Formation and properties of copper chalcogenides thin films on polymers formed using sodium telluropentathionate

The preparative conditions were optimized to get chalcogens layers on the polymer — polyamide PA surface by sorption at room temperature using sodium telluropentathionate, Na₂TeS₄O₆. Further interaction of chalcogenized dielectric with copper’s (I/II) salt solution leads to the formation of mixed Cu_xS_y-Cu_xTe_y layers. Optical, electrical and surface characteristics of the layers are highly controlled by the deposition parameters. The stoichiometry of these layers was established by UV-Visible and AA spectrometry. Optical absorption (transmittance) experiments show the samples are of high optical quality. The band gaps of thin films were obtained from their optical absorption spectra, which were found in the range of 1.44–2.97 eV. XRD was used in combination with AFM to characterize chalcogenides layers’ structural features. XRD analysis confirmed the formation of mixed copper chalcogenides’ layers in the surface of PA with binary phases such as Cu₂Te, Cu_3.18Te₂, copper telluride, Cu_2.72Te₂, vulcanite, CuTe, anilite, Cu₇S₄ and copper sulfide, Cu_1.8S. The crystallite sizes of thin films calculated by the Scherer formula were found to be in the range of 3.07–13.53 nm for Cu_xS_y crystallites and 4.06–20.79 nm for Cu_xTe_y crystallites. At room temperature an electrical resistance of Cu_xS_y-Cu_xTe_y layers varies from 3.0×10³ kΩ□^?1 to 1.0 kΩ□^?1.      

Phenolic compounds,antioxidant activity and Cu,Zn, Cd and Pb content in wild and cultivated cranberries and blueberries

The aim of this study was to determine the content of Cu, Zn, Cd and Pb and the total polyphenol (TP) content as well as the total antioxidant capacity (TAC) in wild cranberries and blueberries collected from different localities of the Slovakia and to compare them with properties of six cranberry and six highbush blueberry cultivars obtained from the research centre. Compared with cultivated cranberries (Cu, Zn, Cd and Pb content: 0.642, 1.496, 0.015 and 0.050 mg/kg FM) in wild fruits, higher Cu (by 37%) and lower Zn, Cd and Pb (by 8%, 7% and 44% respectively) were determined using atomic absorption spectrometry method. In wild blueberries, higher Cu, Zn and Pb (by 16%, 209% and 80% respectively) and similar Cd contents were determined compared with cultivated fruits (Cu, Zn, Cd and Pb content: 0.483, 0.541, 0.003 and 0.055 mg/kg FM). The TP contents estimated by spectrophotometry using Folin–Ciocalteau reagent were in intervals 1405–3161 (cranberries) and 1300–3077 (blueberries) expressed as mg GAE/kg FM. While the average TP content determined in wild cranberries was by 31% lower than that in cultivated cranberries, in wild blueberries it was by 97% higher compared with highbush blueberry cultivars. The values of TAC determined by spectrophotometry method using 2,2-diphenyl-1-picrylhydrazyl were in range 20.67–22.22 (cranberries) and 14.03–24.79 (blueberries) expressed as mmol TE/kg FM. In wild cranberries and blueberries, the lower average TAC values compared with cultivated berries were determined (by 1% and 28%, respectively).     

Catalan Numbers for the Classroom?

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Catalan Numbers for the Classroom?

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On a relative uniform completion of an archimedean lattice ordered group

The notion of a relatively uniform convergence (ru-convergence) has been used first in vector lattices and then in Archimedean lattice ordered groups. Let G be an Archimedean lattice ordered group. In the present paper, a relative uniform completion (ru-completion) of G is dealt with. It is known that exists and it is uniquely determined up to isomorphisms over G. The ru-completion of a finite direct product and of a completely subdirect product are established. We examine also whether certain properties of G remain valid in . Finally, we are interested in the existence of a greatest convex l-subgroup of G, which is complete with respect to ru-convergence. This work was supported by Science and Technology Assistance Agency under the contract No. APVT-20-004104. Supported by Grant VEGA 1/3003/06.     

On the Equality Problem of Conjugate Means

Let ${I\subset\mathbb{R}}$ be a nonvoid open interval and let L : I ²→ I be a fixed strict mean. A function M : I ²→ I is said to be an L-conjugate mean on I if there exist ${p,q\in\,]0,1]}$ and ${\varphi\in CM(I)}$ such that $$M(x,y):=\varphi^{-1}(p\varphi(x)+q\varphi(y)+(1-p-q) \varphi(L(x,y)))=:L_\varphi^{(p,q)}(x,y),$$ for all ${x,y\in I}$ . Here L(x, y) : = A _χ(x, y) ${(x,y\in I)}$ is a fixed quasi-arithmetic mean with the fixed generating function ${\chi\in CM(I)}$ . We examine the following question: which L-conjugate means are weighted quasi-arithmetic means with weight ${r\in\, ]0,1[}$ at the same time? This question is a functional equation problem: Characterize the functions ${\varphi,\psi\in CM(I)}$ and the parameters ${p,q\in\,]0,1]}$ , ${r\in\,]0,1[}$ for which the equation $$L_\varphi^{(p,q)}(x,y)=L_\psi^{(r,1-r)}(x,y)$$ holds for all ${x,y\in I}$ .     

A functional equation with a symmetric binary operation

Let X be a nonempty set containing at least two elements and let \({\circ :X^2\to X}\) be a symmetric binary operation. Furthermore, let A, B, C be real parameters and let \({f,g:X\to\mathbb{R}_+}\) be unknown functions. We investigate the functional equation

$f(x\circ y)[Ag(y)-Bg(x)]=(A+C)f(x)g(y)-(B+C)f(y)g(x)\quad {\rm for\,\,all}\,x,y \in X.$