Managing differences by focusing on communication qualities: Pupils learning mathematics in pairs at a computer

The article presents a study of face-to-face verbal communication when pupils work with geometry in pairs and share a stand-alone computer with Geoboard software. The work sessions of pairs of 9th grade pupils are video recorded, and a screen recorder is used to capture their computer activity. The study focuses on identifying and characterizing good communication practices that enhance mathematics learning through joint research reflections between the pupils, the teacher, and the researcher. The major finding concerns how two of the pupils have diverging perspectives on how to communicate mathematics, yet they manage to have productive collaboration. The differences generate collaborative challenges for the pupils and an opportunity to discuss how pupils’ communication qualities can prove important in fruitfully managing such challenges.     

Functional sample path properties of subsequence's C-R increments for a Wiener process in Hlder norm

In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by H¨older norm, we discuss the functional sample path properties of subsequence's C-R increments for a Wiener process in H¨older normThe obtained results,generalize the corresponding results of Chen and the classic Strassen's law of iterated logarithm for a Wiener process.     

Study of blood collection and sample preparation for analysis of vitamin D and its metabolites by liquid chromatography–tandem mass spectrometry

The analysis of vitamin D status, with special emphasis on 25-hydroxyvitamin D and 1,25-dihydroxyvitamin D, is gaining interest in clinical studies due to the classical and non-classical effects attributed to this prohormone. In this research, the influence of the two steps preceding determination (viz. sample collection and preparation) on the quantitative analysis of vitamin D and its more important metabolites has been studied. Two preparation approaches, deproteination and solid-phase extraction (SPE), have been evaluated in terms of sensitivity to delimit their application, thus establishing that detection of 1,25-dihydroxyvitamin D cannot be addressed by protein precipitation. Concerning sample collection, serum and plasma reported high accuracy (above 83.3%) for vitamin D and metabolites, while precision, expressed as relative standard deviation, was below 12.9% for all analytes in both samples. Statistical analysis revealed that serum and plasma provided similar physiological levels for vitamin D₃, 24,25-dihydroxyvitamin D₃ and 25-hydroxyvitamin D₃, while significantly different levels were obtained for 1,25-dihydroxyvitamin D₃, always higher in plasma than in serum. Sample collection and treatment have proved to be significant in the analysis of vitamin D and its relevant metabolites.     

Insight into copper-mordenite–silica mixtures (CuMOR–SiO2)

A series of ternary CuMOR–SiO₂ mixed materials were prepared by two synthesis approaches (CuMOR1–y–SiO₂ and CuMOR2–y–SiO₂). Extensive characterization was done for both series and some selected materials were tested in CO catalytic oxidation and NO reduction. The presence of CuMOR and SiO₂ segregated phases was observed in both series by XRD, suggesting that silica formation was not inhibited by the mordenite (MOR) presence. UV–Vis results exhibited that Cu ion exchange was successfully done for CuMOR1–y–SiO₂ series. In the CuMOR2–y–SiO₂ series, the amount of copper was below the sensitivity limit of EDS analysis. CuMOR1–50%–SiO₂ catalyst resulted with higher specific surface area and catalytic activity. A possible relation between reduction temperature, the increase in Cu plasmon excitation, and catalytic activity was observed.     

Novel flame retardant paint based on Co(II) and Ni(II) metal complexes as new additives for surface coating applications

The study is focused on the synthesis of a new Co(II) and Ni(II) metal complexes, which is synthesized by the reaction of the isatin 4‐aminoantipyrine Schiff base ligand with selected divalent Co(II) and Ni(II) ions and their possible applications as flame retardant additives in paint formulations for surface coating application. The prepared metal complexes were characterized using a combination of Fourier transform infrared, elemental analysis, proton nuclear magnetic resonance, ¹³C‐NMR spectra, and mass spectroscopy. The prepared Schiff base ligand metal complexes were physically added to alkyd paint formulation to give coating formulations at a laboratory scale and then applied onto plywood and steel panels using a brush. The ignitability and oxygen index values obtained indicated that the paint which contained the prepared Co(II) and Ni(II) metal complexes as additives exhibited very good flame retardant. The physical and mechanical characteristics of the coatings were studied in order to estimate any disadvantages due to the incorporation of the additives. It was discovered that the added substances did not impact the hardness, flexibility, and adhesion of the prepared coating films. The gloss of the paint formulation film was improved due to the incorporation of the aromatic ring into the formulation and the level of the oil percent.     

Methyl orange degradation enhanced by hydrogen spillover onto platinum nanocatalyst surface

Following a thermal reduction method, platinum nanoparticles were synthesized and stabilized by polyvinylpyrrolidone. The colloidal platinum nanoparticles were stable for more than 3 months. The micrograph analysis unveiled that the colloidal platinum nanoparticles were well dispersed with an average size of 2.53 nm. The sol–gel‐based inverse micelle strategy was applied to synthesize mesoporous iron oxide material. The colloidal platinum nanoparticles were deposited on mesoporous iron oxide through the capillary inclusion method. The small‐angle X‐ray scattering analysis indicated that the dimension of platinum nanoparticles deposited on mesoporous iron oxide (Pt‐Fe₂O₃) was 2.64 nm. X‐ray photoelectron spectroscopy (XPS) data showed that the binding energy on Pt‐Fe₂O₃ surface decreased owing to mesoporous support–nanoparticle interaction. Both colloidal and deposited platinum nanocatalysts improved the degradation of methyl orange under reduction conditions. The activation energy on the deposited platinum nanocatalyst interface (2.66 kJ mol^?1) was significantly lowered compared with the one on the colloidal platinum nanocatalyst interface (40.63 ± 0.53 kJ mol^?1).     

Free volume characteristics of 2,2-bistrifluoromethyl-4,5-difluoro-1,3-dioxole-co-tetrafluoroethylene copolymers: Effect of composition and molecular weight

2,2-bistrifluoromethyl-4,5-difluoro-1,3-dioxole-co-tetrafluoroethylene (PDD-TFE) copolymer is a good candidate to prepare gas separation membranes with excellent permeability due to its free volume characteristics. However, the influence of PDD-TFE copolymer structure on its free volume characteristics is less studied. In this paper, PDD-TFE copolymers with different compositions and molecular weights were synthesized, and their free volume characteristics were analyzed by positron annihilation lifetime spectroscopy and a molecular dynamics simulation. It indicated that the molar fraction of PDD in copolymers had a significant effect on free volume characteristics, while the molecular weight of copolymers exerted a slight influence on free volume when the molecular weight exceeded a critical region (intrinsic viscosity [η] > 68 ml g⁻¹). PDD-TFE copolymers with greater PDD molar fractions (i.e., 72% and 84%) showed bimodal distributions in positron lifetime and free volume size distributions, while PDD-TFE copolymers with lower PDD molar fractions (i.e., 27% and 35%) exhibited a single peak. The long-lifetime parameter τ₃ was assigned to micro-cavities formed by [-(TFE)_y-PDD-] segments and τ₄ was attributed to micro-cavities formed by [-(PDD)_x-TFE-] segments. The cis and trans transitions of PDD led to a local multilayer spiral structure with a 2.6–4.3 Å layer spacing, which would also increase the free volume of copolymers.     

Infinite family of transmission irregular trees of even order

Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph $G$. The transmission of a vertex $v$ is the sum of distances from $v$ to all the other vertices of $G$. If transmissions of all vertices are mutually distinct, then $G$ is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees of odd order were presented in Alizadeh and Klav?ar (2018). The following problem was posed in Alizadeh and Klav?ar (2018): do there exist infinite families of transmission irregular trees of even order? In this article, such a family is constructed.     

Extended Open-Chain Polyenides as Versatile Delocalized Anion Ligands for Metal Chain Clusters

Although small cyclic- and open-chain unsaturated hydrocarbon anions such as cyclopentadienide and open-chain pentadienide are used as the strongly electron-donating auxiliary ligands for metal complexes, more extended π-conjugated unsaturated hydrocarbon anions have rarely been used in coordination chemistry, despite their potential ability to serve as the multiply bridging π-ligands for metal clusters. This work reports isolation of metal chain clusters bearing the multi-dentate, open-chain extended unsaturated hydrocarbon anion ligands. The extended open-chain π-conjugated polyenyl ligands could effectively stabilize oxidized palladium chains, including an unprecedented [Pd₄]⁴⁺ chain.     

Conformational Changes and Redox Properties of Bimetallic Single Helicates of Hexapyrrole-α,ω-dicarbaldehydes

The hexapyrrole-α,ω-dicarbaldehydes 1 a and 1 b were metallated with Cu^II, Ni^II, and Pd^II to give bimetallic complexes where a pair of 3 N+O four-coordinate metal planes are helically distorted and the central 2,2′-bipyrrole subunit adopts a cis or trans conformation. X-ray crystallographic analysis of the bisCu complex revealed a closed form with a cis-2,2′-bipyrrole subunit and an open form with a trans-2,2′-bipyrrole subunit. The bisPd complexes took a closed form both in the solid state and in solution. They are regarded as single helicates of two turns and the energy barrier for the interchange between an M helix and a P helix was remarkably influenced by the bulky 3,3′-substituent of the central 2,2′-bipyrrole subunit. Although the bisNi complexes adopt a closed form in the solid state, they exist as a homohelical open C₂-symmetric form or a heterohelical open C_i-symmetric form in solution. A theoretical study suggested that the closed form of 1 a Pd was stabilized by the Pd–Pd interaction. Compound 1 a Pd was reversibly oxidized by one electron at 0.14 V versus ferrocene/ferrocenium (Fc/Fc⁺) and this oxidized species showed Vis/NIR absorption bands at λ=767 and 1408 nm.