Motzkin numbers out of Random Domino Automaton

Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton.     

Preparation of partially functionalised resorcinarene derivatives

The conditions for synthesis of mono-, di- and trifunctionalised resorcinarenes by catalysed Mannich reaction are described. A series of these compounds are functionalised with different functional groups.     

Synthesis of Chitosan-La2O3 Nanocomposite and Its Utility as a Powerful Catalyst in the Synthesis of Pyridines and Pyrazoles

Recently, the development of nanocatalysts based on naturally occurring polysaccharides has received a lot of attention. Chitosan (CS), as a biodegradable and biocompatible polysaccharide, is considered to be an excellent template for the design of a hybrid biopolymer-based metal oxide nanocomposite. In this case, lanthanum oxide nanoparticles doped with chitosan at different weight percentages (5, 10, 15, and 20 wt% CS/La₂O₃) were prepared via a simple solution casting method. The prepared CS/La₂O₃ nanocomposite solutions were cast in a Petri dish in order to produce the developed catalyst, which was shaped as a thin film. The structural features of the hybrid nanocomposite film were studied by FTIR, SEM, and XRD analytical tools. FTIR spectra confirmed the presence of the major characteristic peaks of chitosan, which were modified by interaction with La₂O₃ nanoparticles. Additionally, SEM graphs showed dramatic morphological changes on the surface of chitosan, which is attributed to surface adsorption with La₂O₃ molecules. The prepared CS/La₂O₃ nanocomposite film (15% by weight) was investigated as an effective, recyclable, and heterogeneous base catalyst in the synthesis of pyridines and pyrazoles. The nanocomposite used was sufficiently stable and was collected and reused more than three times without loss of catalytic activity.     

Noncovalent Bonds through Sigma and Pi-Hole Located on the Same Molecule. Guiding Principles and Comparisons

Over the last years, scientific interest in noncovalent interactions based on the presence of electron-depleted regions called σ-holes or π-holes has markedly accelerated. Their high directionality and strength, comparable to hydrogen bonds, has been documented in many fields of modern chemistry. The current review gathers and digests recent results concerning these bonds, with a focus on those systems where both σ and π-holes are present on the same molecule. The underlying principles guiding the bonding in both sorts of interactions are discussed, and the trends that emerge from recent work offer a guide as to how one might design systems that allow multiple noncovalent bonds to occur simultaneously, or that prefer one bond type over another.     

Investigation of Parameters Influencing Tubular-Shaped Chitosan-Hydroxyapatite Layer Electrodeposition

Tubular-shaped layer electrodeposition from chitosan-hydroxyapatite colloidal solutions has found application in the field of regeneration or replacement of cylindrical tissues and organs, especially peripheral nerve tissue regeneration. Nevertheless, the quantitative and qualitative characterisation of this phenomenon has not been described. In this work, the colloidal systems are subjected to the action of an electric current initiated at different voltages. Parameters of the electrodeposition process (i.e., total charge exchanged, gas volume, and deposit thickness) are monitored over time. Deposit structures are investigated by scanning electron microscopy (SEM) and Fourier-transform infrared spectroscopy (FTIR). The value of voltage influences structural characteristics but not thickness of deposit for the process lasting at least 20 min. The calculated number of exchanged electrons for studied conditions suggests that the mechanism of deposit formation is governed not only by water electrolysis but also interactions between formed hydroxide ions and calcium ions coordinated by chitosan chains.     

Two-Parameter Fuzzy-Valued Stochastic Integrals and Equations

This article is concerned with notions of fuzzy-valued stochastic integrals driven by two-parameter martingales and increasing processes. We present their main properties and formulate next two-parameter fuzzy-valued stochastic integral equations. We establish the existence and uniqueness of solutions to such equations as well as their additional properties.     

Influence of cooling rate on crystallisation kinetics on microstructure of cast zinc alloys

In this study, the change of the cooling rate in the range of about 0.1–1 °C s^?1 and the addition of Sr on the crystallization kinetics of the cast zinc alloys of the ZnAlCu type, as well as its relation to the microstructure were also investigated. Therefore, the aim of the rapid crystallisation is the achievement of materials with better properties, which can be obtained by refinement of the dendritic or eutectic microstructure, elimination of segregation, or creation of metastable phases and their morphology changes. In the investigated alloys, the change of cooling rate of 1 °C s^?1 has caused microstructure’s refinement as well as increase in hardness. Increase in the cooling rate causes also morphology changes of the η + α eutectic, and makes generally a global overcooling of the alloy as well as change in the temperatures at the beginning of crystallization T _DN and of the alloy crystallization T _S. The presented investigations concerning the electron microscopy methods, including transmission electron microscopy, allow revealing the crystallographic structure, based on the d-spacing changes, as well as the diffraction method used for phase determination, which is a helpful tool for the explanation of the important points in the thermo-derivative analysis curve, where the relation between the amount of phase and the occurrence of new phases can be determined.