Some notes on PD-operator pairs

This paper points out several remarks on the paper of Pathak and Rai[H. K.Pathak and D. Rai, Common fixed point theorems for PD-operator pairs under relaxed con-ditions with applications, Journal of Computational and Applied Mathematics 239 (2013)103-113]. In fact, under contractive conditions (assumed in the above paper), proving existence of common fixed point by assuming the notion of PD-operator is equivalent to proving the existence of common fixed point by assuming the existence of common fixed point

Fixed point result in controlled fuzzy metric spaces with application to dynamic market equilibrium

summary:In this paper, we introduce $\Theta_f$-type controlled fuzzy metric spaces and establish some fixed point results in this spaces. We provide suitable examples to validate our result. We also employ an application to substantiate the utility of our established result for finding the unique solution of an integral equation emerging in the dynamic market equilibrium aspects to economics

Characterization and hydrogen evolution on Pt/nanoplatelets

Finding suitable catalysts for hydrogen evolution reaction (HER) is key for economic production of hydrogen for use in fuel cells. Reducing the amount of expensive noble metals that are used is one of the ways for obtaining such catalysts. Various combinations of different noble metals and various carbon supports have been studied. In this work nanoplatelets (GNP) was used as a support and on it Pt nanoparticles were electrochemically deposited in sub monolayer nanoislands. Obtained Pt/GNP electrode was characterized by X ray photoelectron spectroscopy (XPS) and scanning electron microscopy (SEM) while its electrocatalytic activity was investigated by cyclic voltammetry (CV), linear sweep voltammetry (LSV) and chronoamperometry . XPS analysis showed that the atomic percentages of Pt in Pt/GNP was 1.3% for electhrochemical deposition and 0.3% for spontaneous deposition, respectively. SEM micrographs of Pt/GNP electrode surface showed that Pt nanoparticles occupy mostly the edges GNP support, while elemental maping confirms the distribution of Pt, C and O over the surface of the electrode. Pt/GNP electrode has shown remarkably good performance for HER reaction in 0.5 M H2SO4 acid solution. Outstanding HER activity was achieved, showing the initial potential close to the equilibrium potential for HER and of -0.003 V and a low Tafel slope of about -30 mV/dec. The chronoamperometric measurement performed over 180 min for hydrogen evolution at the constant potential indicates good stability and durability.Twenty-First Young Researchers’ Conference - Materials Science and Engineering: Program and the Book of Abstracts; November 29 – December 1, 2023, Belgrade, Serbi

Bounded linear and compact operators between the Hahn space and spaces of strongly summable and bounded sequences

We establish the characterisations of the classes of bounded linear operators from the generalised Hahn sequence space hd, where d is an unbounded monotone increasing sequence of positive real numbers, into the spaces wp0, wp and wp∞ of sequences that are strongly summable to zero, strongly summable and strongly bounded by the Cesaro method of order one and index p for 1 ≤ p < ∞. Furthermore, we prove estimates for the Hausdorff measure of noncompactness of bounded linear operators from hd into wp, and identities for the Hausdorff measure of noncompactness of bounded linear operators from hd to wp0. We use these results to characterise the classes of compact operators from hd to wp and wp0. Finally, we provide an example for some applications of our results and visualisations in crystallography.Bulletin t. 153 de l'Académie serbe des sciences et des arts. Classe des sciences mathématiques et naturelles. Sciences mathematiques no 45

Existence of Periodic Fixed Point Theorems in the Setting of Generalized Quasi-Metric Spaces

We introduce the notions of (α-ϕ-ψ)-weaker Meir-Keeler contractive mappings and (α-φ)-stronger Meir-Keeler contractive mappings. We discuss the existence of periodic points in the setting of generalized quasi-metric spaces. Our results improve, extend, and generalize several results in the literature

3D-Microarchitectural patterns of Hyperostosis frontalis interna: a micro-computed tomography study in aged women

Although seen frequently during dissections and autopsies, Hyperostosis frontalis interna (HFI) - a morphological pattern of the frontal bone thickening - is often ignored and its nature and development are not yet understood sufficiently. Current macroscopic classification defines four grades/stages of HFI based on the morphological appearance and size of the affected area; however, it is unclear if these stages also depict the successive phases in the HFI development. Here we assessed 3D-microarchitecture of the frontal bone in women with various degrees of HFI expression and in an age- and sex-matched control group, hypothesizing that the bone microarchitecture bears imprints of the pathogenesis of HFI and may clarify the phases of its development. Frontal bone samples were collected during routine autopsies from 20 women with HFI (age: 69.9 +/- 11.1years) and 14 women without HFI (age: 74.1 +/- 9.7years). We classified the HFI samples into four groups, each group demonstrating different macroscopic type or stage of HFI. All samples were scanned by micro-computed tomography to evaluate 3D bone microarchitecture in the following regions of interest: total sample, outer table, diploe and inner table. Our results revealed that, compared to the control group, the women with HFI showed a significantly increased bone volume fraction in the region of diploe, along with significantly thicker and more plate-like shaped trabeculae and reduced trabecular separation and connectivity density. Moreover, the inner table of the frontal bone in women with HFI displayed significantly increased total porosity and mean pore diameter compared to controls. Microstructural reorganization of the frontal bone in women with HFI was also reflected in significantly higher porosity and lower bone volume fraction in the inner vs. outer table due to an increased number of pores larger than 100m. The individual comparisons between the control group and different macroscopic stages of HFI revealed significant differences only between the control group and the morphologically most pronounced type of HFI. Our microarchitectural findings demonstrated clear differences between the HFI and the control group in the region of diploe and the inner table. Macroscopic grades of HFI could not be distinguished at the level of bone microarchitecture and their consecutive nature cannot be supported. Rather, our study suggests that only two different types of HFI (moderate and severe HFI) have microstructural justification and should be considered further. It is essential to record HFI systematically in human postmortem subjects to provide more data on the mechanisms of its development

PtAu Nanoparticles Supported by Reduced Graphene Oxide as a Highly Active Catalyst for Hydrogen Evolution

PtAu nanoparticles spontaneously deposited on graphene support, PtAu/rGO, have shown remarkably high catalytic activity for hydrogen evolution reaction (HER) in sulfuric acid solution. SEM images of the PtAu/rGO electrode surface showed that Pt nanoparticles that are non-uniform in size occupy both the edges of previously deposited uniform Au nanoparticles and the edges of graphene support. XPS analysis showed that the atomic percentages of Au and Pt in PtAu/rGO were 0.6% and 0.3%, respectively. The atomic percentage of Au alone on previously prepared Au/rGO was 0.7%. Outstanding HER activity was achieved for the PtAu/rGO electrode, showing the initial potential close to the equilibrium potential for HER and a low Tafel slope of −38 mV/dec. This was confirmed by electrochemical impedance spectroscopy. The chronoamperometric measurement performed for 40 min for hydrogen evolution at a constant potential indicated good stability and durability of the PtAu/rGO electrode