Kinetics of the heterobimetallic complexes formation in the reactions between chromium(III) macrocyclic species and [Fe(CN)<Subscript>6</Subscript>]<Superscript>4−</Superscript> ions

Formation of a singly bridged heterobimetallic Cr^III–NC–Fe^II anation product of the cis − [Cr(cycb)(H₂O)₂]³⁺ and trans − [Cr(cyca)(H₂O)₂]³⁺ complexes, where cyca and cycb are meso- and rac-5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane respectively, by [Fe(CN)₆]⁴⁻ ions is accompanied by an intensive absorbance increase within 390–470 nm due to an intermetal electron transition. A bell-shape of the pseudo-first order rate constants/pH profile observed for the reactions which have been studied under a large excess of the iron(II) complex is in accordance with the highest reactivity of the chromium(III) complexes in their monohydroxomonoaqua forms. The reaction mechanism has been discussed based on the determined rate law.     

The L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures

Very recently bounds for the L ^q spectra of inhomogeneous self-similar measures satisfying the Inhomogeneous Open Set Condition (IOSC), being the appropriate version of the standard Open Set Condition (OSC), were obtained. However, if the IOSC is not satisfied, then almost nothing is known for such measures. In the paper we study the L ^q spectra and Rényi dimension of generalized inhomogeneous self-similar measures, for which we allow an infinite number of contracting similarities and probabilities depending on positions. As an application of the results, we provide a systematic approach to obtaining non-trivial bounds for the L ^q spectra and Rényi dimension of inhomogeneous self-similar measures not satisfying the IOSC and of homogeneous ones not satisfying the OSC. We also provide some non-trivial bounds without any separation conditions.     

Possibilistic analysis of arity-monotonic aggregation operators and its relation to bibliometric impact assessment of individuals

A class of arity-monotonic aggregation operators, called impact functions, is proposed. This family of operators forms a theoretical framework for the so-called Producer Assessment Problem, which includes the scientometric task of fair and objective assessment of scientists using the number of citations received by their publications.The impact function output values are analyzed under right-censored and dynamically changing input data. The qualitative possibilistic approach is used to describe this kind of uncertainty. It leads to intuitive graphical interpretations and may be easily applied for practical purposes.The discourse is illustrated by a family of aggregation operators generalizing the well-known Ordered Weighted Maximum (OWMax) and the Hirsch h-index.     

Thermal stability,flammability and fire hazard of butadiene-acrylonitrile rubber nanocomposites

This article presents the effect of the method of NBR cross linking on the thermal properties, flammability and fire hazard of its nanocomposites containing modified montmorillonite (NanoBent or Nanofil), using test results obtained by means of a derivatograph, oxygen index and cone calorimetry. It has been found that the thermal stability and flammability of the nanocomposites investigated depend on both the rubber network structure and the type of montmorillonite. The nanoadditives used reduce the flammability of cross-linked nitrile rubber and considerably limit its fire hazard.     

Dielectric properties of the multicomponent PZT-type solid solution

In this paper the multicomponent PZT-type solid solution doped by barium, calcium, strontium, bismuth and germanium with composition: Pb_0.975Ba_0.01Ca_0.01Sr_0.005(Zr_0.52Ti_0.48)O₃ + 1.4 wt.% Bi₂O₃ + 0.3 wt.% GeO obtained by hot uniaxial pressing method is described. The results of structural, dielectric, ferroelectric and electromechanical studies of these ceramics are presented. It has been stated that introduction to the basic composition PZT admixtures of the barium, calcium, strontium, bismuth and germanium has a positive effect on the electro-physic parameters of obtained ceramic samples. This material has good microstructure, with high value of the dielectric permittivity (with the high temperature of phase transition) as well as low dielectric losses. It allows considering this material as elements for low frequency and high temperature electromechanical transducers.     

Synthesis and properties of new non-symmetric 2,5-bis(4-alkylphenylethynyl)thiophenes

The synthesis and characterisation of new non-symmetric 2,5-bis(4-alkylphenylethynyl)thiophenes are described. Phase transition properties of these non-symmetric homologues are compared to those of the corresponding symmetric analogues. Furthermore, optical, dielectric and elastic data of investigated compounds and nematic mixture are provided. Compounds are characterised by ¹H NMR spectroscopy and mass spectrometry (electron ionization) analysis. They show an enantiotropic nematic behaviour in broad temperature ranges, confirmed by a polarising thermomicroscopy and differential scanning calorimetry. Detailed synthetic procedures are attached, showing a great synthetic versatility of the thiophene ring substitution. Synthesised compounds stand as promising components of highly birefringent liquid crystalline mixtures.     

Synthesis and properties of terphenyl- and quaterphenyl-based chiral diesters

A new synthetic approach for the chiral terphenyl- and quaterphenyl-based diesters, bis[(1S)-1-methylheptyl] 1,1′:4′,1″-terphenyl-4,4″-dicarboxylates and bis[(1S)-1-methylheptyl] 1,1′:4′,1″:4″,1″′-quaterphenyl-4,4″′-dicarboxylates, has been developed and optimised. The approach presented allows the synthesis of a range of laterally substituted oligophenyl diesters in good yield. A number of pairs of S,S and R,R isomers have been synthesised and their thermodynamic properties measured. Most of the compounds have very good solubility in a variety of liquid crystalline host mixtures, and moderate helical twisting power, which has been determined for a number of nematic materials, either dielectrically positive or negative. The high birefringence of the oligophenyl core makes them suitable candidates as chiral dopants for medium to highly birefringent nematic materials for generating cholesteric and blue phase materials.     

Why two clocks synchronize: energy balance of the synchronized clocks

We consider the synchronization of two clocks which are accurate (show the same time) but have pendulums with different masses. We show that such clocks hanging on the same beam beside the complete (in-phase) and antiphase synchronizations perform the third type of synchronization in which the difference of the pendulums' displacements is a periodic function of time. We identify this period to be a few times larger than the period of pendulums' oscillations in the case when the beam is at rest. Our approximate analytical analysis allows to derive the synchronizations conditions, explains the observed types of synchronizations, and gives the approximate formula for both the pendulums' amplitudes and the phase shift between them. We consider the energy balance in the system and show how the energy is transferred between pendulums via oscillating beam allowing pendulums' synchronization.     

Optimized configuration interaction approach for trapped multiparticle systems interacting via contact forces

For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency Ω optimized through the minimization of the eigenenergy of the desired level. It is shown that within the framework of this approach the well-converged results can be achieved at much smaller dimensions of the Hamiltonian matrix than with the standard approach that uses $\mathrm{\Omega }=1$. We present calculations for model systems of identical bosons with harmonic and double-well potentials. Our results show promising potential for diminishing the computational cost of numerical simulations of various systems of trapped ultracold atoms.