A new approach to the Assad–Kirk fixed point theorem

In the present paper, considering the Wardowski’s technique, we give a new approach to the Assad–Kirk fixed point theorem on metrically convex metric spaces.We also provide a nontrivial example showing that our result is a proper extension of the Assad–Kirk fixed point theorem.     

A nonlinear stochastic growth model on discrete time domains

In this paper, we introduce nonlinear stochastic dynamic problems on discrete time domains where events may occur at unevenly spaced time points. We define Euler equation and transversality condition for the problem. We prove that the Euler equation and the transversality condition are sufficient for the existence of the optimal solution. Next we generalize discrete time Cagan type rational expectation model to multivariate case. As an application of the main results, we obtain an explicit solution to a log-linearized nonlinear stochastic growth model.     

On the geometry of complex ‐spaces

It is known that applying an ‐homothetic deformation to a complex contact manifold whose vertical space is annihilated by the curvature yields a condition which is invariant under ‐homothetic deformations. A complex contact manifold satisfying this condition is said to be a complex ‐space. In this paper, we deal with the questions of Bochner, conformal and conharmonic flatness of complex ‐spaces when , and prove that such kind of spaces cannot be Bochner flat, conformally flat or conharmonically flat.     

Understanding Electrochemical Reaction Mechanisms of Sulfur in All-Solid-State Batteries through Operando and Theoretical Studies **

Due to its outstanding safety and high energy density, all-solid-state lithium-sulfur batteries (ASLSBs) are considered as a potential future energy storage technology. The electrochemical reaction pathway in ASLSBs with inorganic solid-state electrolytes is different from Li-S batteries with liquid electrolytes, but the mechanism remains unclear. By combining operando Raman spectroscopy and ex situ X-ray absorption spectroscopy, we investigated the reaction mechanism of sulfur (S₈) in ASLSBs. Our results revealed that no Li₂S_8, Li₂S_6, and Li₂S₄ were formed, yet Li₂S₂ was detected. Furthermore, first-principles structural calculations were employed to disclose the formation energy of solid state Li₂S_n (1≤n≤8), in which Li₂S₂ was a metastable phase, consistent with experimental observations. Meanwhile, partial S₈ and Li₂S₂ remained at the full lithiation stage, suggesting incomplete reaction due to sluggish reaction kinetics in ASLSBs.     

Thermal deformation thermodynamics of a smectite mineral

A method has been purposed to calculate some of the thermodynamic quantities for the thermal deformation of a smectite without using any basic thermodynamic data. The Hanç?l? (Keskin, Ankara, Turkey) bentonite containing a smectite of 88% by volume was taken as material. Thermogravimetric (TG) and differential thermal analysis (DTA) curves of the sample were obtained. Bentonite samples were heated at various temperatures between 25–900°C for the sufficient time (2 h) until to establish the thermal deformation equilibrium.Cation-exchange capacity (CEC) of heated samples was determined by using the methylene blue standard method. The CEC was used as a variable of the equilibrium. An arbitrary equilibrium constant (K _a) was defined similar to chemical equilibrium constant and calculated for each temperature by using the corresponding CEC-value. The arbitrary changes in Gibbs energy (ΔG _a ⁰ ) were calculated from K _a-values. The real change in enthalpy (ΔH ⁰) and entropy (ΔS ⁰) was calculated from the slopes of the lnK vs. 1/T and ΔG vs. T plots, respectively. The real changes in Gibbs energy (ΔG ⁰) and real equilibrium constant (K) were calculated by using the ΔH ⁰ and ΔS ⁰ values. The results at the two different temperature intervals are summarized as below: ΔG ₁ ⁰ =ΔH ₁ ⁰ ?ΔS ₁ ⁰ T=?RTlnK ₁=47000?53t, (200–450°C), and ΔG ₂ ⁰ =ΔH ₂ ⁰ -ΔS ₂ ⁰ T=?RTlnK ₂=132000?164T, (500–800°C).     

Water vapour barrier performance of corn-zein coated polypropylene (PP) packaging films

The novel film structure of corn-zein coated on polypropylene (PP) synthetic film for packaging industry was developed to examine the feasibility of resulting coated films as an alternative water barrier performance for food packaging. The effects of coating formulation (solvent, corn-zein, plasticizer concentration and plasticizer type) on final properties of films were observed. Corn-zein is the most important protein of corn and has good film forming property. Composites structures of PP films coated with corn-zein were obtained through a simple solvent casting method. Polyethylene glycol (PEG) and glycerol (GLY) were used as plasticizer to increase film flexibility. Statistical analysis based on full factorial design was performed to observe coating formulation effects. The high water vapour barriers were obtained for films coated with coating formulation consisting of higher amounts of corn-zein plasticized by GLY. The lower glass transition temperatures (T _g) of films were obtained by plasticization of films and T _g decreased by increasing plasticizer content. The statistical analysis defined the key parameters of coating formulation that had major effects on the final properties of coated PP films as corn-zein, plasticizer concentration and plasticizer type. In conclusion, corn-zein coatings could have potential as an alternative to conventional synthetic polymers used in composite multilayer structures for food packaging applications.     

On the Riesz difference sequence space

In the present paper, we define the difference sequence space r ^q (p, Δ), which is defined as follows:

Methoxy-activated indole-7-carbohydrazides; synthesis,antioxidant, and anticancer properties

Indole has been known as a key heterocyclic motif in the development of new structures for both chemical and biological properties. In this current study, a new range of indole-7-carbohydrazides has been successfully synthesized starting from the readily available 3-phenyl and 2,3-diphenyl 4,6-dimethoxyindoles. The structures of the novel compounds were confirmed by utilizing ¹H NMR, ¹³C NMR, FT-IR, high-resolution mass spectrometry, and single crystal X- ray diffraction techniques. In addition, the indole-7-carbohydrazides showed promising antioxidant results in preliminary screens. Some of the new compounds generated from dimethoxy indoles were also screened for their anticancer activity against SH-SHY5Y (human neuroblastoma), AGS (human gastric adenocarcinoma), and MDA-MB-231 (human breast adenocarcinoma) cell lines. The results revealed that the compound 12 was the promising candidate, showing cytotoxic effects on both neuroblastoma, stomach, and breast cancer cells.     

Synthesis,characterization, and histological activity of novel polydentate azo ligands and their cobalt(II), copper(II) and nickel(II) complexes

We describe the synthesis and characterization of two novel azo ligands, 4,5-dihydroxy-3,6-bis(2-hydroxyphenylazo)-2,7 naphthalene disulfonic acid (H₂L) and 4,5-dihydroxy-3,6-bis(2-hydroxy-4-sulfophenylazo)-2,7-naphthalenedisulfonic acid (H₂L¹). The Cu(II), Ni(II), and Co(II) complexes of these ligands were prepared and characterized by infrared, UV–Vis, ¹H- and ¹³C-NMR spectra, atomic absorption spectroscopy, mass spectrometry, elemental analyses, thermogravimetric analysis, conductivity, cyclic voltammetry, and magnetic measurements. The results suggest that the complexes have a 2:1 (metal:ligand) molar ratio, involving binuclear azo ligands with an ONO donor set. Metal ion uptake studies were conducted with a batch technique. Preliminary histological studies were also made. The results indicate that the azo ligands have high thermal stability, good metal extraction capacity, and favorable dying properties with certain tissues.