Semitransitive subsemigroups of the symmetric inverse semigroups

We initiate the study of semitransitive transformation semigroups. In the paper we describe the structure of semitransitive subsemigroups of the finite symmetric inverse semigroup of the minimal cardinality modulo the classification of transitive subgroups of the minimal cardinality of finite symmetric groups, and state the results on minimal transitive subsemigroups. The authors were supported in part by Ukrainian-Slovenian bilateral research grants from the Ministry of Education and Science, Ukraine, and the Research Agency of the Republic of Slovenia.     

Biosynthesis of the angiogenesis inhibitor borrelidin by Streptomyces parvulus Tü4055: cluster analysis and assignment of functions

The biosynthetic gene cluster for the angiogenesis inhibitor borrelidin has been cloned from Streptomyces parvulus Tü4055. Sequence analysis indicates that the macrolide ring of borrelidin is formed by a modular polyketide synthase (PKS) (borA1-A6), a result that was confirmed by disruption of borA3. The borrelidin PKS is striking because only seven rather than the nine modules expected for a nonaketide product are encoded by borA1-A6. The starter unit of the PKS has been verified as trans-cyclopentane-1,2-dicarboxylic acid (trans-1,2-CPDA), and the genes involved in its biosynthesis identified. Other genes responsible for biosynthesis of the nitrile moiety, regulation, and self-resistance were also identified.     

Synthesis and Structural Investigation of Brightly Colored Organoammonium Violurates

Nine new organoammonium violurates [R¹R²R³NH][C₄H₂N₃O₄] [R¹ = R² = H, R³ = c‐C₃H₅ ( 2 ), R³ = tBu ( 3 ), R³ = adamantyl ( 4 ), R³ = C₆H₂Me₂‐4,5‐NH₂‐2 ( 5 ); R¹ = H, R² = R³ = Et ( 6 ), iPr ( 7 ); R¹ = H, R²/R³ = (–CH₂–)₄ ( 8 ); R¹ = R² = R³ = Et ( 9 ); R¹ = R² = Me, R³ = (CH₂)₂NMe₂ ( 10 )] were prepared by treatment of violuric acid ( 1 ) with a variety of primary, secondary, and tertiary amines. With the exception of orange 5 , all these violurate salts form bright blue or blue‐purple crystalline solids. The acidic triethylammonium violurate [NHEt₃]H[C₄H₂N₃O₄]₂ · H₂O ( 9a ) was isolated in the form of red‐violet, plate‐like crystals by the reaction of violuric acid hydrate with triethylamine in a molar ratio of 2:1 in ethanol. All compounds were fully characterized by their IR and NMR (¹H, ¹³C) data as well as elemental analyses. X‐ray crystal structures determinations of 2 , 7 , and 9a revealed supramolecular self‐assembly through networks of N–H ··· N and N–H ··· O hydrogen bonds in the crystalline state.     

Finite state wreath powers of transformation semigroups

The finite state wreath power of a transformation semigroup is introduced. It is proved that the finite state wreath power of nontrivial semigroup is not finitely generated and in some cases even does not contain irreducible generating systems. The free product of two monogenic semigroups of index 1 and period m is constructed in the finite state wreath power of corresponding monogenic monoid.     

Treatment of humic acids with ferric, aluminum, and chromium ions in water

The interaction of ferric, aluminum, and chromium ions with humic acids at different pH of mixture has been investigated. The concentration of metal ions, bound with humic acid is proportional to the concentration of metal ion in water solution at pH 3 at low metal ion concentrations. The ratio of the number of ferric ions, bound with humic acid, to the number of acidic groups in humic acid is more than 1.5 at high ferric ion concentration in solution. That is bound with the formation of dimers of ferric ions and their treatment with acidic groups of humic acid. The radius of particles formed in the reaction of humic acid with ferric ion does not depend on the pH and decreases in the reaction with chromium and aluminum ions at pH higher than 4. An increase of metal ion concentration leads to the increase of the particle radius at low metal ion concentration reaching the constant value at high metal ion concentration and pH 6.1.     

The model of the rheological behavior of gelatinized starch at low concentrations

The optical density at the wavelength from 300 to 800 nm and the rheological behavior of gelatinized starch at its concentration from 3 to 30 g/L and the medium pH from 2 to 11 were investigated. The volume concentration of the swelling associates of macromolecules or their globules increases when pH of gelatinized starch rises. An influence of the volume concentration of gelatinized starch on the dependence of the shear stress on shear rate was studied. The dynamic viscosity is proportional to the volume concentration at the gelatinized starch concentration lower than 25% and proportional to the logarithm of the volume concentration at the starch concentration greater than 25%. Proposed mathematical model takes into account an influence of the volume concentration of swelling starch globules and the concentration of glucoside links of macromolecules between the globules of macromolecules or their associates on the dynamic viscosity of gelatinized starch. This model allows to describe the experimental data obtained.     

Future Stability of the FLRW Fluid Solutions in the Presence of a Positive Cosmological Constant

We introduce a new method for establishing the future non-linear stability of perturbations of FLRW solutions to the Einstein–Euler equations with a positive cosmological constant and a linear equation of state of the form p = Kρ. The method is based on a conformal transformation of the Einstein–Euler equations that compactifies the time domain and can handle the equation of state parameter values 0 < K ≤ 1/3 in a uniform manner. It also determines the asymptotic behavior of the perturbed solutions in the far future.     

Dynamical Compact Elastic Bodies in General Relativity

We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.