General variable neighborhood search for the continuous optimization

We suggest a new heuristic for solving unconstrained continuous optimization problems. It is based on a generalized version of the variable neighborhood search metaheuristic. Different neighborhoods and distributions, induced from different metrics are ranked and used to get random points in the shaking step. We also propose VNS for solving constrained optimization problems. The constraints are handled using exterior point penalty functions within an algorithm that combines sequential and exact penalty transformations. The extensive computer analysis that includes the comparison with genetic algorithm and some other approaches on standard test functions are given. With our approach we obtain encouraging results.     

On congruences and ideals of partially ordered quasigroups

Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.     

Molecular distortion effect on ff-emission in a Pr(III) complex with 4,7-diphenyl-1,10-phenanthroline.

The electronic and structural behaviour of a Pr(III) complex with 4,7-diphenyl-1,10-phenanthroline, [Pr(bathophen)(2)(NO(3))(3)], is investigated with respect to the effect of configuration changes on the Pr(III) centre. [Pr(bathophen)(2)(NO(3))(3)] luminesces from the excited states of the ligand and the metal ion. The fluorescence, ff-emission ((1)D(2)-->(3)H(4)), and phosphorescence bands appear at 394, 608.2 and 482 nm, respectively, in the solid state. In acetonitrile, the complex also shows multiple emissions. From the time-resolved emission and the lifetime measurements, the excitation energy-transfer in [Pr(bathophen)(2)(NO(3))(3)] is clarified, that is, the upper excited triplet level of the ligand acts as an energy donor, while the (1)D(2) levels of Pr(III) is the acceptor. Additionally, the emission phenomena of the complex can be modified by molecular distortion, particularly by rotation of the phenyl groups in the ligand.     

Quadrupole Splitting Distributions in Purpurite and Related Minerals

The quadrupole splitting distributions (QSDs) from the Mössbauer spectra of triphylite, ferrisicklerite and purpurite at 298 K and 80 K were obtained by the use of the Voigt-based quadrupole splitting distribution (QSD) method for the first time. QSDs of Fe²⁺ and Fe³⁺ are attributed to Fe²⁺ and Fe³⁺ at the corresponding octahedrally coordinated sites in the crystal structures of the three phosphate minerals. The influence on the distortion of the M2 site by different next-nearest neighbor (NNN) configurations was discussed based on the Jahn–Teller effect in purpurite, and the authors propose two M2 subsites with different distortions in purpurite. Two QSDs of Fe³⁺ in the Mössbauer spectra of purpurite are tentatively assigned to Fe³⁺ at the two M2 subsites, and next-nearest neighbor (NNN) effects were used to interpret the Mössbauer spectra of purpurite.     

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.