A Monte Carlo algorithm for solving systems of non-linear equations

A Monte Carlo method for solving systems of non-linear equations is presented and discussed. The method does not require the differentiation of left side functions of the system and provides the solution with arbitrary accuracy, although it may be applied only to systems with not too large a number of equations. Illustrative examples are given.     

On the exponential exponents of discrete linear systems

In this paper we introduce the concepts of exponential exponents of discrete linear time varying systems. It is shown that these exponents describe the possible changes in the Lyapunov exponents under perturbation decreasing at infinity at exponential rate. Finally we present formulas for the exponential exponents in terms of the transition matrix of the system.     

Periodic solutions of nonlinear hyperbolic evolution systems

We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation operator associated with the nonlinear evolution system, expressed in terms of the topological degree. The abstract results shall be applied to the damped hyperbolic partial differential equation.     

Transformations of 5-(2-arylethynyl)-2-methyl-2H-tetrazoles under superelectrophilic activation

Reaction of 5-arylethynyl-2-methyl-2H-tetrazoles (acetylene tetrazoles) with arenes under the action of Brønsted superacid CF₃SO₃H or acidic zeolite HUSY CBV-720 gives rise to E-/Z-5-(2,2-diarylethenyl)-2-methyl-2H-tetrazoles, as products of hydroarylation of acetylene bond, in yields up to 98% with predominant formation of E-isomers. Cationic intermediates of these reactions have been studied theoretically by DFT calculations. Addition of CF₃SO₃H to the triple bond of acetylene tetrazoles leads to the corresponding E-/Z-vinyl triflates in high yields. Hydration of triple bond in these tetrazoles in H₂SO₄ results in the formation of 5-(2-aryl-2-oxoethyl)-2-methyl-2H-tetrazoles. Tandem hydroarylation-ionic hydrogenation of acetylene tetrazoles in the systems acid(CF₃SO₃H or AlCl₃)-arene-cyclohexane affords 5-(2,2-diarylethyl)-2-methyl-2H-tetrazoles.     

Pd electrodeposited from membrane-separated thin layer cell

Polycarbonate (PC) membranes of different porosity (from 50 nm to 400 nm pore size) were used as separators in a thin layer cell for palladium electrodeposition. Atomic force microscopy (AFM) confirmed the formation of Pd layer between the cathode and porous membrane, with subsequent growth inside the pores induced by space limitations of further growth of initial layer. Our estimates confirm that at this stage Pd deposit feels the pronounced mechanical pressure and consider it as a possible reason of specific hydrogen sorption behaviour in the region of β-phase hydride formation. Up to c.a. 1.0 H/Pd atomic ratio is observed for some samples. We consider possible (nano)structural peculiarities responsible for this behaviour.     

Benefiting from information-rich multi-frequency AC voltammetry coupled with chemometrics on the example of on-line monitoring of leveler component of electroplating bath

Simultaneous application of multiple sinusoidal waveforms perturbations superimposed onto DC staircase step significantly enriches current response. The measured current is characterized by a matrix of data rather than a conventional voltammetric output in a form of a vector. This increase of the dimensionality of the current response and therefore the wealth of analytical information is achieved without compromising the time of analysis. The natural approach for compression of such data and extraction of relevant information is by utilizing multi-way chemometric decomposition techniques. An electroplating solution presents a very challenging analyte for electroanalysis as its constituents interact synergistically with each other during both the plating process and its simulation during electroanalysis. For some components the mechanism is not entirely understood. Therefore, the only way to benefit from the analytical data is by employing soft modeling. The electrode processes involving additives rely heavily on adsorption and, indirectly, on electron transfer kinetics for which AC voltammetry is an analytical technique capable of delivering informative signals. This paper presents a rigorous universal method for calculating and validating an exemplary multi-way calibration of a leveler component in a copper electroplating bath used in the semiconductor industry. The method presented employs comparatively Parallel Factor Analysis coupled with Inverse Least Squares Regression and multi-linear Partial Least Squares. The calibration training set consists of multi-frequency AC voltammetric data subjected to pretreatments aiming to select informative independent variables and exclude outliers.     

Synthesis and structure of novel copper(II) complexes with pyrazole derived ligands and metal–ligand interaction in solution

Two new ligands of the coumarin type have been synthesized and characterized by ¹H, ¹³C NMR, IR and MS. The crystal and molecular structures of ligand 2, determined by the X-ray diffraction method, are presented. With copper(II) these ligands create solid complexes of the type CuLCl₂, where L is 5-(2-hydroxybenzoyl)-3-methyl-1-(2-pyridinyl)pyrazol-4-carboxylic acid methyl ester (2) or 3-methyl-1-(2-pyridinyl)-1H-chromene[4,3-c]pyrazol-4-on (3). The new copper(II) complexes have been characterized by elemental analysis and solid state FT-IR. The protonation constants of ligands 2 and 3 have been determined in 5% v/v 1,4-dioxane–water solution (25 °C). The coordination modes in the complexes with copper(II) are discussed for 2 on the basis of potentiometric and UV–Vis data.     

Presmectic wetting and supercritical-like phase behavior of octylcyanobiphenyl liquid crystal confined to controlled-pore glass matrices

The influence of controlled-pore glass (CPG) confinement on the phase behavior of octylcyanobiphenyl liquid crystal (LC) is studied by means of x-ray scattering and high precision calorimetry. For CPG samples with pore diameter 2R>24 nm, the smectic order parameter temperature dependence eta(T) reveals apparent presmectic ordering far above the bulk smectic A-nematic (SmA-N) phase transition for both nontreated and silane-treated CPG matrices. The behavior of eta(T) is qualitatively similar in all samples, well obeying the mean field approach (MFA) in which the surface wetting tendency plays the dominant role. In contrast, the critical fluctuations remain important in the specific heat data, which cannot be described within the MFA. We show experimentally that randomness and surface wetting become dominant over finite-size effects for 2R approximately<10 nm, in agreement with theoretical analysis. In nontreated samples, the noncritical character of the static disorder and the interfacial LC-CPG coupling almost completely suppress the quasi-SmA-N and nematic-isotropic phase transitions at 2R approximately 15.1 and approximately 7.5 nm, respectively.     

Polymer composites of nano-sized particles isolated in matrix

The kinetic and mechanism of thermal decay of transition metal acrylates or its cocrystallites are studied. At 200–300°C the rate of thermal decay can be described by first-order rate equations. The thermal transformations of the metal-containing monomers under study involve dehydration, solid-phase polymerization and thermolysis processes. The composition of products of the thermal transformations are studied. The products of the decay are analyzed by optical and electron microscopy as well as by magnetic measurements, IR and mass spectroscopy. The main solid-state products of decomposition are nanometer-sized particles of metal or its oxide and ferrites with a narrow size distribution stabilized by the polymeric matrix. The average particle sizes, L_av, are 6.0–13.0 nm in the case of FeAcr₃ and 6.0 nm for cocrystallites FeCoAcr and Fe₂CoAcr. © 1998 John Wiley & Sons, Ltd.     

Highly regioselective synthesis of trifluoromethyl derivatives of pyrazolo[1,5-a]pyrimidines bearing fused cycloalkane rings using (2-ethoxycycloalkenyl)-2,2,2-trifluoroethanones

8-Trifluoromethyl-6,7-dihydro-5H-1,4,8a-triaza-s-indacene and 9-trifluoromethyl-5,6,7,8-tetrahydropyrazolo[5,1-b]quinazolines were efficiently generated by condensation of 5(3)-aminopyrazoles with (2-ethoxycycloalkenyl)-2,2,2-trifluoroethanones and isolated in excellent yields. The regiochemistry of the prepared compounds was established by ¹H, ¹³C and ¹⁹F NMR spectroscopy and X-ray diffraction analysis.