Homogenization of the Spectral Problem for Periodic Elliptic Operators with Sign-Changing Density Function

The paper deals with the asymptotic behaviour of spectra of second order self-adjoint elliptic operators with periodic rapidly oscillating coefficients in the case when the density function (the factor on the spectral parameter) changes sign. We study the Dirichlet problem in a regular bounded domain and show that the spectrum of this problem is discrete and consists of two series, one of them tending towards +∞ and another towards −∞. The asymptotic behaviour of positive and negative eigenvalues and their corresponding eigenfunctions depends crucially on whether the average of the weight function is positive, negative or equal to zero. We construct the asymptotics of eigenpairs in all three cases.     

Effects of Phytohormones and Jasmonic Acid on Glucosinolate Content in Hairy Root Cultures of Sinapis alba and Brassica rapa

Although some study have established hairy root cultures from brassicaceous plants with glucosinolates (GS) as characteristic secondary metabolite, studies are missing which compare hairy roots with the corresponding mother plants. Therefore, two different plant species—Sinapis alba and Brassica rapa subsp. rapa pygmeae teltoviensis—were transformed with the Agrobacterium rhizogenes strain A4. Aliphatic and indolyl GS were present in B. rapa, exhibiting larger quantities in leaves than in roots. Aromatic p-hydroxybenzyl GS were found particularly in the leaves of S. alba. However, the proportion of indolyl GS increased suddenly in transformed hairy roots of S. alba and B. rapa. Cultivation with the phytohormone kinetin (0.5 mg?L^?1) enhanced GS accumulation in B. rapa hairy roots, however not in S. alba, but 2,4-D (0.4 mg?L^?1) induced de-differentiation of roots in both species and reduced GS levels. GS levels especially of 1-methoxyindol-3ylmethyl GS increased in hairy roots in response to JA, but root growth was inhibited. While 2 weeks of cultivation in 100 to 200 μM JA were determined at optimum for maximum GS yield in S. alba hairy root cultures, 4 weeks of cultivation in 50 to 100 μM JA was the optimum for B. rapa.     

Chiral memory and self-replication study of porphyrin and bilirubin aggregates formed on polypeptide matrices

Porphyrin heteroaggregates composed of meso-tetrakis(N-methylpyridinium-4-yl)porphinatocopper(II) and meso-tetrakis(4-sulfonatophenyl)porphyrin formed in the presence of a polyglutamic matrix possess chiral memory and an ability to self-replicate their supramolecular structures. By means of electronic circular dichroism spectroscopy, it has been shown that the self-replication process is not influenced by changes in pH or ionic strength. The average molecular weight of the polyglutamic matrix used for porphyrin aggregate preparation plays a crucial role with regard to the form of the resulting CD spectrum. In the second part of our study, a complex composed of polylysine and bilirubin as a model system for a structured homoaggregate formed on the chiral matrix has been tested for chiral memory phenomena. The results indicate that the bilirubin homoaggregate shows chiral memory.     

Pressure-induced order transition in nanodot-forming diblock copolymers at the air/water interface

Understanding and controlling the processes in block copolymer (BC) monolayers at the air/water interface during surface area compression is a key issue for producing ultrathin films of predetermined morphology with well-defined order and known dimensions. Langmuir isotherms of nanodot-forming BC monolayers generally display a plateau indicative of a 2D phase transition, which has been the subject of various interpretations in the literature. Here, based on investigations of Langmuir-Blodgett and Langmuir-Schaefer nanodot films of PS-P4VP mixed with 3-n-pentadecylphenol (PDP), we show by atomic force microscopy (AFM) that it involves a change in nanodot packing order (from quasi-hexagonal to quasi-square), argued to be a general phenomenon for nanodot BC monolayers. It is accompanied by system-specific conformational changes (as discussed in previous literature), which, in the present case, implicate PDP alkyl chain ordering, as deduced previously from in situ infrared data and indirectly supported here by AFM imaging.     

Synthesis, structure, spectroscopic properties, and antiproliferative activity in vitro of novel osmium(III) complexes with azole heterocycles

Reactions of (H 2azole) 2[OsCl 6], where Hazole = pyrazole, Hpz, ( 1), indazole, Hind, ( 2), imidazole, Him, ( 3) and benzimidazole, Hbzim, ( 4) with the corresponding azole heterocycle in 1:4 molar ratio in boiling isoamyl alcohol or hexanol-1 afforded novel water-soluble osmium(III) complexes of the type trans-[OsCl 2(Hazole) 4]Cl, where Hazole = Hpz ( 5a), Hind ( 6a), Him ( 7a), and Hbzim ( 9a) in 50-70% ( 5a, 7a, 9a) and 5% ( 6a) yields. The synthesis of 7a was accompanied by a concurrent reaction which led to minor formation (<4%) of cis-[OsCl 2(Him) 4]Cl ( 8). The complexes were characterized by elemental analysis, IR spectroscopy, UV-vis spectroscopy, ESI mass spectrometry, cyclic voltammetry, and X-ray crystallography. 5a, 7a, and 9a were found to possess remarkable antiproliferative activity in vitro against A549 (non-small cell lung carcinoma), CH1 (ovarian carcinoma), and SW480 (colon carcinoma) cells, which was compared with that of related ruthenium compounds trans-[RuCl 2(Hazole) 4]Cl, where Hazole = Hpz (5b), Hind (6b), Him (7b), and Hbzim (9b).     

About the existence of a Lifshitz point on the phase diagram of Sn2P2(Se x S1– x )6 solid solutions: acoustic and optical studies

On the basis of combined studies of the acoustic and optical properties of Sn₂P₂(Se _x S_{1– x} )₆ solid solutions with x?=?0 and 0.28 it is shown that two special points exist on the x,T-phase diagram of these ferroelectric crystals, a tricritical point and a triple one. With increasing Se concentration, the phase transition changes its character at x?≈?0.28 from second-order to first-order. The phase transition becomes split at x?≈?0.4, with the appearance of an intermediate incommensurate phase.     

Representation type of Jordan algebras

The problem of classification of Jordan bimodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0.     

Colloidal and chemical aspects of nanosized hydrated zirconium dioxide synthesized via a sol-gel process

The processes of coagulation and gelation of sols in zirconium oxychloride aqueous solutions and the properties of hydrated zirconium dioxide sols (pH, particles size, dynamic viscosity) depending on the aging conditions of partially neutralized zirconium oxychloride feedstock solution-zirconyl hydroxychloride used for the synthesis and molar ratio of initial reagents (Zr/NaOH, Zr/CH(3)COO(-)) were first studied in the paper. The concentration and temperature limits of hydrated zirconium dioxide sols stability were determined. The coagulation constant, gelation activation energy, and gelation thermal effect values were found.     

The Thorpe-Ziegler-type reaction of 3-cyanopyridine-2(1H)-thiones with Biginelli 6-bromomethyl-3,4-dihydropyrimidin-2(1H)-ones: cascade assembling of tetra- and pentacyclic heterocyclic scaffolds

3-Cyanopyridine-2(1H)-thiones have been shown to react with Biginelli-type ethyl 4-aryl-6-(bromomethyl)-2-oxo-1,2,3,4-tetrahydropyrimidine-5-carboxylates upon heating in DMF giving rise to ethyl 4-aryl-6-{[(3-cyanopyridin-2-yl)thio]methyl}-2-oxo-1,2,3,4-tetrahydropyrimidine-5-carboxylates. The latter upon treatment with an excess of NaH or t-BuOK in boiling DMF undergo a tandem Thorpe-Ziegler-type heterocyclization to give pyrido[3″,2″:4′,5′]thieno[2′,3′:5,6]pyrido[4,3-d]pyrimidine derivatives in good yields. Selected compounds were tested for antibacterial and antifungal activity.