Approximation by some operators of Szasz-Mirakyan type

In this paper we give theorems on the degree of approximation of functions of one and two variables by certain operators of the Szasz-Mirakyan type.     

Influence of d-Electron Divalent Metal Ions in Complex Formation with L-Tartaric and L-Malic Acids

Binary complexes of α-hydroxy acids (L-Tartaric acid and L-Malic acid) with d-electron metal ions (copper, cobalt, nickel) were investigated. Potentiometric measurements have been performed in aqueous solution with computer analysis of the data for determination of the stability constants of complexes formed in the studied systems. The coordination mode of the complexes was defined using spectroscopic methods: electron paramagnetic resonance (EPR), ultraviolet-visible (UV-Vis), circular dichroism (CD), and infrared (IR). Results of the equilibrium studies have provided evidence for the formation of dimers with copper(II) ions and monomers with cobalt(II) and nickel(II) ions.     

Hydrogen Bonding Directed Self-Assembly of a Binuclear Ag(I) Metallacycle into a 1D Supramolecular Polymer

An Ag(I) metallacycle obtained unexpectedly during the preparation of Pd(II) complexes of the bifunctional ligand 5-([2,2′-bipyridin]-5-yl)pyrimidine-2-amine (L) has been characterized using X-ray structure determination as a binuclear, metallacyclic species [Ag₂L₂](SbF₆)₂, where both the bipyridine and pyrimidine-N donors of L are involved in coordination to the metal. The full coordination environment of the Ag(I) defines a case of highly irregular 4-coordination. In the crystal, the Ag-metallacycles assemble into one-dimensional supramolecular metalladynamers linked together by hydrogen-bonding interactions.     

MA-XRF study of 15th–17th century icons from the collection of the National Museum in Krakow,Poland

In 2015, the National Museum in Krakow, Poland, started a grant from the National Programme for the Development of Humanities, its goal to investigate an important collection of old Orthodox painting, including more than 50 15th to 17th century icons originating from the territory of the historical Orthodox Diocese of Przemyśl within the borders of the Polish Kingdom. The aim of researching the iconography, provenance, and technology of the artworks was to describe their specific features and destination, in detail, and to characterise their artistic milieu. Many different techniques were used during research, such as X-ray fluorescence (XRF), X-ray diffraction, reflectography, radiography, ultraviolet–visible imaging, Fourier-transform infrared spectroscopy, scanning electron microscopy with energy-dispersive X-ray spectroscopy of prepared paint layer cross sections, and dendro-chronological analysis. This paper focuses on highlighting the advantages and disadvantages of the spatially resolved macro-XRF scanning (MA-XRF) technique. Most interesting results concluded from elemental distribution maps obtained through the use of Bruker, M6 Jetstream MA-XRF scanner include the following: characterisation of the type of gold and silver foil used in the icons; determination of main pigments, including the use of lead tin yellow unusual in iconography; and the noting of an interesting distribution of blue pigments as well as the presence of orpiment. Surprisingly, a considerable amount of zinc with azurite addition was observed in brown layers. The results obtained primarily highlight all the typical features of local Carpathian icon craft.     

Invariant Metrics on G-Spaces

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an invariant metric on X. We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and locally connected metric space.     

Computational Analysis of Ca2+ Oscillatory Bio-Signals: Two-Parameter Bifurcation Diagrams

Two types of bifurcation diagrams of cytosolic calcium nonlinear oscillatory systems are presented in rectangular areas determined by two slowly varying parameters. Verification of the periodic dynamics in the two-parameter areas requires solving the underlying model a few hundred thousand or a few million times, depending on the assumed resolution of the desired diagrams (color bifurcation figures). One type of diagram shows period-n oscillations, that is, periodic oscillations having n maximum values in one period. The second type of diagram shows frequency distributions in the rectangular areas. Each of those types of diagrams gives different information regarding the analyzed autonomous systems and they complement each other. In some parts of the considered rectangular areas, the analyzed systems may exhibit non-periodic steady-state solutions, i.e., constant (equilibrium points), oscillatory chaotic or unstable solutions. The identification process distinguishes the later types from the former one (periodic). Our bifurcation diagrams complement other possible two-parameter diagrams one may create for the same autonomous systems, for example, the diagrams of Lyapunov exponents, Ls diagrams for mixed-mode oscillations or the 0–1 test for chaos and sample entropy diagrams. Computing our two-parameter bifurcation diagrams in practice and determining the areas of periodicity is based on using an appropriate numerical solver of the underlying mathematical model (system of differential equations) with an adaptive (or constant) step-size of integration, using parallel computations. The case presented in this paper is illustrated by the diagrams for an autonomous dynamical model for cytosolic calcium oscillations, an interesting nonlinear model with three dynamical variables, sixteen parameters and various nonlinear terms of polynomial and rational types. The identified frequency of oscillations may increase or decrease a few hundred times within the assumed range of parameters, which is a rather unusual property. Such a dynamical model of cytosolic calcium oscillations, with mitochondria included, is an important model in which control of the basic functions of cells is achieved through the Ca2+ signal regulation.