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The aim of this paper is to introduce the concept of a new nonlinear multi-valued mapping so called weakly (α, ψ, ξ)-contractive mapping and prove fixed point results for such mappings in metric spaces. Our results unify, generalize and complement various results from the literature. We give some examples which support our main results while previous results in literature are not applicable. Also, we analyze the existence of fixed points for mappings satisfying a general contractive inequality of integral type. Many fixed point results for multi-valued mappings in metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph are given here to illustrate the results in this paper.

This article exhibits the thermoelastic interactions because of a consistent heat source in an isotropic, homogeneous, unbounded elastic solid with regards to the modified theory of thermoelasticity without energy dissipation. A novel modification for the three-phase-lag Green–Naghdi (TPL G–N) heat conduction equation is proposed for this purpose. A new potential function is employed to help in solving the present problem together with Laplace and Hankel transforms. After inverting Laplace transforms, the small-time approximated solutions are used to obtain expository expressions for the field variables inside the medium. The trend of variations in all quantities past the elastic wavefront to the heat wavefront is investigated. The quantities suddenly bounce to a high worth just previously the situation of the heat wavefront and from that point hop again to zero qualities. [ABSTRACT FROM AUTHOR]

This article has been devoted to investigating the thermoelastic diffusion problem of an infinite medium. The simple and refined single/dual-phase-lag Green–Naghdi models with and without energy dissipation are proposed. The exact solution of thermodiffusion coupling equations has been obtained considering the regularity conditions. The distributions of the non-dimensional temperature, dilatation, displacement, stresses, concentration and chemical potential are obtained and illustrated graphically. The validity of results is acceptable by comparing all outcomes. Benchmark results are reported to help other investigators in their future comparisons. [ABSTRACT FROM AUTHOR]

The MnO2-based heterogeneous catalyst has been considered as one of the most efficient catalysts for enzyme-like catalysis, however, it usually suffers from low stability and difficulty in recycling and reuse. Herein, MnO2 nanosheets supported on nickel foam (NF@MnO2) have been fabricated, via a facile one-step hydrothermal process, as an artificial oxidase for the detection and quantification of ascorbic acid (AA). NF, as a magnetic support, possesses a three-dimensional (3D) skeleton and excellent conductivity, which greatly facilitate the utilization of active sites, electron transfer, as well as separation from the solution with an external magnet. Owing to this unique architecture and the synergistic effect between NF and MnO2, the designed NF@MnO2 composites show enhanced enzyme-like activity toward the oxidation of 3,3′,5,5′-tetramethylbenzidine (TMB) as compared to NF or MnO2 alone. By virtue of the reducing ability of ascorbic acid (AA), the AA selectively inhibited this reaction with a detection limit of 0.1 μM. More importantly, this kind of NF-based design can be easily extended to the synthesis of other functional materials for enzyme-like catalytic applications. [ABSTRACT FROM AUTHOR]

Supported nonprecious metal nanoparticles (NPs) have attracted considerable interest for their low cost and excellent properties. However, immobilizing them with good dispersion on supports is still a great challenge. Herein, we report a one-pot Stöber method to prepare a high coverage of nickel (Ni) NPs anchored to a resorcinol–formaldehyde (RF)-derived graphic carbon layer on silica. By simple removal of the Ni NPs and silica cores, highly desired hollow graphitic carbon spheres with distinctive properties can be fabricated. Notably, nickel ions not only boost the polymerization of RF-Ni2+ but also control nickel-induced carbon graphitization when Ni NPs are generated from the nickel ions. Meanwhile, the RF-Ni2+ polymer can be finely covered on various supports, including MnO2 nanowires, graphene oxide, and carbon nanofibers, and can easily result in well-dispersed Ni NPs on these supports. Moreover, resorcinol can be replaced by similar chemicals like 3-aminophenol, melamine, and 2,4-dihydroxybenzoic acid to synthesize various polymers, greatly expanding the versatility of this method. Additionally, by a change of the molar ratio of resorcinol to nickel ion or control of the annealing temperature, the coverage and size of Ni NPs could be finely adjusted. Because of the high coverage of Ni NPs with good dispersion, the resultant SiO2@C-Ni hybrids display excellent performance in both the reduction of 4-nitrophenol and adsorption on histidine-rich proteins. [ABSTRACT FROM AUTHOR]

Conversion‐type transition metal oxide MoO3 has attracted considerable interest as a promising anode material for lithium ion batteries (LIBs), but it suffers from the low electronic conductivity and the large volume changes upon lithiation/delithiation. To overcome these drawbacks, we herein report the full encapsulation of core‐shelled MoO3‐TiO2 into the carbon nanofibers (CNFs) via a facile coaxial electrospinning followed by a two‐step annealing process. TiO2 shells and MoO3 cores were coaxially integrated into the porous CNFs (denote the composite as TiO2/MoO3@CNFs). The two‐step annealing strategy (carbonization in Ar and then oxidization in air) allows the readily encapsulation of MoO3 into CNFs. When applied as anode materials for LIBs, the coaxial TiO2/MoO3@CNFs demonstrate superior lithium storage performance, delivering a high reversible capacity of 561 mAh/g after 300 cycles at 1000 mA/g with a much higher capacity retention of 70.8% than that of the MoO3@CNFs without TiO2 layers (only 42.3%). The results clearly demonstrate that the CNFs matrices and the TiO2 shells together efficiently enhance the electrode conductivity and buffer the volume changes of MoO3 upon cycling. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce α-generalized multi-valued contractions in cone metric spaces over Banach Algebras with solid cones and show the existence of fixed points of these contractions in this context. Our results generalize and extend several known results in metric and cone metric spaces given by some authors. Also, we give one example to illustrate significance of the main result in this paper. [ABSTRACT FROM AUTHOR]