Solitons generated by self-organization in bismuth germanium oxide single crystals during the interaction with laser beam

We present here the experimental, theoretical, and numerical investigations of Kerr solitons generated by self-organization in black and yellow high quality bismuth germanium oxide (Bi₁₂GeO₂₀) single crystals. A picosecond laser beam of increasing power induces competing cubic and quintic nonlinearities. The numerical evolution of two-dimensional complex cubic-quintic nonlinear Schrödinger equation with measured values of nonlinearities shows the compensation of diffraction by competing cubic and quintic nonlinearities of opposite sign, i.e., the self-generation and stable propagation of solitons. Experiments as well as numerical simulations show higher nonlinearity in the black Bi₁₂GeO₂₀ than in the more transparent yellow one.     

Development of Gradient Retention Model in Ion Chromatography. Part I: Conventional QSRR Approach

New retention methodology that integrates the conventional quantitative structure-retention relationship (QSRR) approach and gradient retention modeling based on isocratic retention data is developed and presented in this paper. Such an integrated approach removes the general QSRR limitation of highly predefined application conditions (i.e., QSRR are generally applicable only under the conditions used during model development) and allows the prediction of retentions over a wide range of different elution conditions (practically for any isocratic or gradient elution profile). At the same time, it retains the ability to predict retention of components unknown to the model, i.e., the components that have not been used in modeling. Ion-exchange chromatography (IC) analysis of carbohydrates was selected as modeling environment. Three regression techniques were applied and compared during QSRR modeling, namely: stepwise multiple linear regression, partial least squares (PLS), and uninformative variable elimination–PLS regression. The obtained prediction results of the best QSRR model (root-mean-square error of prediction = 22.69 %) were similar to those found in the literature. The upgrade from QSRR to the integrated model did not diminish the predictive ability of the model, indicating an excellent potential of the developed methodology not only in IC but also in chromatography in general.     

Biprobability logic with conditional expectation

This paper is devoted to fill the gap in studying logics for biprobability structures. We introduce the logic $L_{\mathbb AE_1E_2}^a$ with two conditional expectation operators and prove the completeness theorem. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Symmetry properties of resolving sets and metric bases in hypercubes

In this paper we consider some special characteristics of distances between vertices in the \(n\)-dimensional hypercube graph \(Q_n\) and, as a consequence, the corresponding symmetry properties of its resolving sets. It is illustrated how these properties can be implemented within a simple greedy heuristic in order to find efficiently an upper bound of the so called metric dimension \(\beta (Q_n)\) of \(Q_n\), i.e. the minimal cardinality of a resolving set in \(Q_n\). This heuristic was applied to generate upper bounds of \(\beta (Q_n)\) for \(n\) up to \(22\), which are for \(n\ge 19\) better than the existing ones. Starting from these new bounds, some existing upper bounds for \(23\le n\le 90\) are improved by a dynamic programming procedure.     

Formation of two-dimensional (2D) lead dendrites by application of different regimes of electrolysis

Electrodeposition of lead from nitrate electrolyte in constant regimes of electrolysis was analyzed and the obtained powder lead deposits were examined by scanning electron microscopy. Polarization curve for lead electrodeposition consisted of two parts separated by an inflection point. The first part of the polarization curve was characterized by a linear dependence of the current density on overpotential. The linear part of the polarization curve corresponded to ohmic-controlled electrodeposition and single lead crystals were formed in this range of overpotentials. A rapid increase in the current density with increasing overpotential was observed after the inflection point (the second part of the polarization curve). Two-dimensional dendrites were the dominant morphological forms obtained at overpotentials and current densities belonging to the second part of the polarization curve, indicating that the rapid increase of the current density with increasing overpotential corresponded to activation controlled electrodeposition at the tips of the formed dendrites. Comparing the morphologies of the obtained lead deposits with those belonging to the same group of metals (metals characterized by a high exchange current density), such as silver, cadmium, and tin, a strong dependence between the nucleation type and the shape of dendrites for the metals belonging to the same group was established.     

Friction memory effect in complex dynamics of earthquake model

In present paper, an effect of delayed frictional healing on complex dynamics of simple model of earthquake nucleation is analyzed, following the commonly accepted assumption that frictional healing represents the main mechanism for fault restrengthening. The studied model represents a generalization of Burridge–Knopoff single-block model with Dieterich–Ruina’s rate and state dependent friction law. The time-dependent character of the frictional healing process is modeled by introducing time delay τ in the friction term. Standard local bifurcation analysis of the obtained delay-differential equations demonstrates that the observed model exhibits Ruelle–Takens–Newhouse route to chaos. Domain in parameters space where the solutions are stable for all values of time delay is determined by applying the Rouché theorem. The obtained results are corroborated by Fourier power spectra and largest Lyapunov exponents techniques. In contrast to previous research, the performed analysis reveals that even the small perturbations of the control parameters could lead to deterministic chaos, and, thus, to instabilities and earthquakes. The obtained results further imply the necessity of taking into account this delayed character of frictional healing, which renders complex behavior of the model, already captured in the case of more than one block.     

1H and 13C NMR data of methyl tetra‐O‐benzoyl‐D‐pyranosides in acetone‐d6

Complete assignments of ¹H‐ and ¹³C‐NMR resonances of five methyl tetra‐O‐benzoyl‐D‐pyranosides based on ¹H, ¹³C, 2D DQF–COSY, HMQC, HMBC and HSQC–TOCSY experiments have been performed. Copyright © 2009 John Wiley & Sons, Ltd.     

Hartwig’s triple reverse order law revisited

We extend the classical Hartwig’s triple reverse-order law for the Moore–Penrose inverse to closed range bounded linear operators on infinite dimensional Hilbert spaces.     

The protective effects of silymarin against doxorubicin-induced cardiotoxicity and hepatotoxicity in rats

Silymarin is a complex of five major compounds, and silibinin is the most biologically active component of the complex. The aim of this study was to investigate, evaluate and confirm the potential cardioprotective and hepatoprotective effects of administration of silymarin, rich in silibinin, at a dose of 60 mg/kg orally for a time-span of 12 days on doxorubicin induced toxicity in male Wistar rats. The in vivo model was used to explore whether silymarin could prevent damage of liver and heart tissue induced by doxorubicin administered every other day at dose of 1.66 mg/kg intraperitoneally for twelve days. In the study the change of body weight, ECG changes, biochemical parameters of oxidative stress, serum activity of alanine and aspartate transaminase, lactate dehydrogenase, creatine kinase and histological preparations of heart and liver samples of treated animals were examined. According to physiological, pharmacological, microscopic and biochemical results, we confirmed that at the examined dose, silymarin exhibits a protective influence on the heart and liver tissue against toxicity induced by doxorubicin.     

2-Supernilpotent Mal’cev algebras

In this note we prove that a Mal’cev algebra is 2-supernilpotent ([1, 1, 1] =  0) if and only if it is polynomially equivalent to a special expanded group. This generalizes Gumm’s result that a Mal’cev algebra is abelian if and only if it is polynomially equivalent to a module over a ring.