The Simple Connectedness of Tame Algebras with Separating Almost Cyclic Coherent Auslander–Reiten Components

We study the simple connectedness of the class of finite-dimensional algebras over an algebraically closed field for which the Auslander–Reiten quiver admits a separating family of almost cyclic coherent components. We show that a tame algebra in this class is simply connected if and only if its first Hochschild cohomology space vanishes.

     

On the composition factors of indecomposable modules in almost cyclic coherent Auslander-Reiten components

We prove that the indecomposable modules without selfextensions in generalized standard almost cyclic coherent Auslander-Reiten components without external short paths of artin algebra are uniquely determined by their composition factors. Moreover, we prove that there is a common bound on the numbers of indecomposable modules with the same composition factors lying in a generalized standard almost cyclic coherent Auslander-Reiten component without external short paths of artin algebra.     

Cooperative Boolean systems with generically long attractors I

We study the class of cooperative Boolean networks whose only regulatory functions are COPY, binary AND and binary OR. We prove that for all sufficiently large N and c < 2 there exist Boolean networks in this class that have an attractor of length >c ^N whose basin of attraction comprises an arbitrarily large fraction of the state space. The existence of such networks sharply contrasts with results on continuous dynamical systems that imply non-genericity of non-steady-state attractors under the assumption of cooperativity.     

Composition,Anti-MRSA Activity and Toxicity of Essential Oils from Cymbopogon Species

Many of the essential oils obtained from medicinal plants possess proven antimicrobial activity and are suitable for medicinal purposes and applications in the food industry. The aim of the present work was the chemical analysis of 19 essential oils (EOs) from seven different Cymbopogon species (C. nardus, C. citratus, C winterianus, C. flexuosus, C. schoenanthus, C. martinii, C. giganteus). Five different chemotypes were established by GC/MS and TLC assay. The EOs, as well as some reference compounds, i.e., citronellol, geraniol and citral (neral + geranial), were also tested for their antimicrobial and antibiofilm activity against methicillin-resistant Staphylococcus aureus (MRSA) by the microdilution method and direct bioautography. The toxicity of EOs was evaluated by Danio rerio ‘Zebrafish’ model assay. All examined EOs showed moderate to high activity against MRSA, with the highest activity noted for C. flexuosus—lemongrass essential oil, both in microdilution and direct autobiography method. Significant difference in the toxicity of the examined EOs was also detected.     

Performance of revised STO(1M)-3G basis set for prediction of 5-fluorocytosine chemical shifts

Nuclear shieldings and chemical shifts of 5-fluorocytosine (5FC) were predicted in the gas phase and DMSO solution modeled by polarizable continuum model using B3LYP density functional and revised STO(1M)-3G basis set. For comparison, eight arbitrary selected basis sets including STO-3G and medium-size Pople-type and larger dedicated Jensen-type ones were applied. The former basis sets were significantly smaller, but the calculated structural parameters, harmonic vibrational frequencies, were very accurate and close to those obtained with larger, polarization-consistent ones. The predicted ¹³C and ¹H chemical shieldings of 5FC and cytosine, selected as parent molecule, were acceptable (root mean square for ¹³C chemical shifts in DMSO of about 5 ppm and less) though less accurate than those calculated with large basis sets, dedicated for prediction of nuclear magnetic resonance parameters.     

Infinite Components of An Auslander-Reiten Quiver with Finite DTr-Orbits

Abstract

Let A be a basic connected finite dimensional algebra over an algebraically closed field. We show that if Γ is an infinite connected component of the Auslander-Reiten quiver Γ_A of A in which each Γ_A-orbit contains only finitely many vertices, then the number of indecomposable direct summands of the middle term of any mesh, whose starting vertex belongs to the infinite stable part of Γ, is less than or equal to 3. Moreover, if the nonstable vertices belong to τ_A-orbits of exceptional projectives in Γ, then Γ can be obtained from a stable tube by a finite number of multiple coray-ray insertions of type α?γ and multiple coray-ray insertions of type α?γ.     

NO2 disproportionation for the IR characterisation of basic zeolites

NO2 disproportionation on alkaline zeolites is used to generate nitrosonium (NO+) and nitrate ions on the surface, and the infrared vibrations observed are very sensitive to the cation chemical hardness and to the basicity of zeolitic oxygen atoms.