increasing pressure. At 10.3?GPa, τ is about 1.36 times higher than at ambient pressure. The obtained trend was explained by a model which considered the effect of pressure on τ through an induced change of line position, inter-ionic distance, compressibility, and molecular polarizability. A good agreement between the calculated and experimental values for τ was obtained.     

Orthogonal sums of semigroups

The purpose of this paper is to prove that every semigroup with the zero is an orthogonal sum of orthogonal indecomposable semigroups. We prove that the set of all 0-consistent ideals of an arbitrary semigroup with the zero forms a complete atomic Boolean algebra whose atoms are summands in the greatest orthogonal decomposition of this semigroup. Supported by Grant 0401A of RFNS through Math. Inst. SANU.     

Packing triangles in low degree graphs and indifference graphs

We consider the problems of finding the maximum number of vertex-disjoint triangles (VTP) and edge-disjoint triangles (ETP) in a simple graph. Both problems are NP-hard. The algorithm with the best approximation ratio known so far for these problems has ratio 3/2+?, a result that follows from a more general algorithm for set packing obtained by Hurkens and Schrijver [On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems, SIAM J. Discrete Math. 2(1) (1989) 68-72]. We present improvements on the approximation ratio for restricted cases of VTP and ETP that are known to be APX-hard: we give an approximation algorithm for VTP on graphs with maximum degree 4 with ratio slightly less than 1.2, and for ETP on graphs with maximum degree 5 with ratio 4/3. We also present an exact linear-time algorithm for VTP on the class of indifference graphs.     

New compounds in ring‐opening reaction of 5‐substituted epoxyisoindolines

Methoxy or nitro group present in the furan ring of tertiary alkenylfurfurylamine changes the expected results of both, the intramolecular [4+2]cycloaddition and the acid catalyzed ring‐opening reaction of the derived oxatricycloadduct. With a 5‐methoxy group, in addition to the expected 5‐methoxyisoindoline 3 , the corresponding hydroxy derivative 5 was obtained. On the other hand a 5‐nitro group changes the outcome of the reaction even more profoundly. Instead of the expected 5‐nitroisoindoline 12 , 5‐nitro‐substituted epoxy‐isoindoline 6 submitted to ring‐opening reaction with the mixture of hydrobromic and acetic acid, yielded the mixture of bromo‐substituted epoxy compounds 7,8, 9 and/or bromo‐substituted isoindolines 10 and 11 .