Asynchronous Exponential Growth of a General Structured Population Model

We consider a class of structured cell population models described by a first order partial differential equation perturbed by a general birth operator which describes in a unified way a wide class of birth phenomena ranging from cell division to the McKendrick model. Using the theory of positive stochastic semigroups we establish new criteria for an asynchronous exponential growth of solutions to such equations.     

Linear liftings of skew symmetric tensor fields of type (1, 2) to Weil bundles

The paper contains a classification of linear liftings of skew symmetric tensor fields of type (1, 2) on n-dimensional manifolds to tensor fields of type (1, 2) on Weil bundles under the condition that n ⩾ 3. It complements author’s paper “Linear liftings of symmetric tensor fields of type (1, 2) to Weil bundles” (Ann. Polon. Math. 92, 2007, pp. 13–27), where similar liftings of symmetric tensor fields were studied. We apply this result to generalize that of author’s paper “Affine liftings of torsion-free connections to Weil bundles” (Colloq. Math. 114, 2009, pp. 1–8) and get a classification of affine liftings of all linear connections to Weil bundles.     

Bernstein approximations of nonlinear Sturm-Liouville problems

In this paper we deal with Sturm-Liouville boundary value problems

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Screening of transformation products in soils contaminated with unsymmetrical dimethylhydrazine using headspace SPME and GC-MS

The paper describes a novel SPME-based approach for sampling and analysis of transformation products of highly reactive and toxic unsymmetrical dimethylhydrazine (UDMH) which is used as a fuel in many Russian, European, Indian, and Chinese heavy cargo carrier rockets. The effects of several parameters were studied to optimize analyte recovery. It was found that the 85 μm Carboxen/polydimethylsiloxane fiber coating provides the highest selectivity for selected UDMH transformation products. Optimal sampling/sample preparation parameters were determined to be 1-h soil headspace sampling time at 40 °C. The GC inlet temperature was optimized to 170 °C held for 0.1 min, then 1 °C s⁻¹ ramp to 250 °C where it was held for 40 min. Temperature programing resulted in a fast desorption along with minimal chemical transformation in the GC inlet. SPME was very effective extracting UDMH transformation products from soil samples contaminated with rocket fuel. The use of SPME resulted in high sensitivity, speed, small labor consumption due to an automation and simplicity of use. It was shown that water addition to soil leads to a significant decrease of recovery of almost all target transformation products of UDMH. The use of SPME for sampling and sample preparation resulted in detection of the total of 21 new compounds that are relevant to the UDMH transformation in soils. In addition, the number of confirmed transformation products of UDMH increased from 15 to 27. This sampling/sample preparation approach can be recommended for environmental assessment of soil samples from areas affected by space rocket activity.     

Crystal and supramolecular structures of dioxomolybdenum(VI) and dioxotungsten(VI) complexes of dihydroxybenzoic acids

The tetramethylammonium salts (NMe₄)₂[MO₂(2,3-Hdhb)₂]·2H₂O and (NMe₄)₂[MO₂(3,4-Hdhb)₂]·6H₂O (M = Mo, W; Hdhb = monoprotonated form of 2,3- or 3,4-dihydroxybenzoic acid, 2,3-H₃dhb or 3,4-H₃dhb) were prepared and their crystal structures determined. The structure of [Mg(H₂O)₆](NMe₄)₄[MoO₂(3,4-dhb)(3,4-Hdhb)]₂·13H₂O, obtained by the recrystallization of (NMe₄)₂[MoO₂(3,4-Hdhb)₂] in the presence of magnesium ions, is also reported. The supramolecular interactions of the five structures are discussed in detail concerning the hydrogen bonding patterns involving complexes and water molecules of crystallization.     

Current trends in solid-phase microextraction (SPME) fibre coatings

This critical review presents information on known and innovative approaches to the manufacture of fibre coatings used in solid-phase microextraction (SPME). The properties, advantages and drawbacks of the different types of commercially available SPME fibre coatings are discussed in detail, as are those of novel types of coatings and the methodologies of their preparation. The applications of fibre coatings in the solid-phase microextraction of a broad spectrum of analytes are analysed, with particular emphasis on the sampling of polar analytes from polar matrices (174 references).     

Trianglamines--readily prepared, conformationally flexible inclusion-forming chiral hexamines

Trianglamines, macrocyclic heteraphanes, were readily synthesised through a [3+3] cyclocondensation of (R,R)-1,2-diaminocyclohexane with terephthalaldehyde, followed by NaBH4 reduction and N-alkylation. The macrocyclic ring shows a remarkable ability to change its conformation, as a consequence of rotation about the C-N bonds or nitrogen inversion due to protonation or N-alkylation, as revealed by circular dichroism spectra, computational modelling and X-ray diffraction analysis. The flexible natures of the trianglamine macrocycles allow ready accommodation of a variety of guest molecules to form crystalline inclusion complexes of highly diversified interpenetrating structures.     

Effect of hydroxylic solvent on the fluorescence behavior of some bioactive 9-oxo-imidazo[1,2-a]purine derivatives

The spectral and photophysical behavior of four fluorescent 9-oxo-imidazo[1,2-a]purine derivatives containing pyridyl, pyridylphenyl, phenyl, and biphenylyl substituents at the C(6) position of the tricyclic skeleton is described. The studies were performed in several aprotic and protic organic solvents using absorption spectroscopy as well as steady-state and time-resolved fluorescence spectroscopy. The results are also presented of TDDFT calculations on singlet-singlet excitation energies and oscillator strengths for two models of 9-oxo-imidazo[1,2-a]purine, with phenyl or pyridyl substituents, both in the gas phase and in methanol solution. While the derivatives with aryl substituents did not show any significant dependence of their static and dynamic fluorescence properties on the nature of the solvent, the compounds containing a pyridine residue exhibited a remarkable reduction of their fluorescence quantum yields and lifetimes in the alcoholic solutions. The solute-solvent hydrogen-bonding interaction in the first excited singlet state is responsible for the fast radiationless decay rates determined for pyridyl- and pyridylphenyl-substituted compounds in protic solvents. The results of experimental and theoretical studies show that the hydrogen of the alcohols' hydroxyl group and the nitrogen atom of the pyridine moiety are involved in the interaction. The fluorescence-quenching experiments performed for the pyridyl-substituted 9-oxo-imidazo[1,2-a]purine derivative using trifluoroethanol, methanol, and butanol as quenchers revealed that the quenching efficiencies, expressed by the Stern-Volmer quenching constants, correlate with the H-bond donating abilities of the alcohols. The quenching is a dynamic process, and the H-bonded complex formed is nonfluorescent. The experimentally determined and the calculated values of the dipole moment change associated with the electronic excitation indicate that the excited S(1) states of all of the molecules studied in this work have an intramolecular charge-transfer character and that electronic charge is transferred to the C(6) substituent upon excitation. Thus, the ability of the pyridyl substituent nitrogen atom to act as an H-bond acceptor in the excited S(1) state is enhanced. The 6-pyridyl-9-oxo-imidazo[1,2-a]purine presents a novel fluorophore, which, besides its medical applications, may be useful as a sensor of hydroxyl groups in microorganized systems.     

Lattice model of equilibrium polymerization. V. Scattering properties and the width of the critical regime for phase separation

Dynamic clustering associated with self-assembly in many complex fluids can qualitatively alter the shape of phase boundaries and produce large changes in the scale of critical fluctuations that are difficult to comprehend within the existing framework of theories of critical phenomena for nonassociating fluids. In order to elucidate the scattering and critical properties of associating fluids, we consider several models of equilibrium polymerization that describe widely occurring types of associating fluids at equilibrium and that exhibit the well defined cluster geometry of linear polymer chains. Specifically, a Flory-Huggins-type lattice theory is used, in conjunction with the random phase approximation, to compute the correlation length amplitude xi(o) and the Ginzburg number Gi corresponding, respectively, to the scale of composition fluctuations and to a parameter characterizing the temperature range over which Ising critical behavior is exhibited. Our calculations indicate that upon increasing the interparticle association energy, the polymer chains become increasingly long in the vicinity of the critical point, leading naturally to a more asymmetric phase boundary. This increase in the average degree of polymerization implies, in turn, a larger xi(o) and a drastically reduced width of the critical region (as measured by Gi). We thus obtain insight into the common appearance of asymmetric phase boundaries in a wide range of "complex" fluids and into the observation of apparent mean field critical behavior even rather close to the critical point.