Some Results Connected with the Class Number Problem in Real Quadratic Fields

We investigate arithmetic properties of certain subsets of square-free positive integers and obtain in this way some results concerning the class number h（d） of the real quadratic field Q（√d）. In particular, we give a new proof of the result of Hasse, asserting that in this case h（d） = 1 is possible only if d is of the form p, 2q or qr. where p.q. r are primes and q≡r≡3（mod 4）.     

The acid-catalysed reaction of thiols with alkyl 2,3-dideoxy-glyc-2-enopyranosides or glycals

The acid-catalysed (HCl or SnCl₄) reaction of alkyl 2,3 dideoxy-glyc-2-enopyranosides or 3,4,6-tri-O-acetyl-D-glycals with thiols leads to mixtures of alkyl 2,3-dideoxy-1-thio-glyc-2-enopyranosides and 3-S-alkyl-3-thioglycals. Under equilibrium conditions the latter are the preponderant products of the reaction. Cross experiments have confirmed the intermediacy of the allylic carbocation in the reaction. A rationalization of the substitution reactions of 1,2- and 2,3-unsaturated sugars based on HSAB principle has been proposed.     

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.     

The kinetics of cation exchange in network calyxarene-containing polymers: the nanoreactor effect

The kinetics of cation exchange from aqueous solutions of electrolytes in network calyxarene-containing polymers with sulfo acid and phenol ionic groups was studied. It was shown that the interaction of the polymers with aqueous solutions of LiCl, NaCl, AgNO₃, LiOH, NaOH, and (CH₃)₄NOH was controlled by ion diffusion in the polymer phase. The nanoreactor effect, that is, a significant increase in the ion exchange rate in sulfonated calyxarene-containing polymers, was observed. The spherical layer model was used to obtain an analytic dependence of conversion on the interdiffusion coefficient and ion exchange duration in bifunctional cationites.     

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.