A sharp condition for existence of an inertial manifold

It is shown that a perturbation argument that guarantees persistence of inertial (invariant and exponentially attracting) manifolds for linear perturbations of linear evolution equations applies also when the perturbation is nonlinear. This gives a simple but sharp condition for existence of inertial manifolds for semi-linear parabolic as well as for some nonlinear hyperbolic equations. Fourier transform of the explicitly given equation for the tracking solution together with the Plancherel's theorem for Banach valued functions are used.     

Supramolecular dimer formation through hydrogen bond extensions of carboxylate ligands – Path for magnetic exchange

A new complex of unusual composition [Cu(3-O₂Nbz)₂(nia)(H₂O)₂] (1) (nia = nicotinamide, 3-O₂Nbz = 3-nitrobenzoate) has been prepared and studied together with two other complexes of composition [Cu(4-O₂Nbz)₂(nia)₂(H₂O)₂] (2) and [Cu(4-O₂Nbz)₂(nia)₂]?(4-O₂NbzH)₂ (3) (4-O₂Nbz = 4-nitrobenzoate). The composition of all complexes has been determined by elemental analysis, the complexes have been studied by electronic, infrared and EPR spectroscopy, as well as by magnetization measurements over the temperature range 1.8–300 K, and their structures have been solved. The structure of complex (1) consists of molecules, where Cu(II) atom is monodentately coordinated by the pair of 3-nitrobenzoato anions in trans  -positions together with water and nicotinamide molecules, forming nearly tetragonal basal plane, and by another water molecule in axial position of tetragonal-pyramidal coordination polyhedron. The neighboring molecule coordination polyhedron basal planes are coplanar and allow formation of supramolecular dimers with strong H-bonds between hydrogen atoms from equatorially coordinated water molecules and uncoordinated carboxylate oxygen atoms thus giving the nearest Cu?$?$Cu distance of 4.886(2) Å. Magnetization measurements showed that complex (1) exhibits maximum of magnetic susceptibility at 6.5 K and a fit to Bleaney-Bowers equation gave singlet–triplet energy gap 2J = −6.25 cm⁻¹, and zJ′ = −0.03 cm⁻¹. This might be an experimental proof that the carboxylate bridges extended with hydrogen bonds are the pathway of the spin–spin interactions. The temperature dependence of changes in EPR spectra of (1) and the spectrum at 4.2 K have confirmed its hydrogen bonded dimeric structure. The calculated Cu?$?$Cu distance 4.8 Å is in very good agreement with the value obtained from crystal structure. The complexes (2) and (3) at 300 K exhibit magnetic moment μ_eff = 1.98 B.M. and μ_eff = 1.84 B.M., respectively. These values practically do not change with lowering the temperature up to 5 K and only small drops to μ_eff = 1.87 B.M. (for (2)) and μ_eff = 1.79 B.M. (for (3)) at 1.8 K have been observed. The EPR spectra of complex (2) at room temperature as well as at 77 K are of axial type with g_⊥ = 2.062 and g_|| = 2.285 and exhibit resolved parallel hyperfine splitting with A_|| = 160 Gauss. The EPR spectra of complex (3) at room temperature as well as at 77 K are of axial type with g_⊥ = 2.065 and g_|| = 2.235 and exhibit unresolved parallel hyperfine splitting. EPR spectra of (2) and (3) are consistent with the X-ray structure.     

On‐line flow‐through extraction–preconcentration‐large volume injection‐RP LC for trace determination of pyrethroids in Slovak soil

A rapid micro‐analytical multiresidue method was developed for analysis of pyrethroids (kadethrin K, cypermethrin C and permethrin P) in soil micro‐sample (200 mg). It uses on‐line flow‐through extraction of soil micro‐samples (packed into a short glass column) with a methanol‐aqueous citric acid buffer mixture, successive on‐line SPE preconcentration of analytes from the extract and on‐line RP‐HPLC analysis with UV photometric detection. The separation of pyrethroids is performed on a Purospher RP‐18e column with methanol/water as mobile phase. Effects of sorbent placed at the bottom of a short column holding the soil sample and different kinds of on‐line SPE columns were tested. Besides, the influence of volume of the effluent on the pyrethroids recovery was also studied. Calibration curves were linear over the range assayed from 0.01 to 0.2 μg/mL with correlation coefficients of linear regression (least‐squares method) in the range 0.998–0.999. Recovery studies were carried out at 0.25–1.00 μg/g dry soil fortification level and obtained recoveries were for K 81–84%, C 56–59% and for P 58–63%. Achieved LOD (confidence band) of studied pyrethroids were for large‐volume injection (1 mL) 4.5 ng K, 3.7 ng C, 3.6 ng P or 27 ng/g K, 32 ng/g C and 29 ng/g P in dry soil “solid sampling HPLC”.     

Raman spectroscopic study of the uranyl sulphate mineral zippeite: low wavenumber and U–O stretching regions

The uranyl sulphate mineral zippeite was studied by Raman spectroscopy. The phase purity of the sample was initially checked by X-ray powder diffraction and its chemical composition was defined by electron microprobe (wavelength dispersive spectroscopy, WDS) analysis. The Raman spectroscopy research focused on the low wavenumber and uranyl stretching vibration regions. Vibration bands down to 50 cm^–1 were tentatively assigned. The U–O bond lengths were calculated based on empirical relations. Inferred values are consistent with those obtained from the crystal structure analysis of synthetic zippeite. Number of bands was interpreted on the basis of factor group analysis.     

[Cu(X-salicylato)2(N,N-diethylnicotinamide)2(H2O)2] complexes: conformational polymorphism and its consequence in supramolecular hydrogen-bonding networks formation

Novel copper(II) X-salicylate complexes with N,N-diethylnicotinamide (dena) of the formula [Cu(RCOO)₂(dena)₂(H₂O)₂] (RCOO = 3-methylsalicylate anion (3-Mesal, 1), 4-methylsalicylate anion (4-Mesal, 2), 5-methylsalicylate anion (5-Mesal, 3), 5-methoxysalicylate anion (5-MeOsal, 4) or 4-methoxysalicylate anion (4-MeOsal, 5)), and complex [Cu(3-MeOsal)₂(dena)₂(H₂O)₂]∙2H₂O (3-MeOsal = 3-methoxysalicylate anion (6)) have been prepared in the crystalline forms and characterized by spectroscopic methods (IR, Vis–UV, EPR). All the compounds according to their composition (1–5) seem to possess octahedral copper(II) stereochemistry. The complex 1 has been prepared in two different forms. X-ray analyses of the complexes 1, 4, and 5 were carried out and they featured a tetragonal-bipyramidal geometry around the copper atoms. The tetragonal planes are created by X-salicylate anions bonded to the copper(II) atoms via unidentate carboxylate oxygen atoms and the pyridine ring nitrogen atoms of the neutral ligand N,N-diethylnicotinamide, while in axial positions are water molecules. The two forms of complex 1 present conformation polymorphs and supramolecular isomers.     

Photo- and radiation-induced preparation of nanocrystalline copper and cuprous oxide catalysts

Spherical copper nanoparticles have been prepared by photo- or radiation-induced reduction of aqueous solutions containing 10⁻³ mol.dm⁻³ copper sulphate or formate, 1.3 mol.dm⁻³ propan-2-ol and polyvinyl alcohol as a stabilizer. Increase of initial copper concentration to 10⁻² mol.dm⁻³ resulted in formation of different reaction product—octahedral cuprous oxide nanoparticles. Solutions were irradiated by means of electron beam, ⁶⁰Co γ rays (dose rate 70 Gy.h⁻¹) or by 400 W medium-pressure mercury lamp and were characterised by UV-Vis spectrophotometry, X-Ray Powder Diffraction, TEM and SEM. Pink to violet colour of colloidal copper solutions corresponded to measured copper surface plasmon band at circa 580 nm and has been found to be very sensitive to oxygen, which causes dissolution of particles. Therefore, the influence of purging by nitrogen gas prior to irradiation was thoroughly examined and has been found to only hinder, not alter irradiation effects. Moreover, the evolution of absorption spectrum of colloidal copper solution in contact with air has been measured, revealing interesting non-monotonous dependence on the air exposure time, probably caused by formation of protective oxide layer. Catalytic activity of prepared cuprous oxide has been measured by catalytic decomposition of hydrogen peroxide and has been found to be higher or comparable to commercial cuprous oxide.     

Development of metallocomplex amino acids synthons for the asymmetric preparation of α-amino acids by stereoselective introduction of a side chain. Evaluation of the model asymmetric preparation of alanine and β-13C monolabelled α-aminoisobutyric acid

In this communication the evaluation of eleven new metallocomplex alanine synthons bearing C₂-symmetric benzyl groups with electron-donating and electron-withdrawing substituents is described. α-Methylated glycine synthons (alanine complexes) were evaluated alongside alanine synthons in order to obtain a deeper understanding of the relationship between their structures and stereochemistry of monoalkylated products and to choose several candidates for their further tests for stereospecific preparation of 6-[¹⁸F]FDOPA. Glycine-derived analogues of the complexes 3–5 are the best candidates for the development of a 6-[¹⁸F]FDOPA preparation procedure. In the model epimerisation reaction they demonstrated the best performance, much better compared to the previously described compound 2. Complexes 3, 5 and 8 are the best in asymmetric preparation of β-¹³C monolabelled α-aminoisobutyric acid. They have to be tested in the preparation of α-methyl amino acids like 6-[¹⁸F]-α-methylDOPA and 2-[¹⁸F]-α-methyltyrosine.     

Radionuclide concentrations in samples of medicinal herbs and effective dose from ingestion of ¹³⁷Cs and natural radionuclides in herbal tea products from Serbian market

The objective of this study is to evaluate natural and artificial radioactivity levels in 18 different samples of medicinal herbs from Serbian market. The activity concentrations of (238)U, (232)Th, (40)K, and (137)Cs were measured using gamma spectroscopy system with a high-purity germanium detector. The activity concentrations of (238)U, (232)Th, (40)K, and (137)Cs were found to be in a range of 0.6-8.2, 1.7-15.1, 126-1243.7, and 0.3-8.8 Bq/kg, respectively. The annual whole body doses from ingestion of (137)Cs and natural radionuclides for an adult person who consumed herbal tea from these medicinal herbs were found to be 2.5-469.9 nSv for (137)Cs, 0.7-9.7 nSv for (238)U, 0.3-2.8 nSv for (232)Th, and 1026.0-10,132.0 nSv for (40)K. These doses are not hazardous to public health. The obtained results were compared with correspondent studies conducted worldwide.     

On the Leverrier-Faddeev algorithm for computing the Moore-Penrose inverse

We present an improvement in the implementation of the Leverrier-Faddeev algorithm for symbolic computation of the Moore-Penrose inverse of one-variable polynomial matrices, introduced in Linear Algebra Appl. 252, 35–60 (1997). Complexity analysis of the original algorithm and its improvement is presented. Algorithm and its improvement are implemented and compared in the symbolic computational package MATHEMATICA. We compare CPU time required for computation of some test matrices by means of the original algorithm and its improvement.