On the extended version of Krasnosel'skii's fixed point theorem for Kannan type equicontraction mappings

A sufficient condition is established for the existence of a solution to the equation $\mathcal{T}(u,\mathcal{C}(u))=u$, by considering a class of Kannan type equicontraction mappings $\mathcal{T}:\mathcal{A}\times \overline{\mathcal{C}(\mathcal{A})}\to \Xi$, where $\mathcal{A}$ is a convex, closed and bounded subset of a Banach space $\Xi$ and $\mathcal{C}$ is a compact mapping. To fulfil the desired purpose, we engage the Sadovskii's theorem, involving the measure of noncompactness. The relevance of the acquired results has been illustrated by considering a certain class of initial value problems

Boyd-Wong contractions in F-metric spaces and applications

[EN] The main aim of this paper is to  study the Boyd-Wong type fixed point result in the  F-metric context and apply it to obtain  some existence and uniqueness criteria of solution(s) to a second order initial value problem and a Caputo fractional differential equation. We substantiate our obtained result  by finding a suitable non-trivial example.The Research is funded by the Ministry of Human Resource and Development, Government of India and by the Council of Scientific and Industrial Research (CSIR), Government of India under the Grant Number: 25(0285)/18/EMR-II. This project is funded by National Research Council of Thailand (NRCT) N41A640092.Bera, A.; Dey, LK.; Som, S.; Garai, H.; Sintunavarat, W. (2022). Boyd-Wong contractions in F-metric spaces and applications. Applied General Topology. 23(1):157-167. https://doi.org/10.4995/agt.2022.1535615716723

On Maia type fixed point results via implicit relation

In order to study Maia type fixed point results for several well-known contractions, we suggest two novel contractions called $\mathcal{A}$-contraction and $\mathcal{A}'$-contraction. The majority of the Maia type fixed point results for various contractions can now be unified through these, which eliminate the need to manage various contractions individually. The advantage of including such contractions in the study of Maia type fixed point results has been demonstrated in suitable examples. We present an application of one of our established results towards the conclusion of the paper

Role of Lipid, Protein-Derived Toxic Molecules, and Deficiency of Antioxidants behind the Pathogenesis of Diabetic Retinopathy (DR) in Type 2 Diabetes Mellitus

To determine the role of NADPH-oxidase mediated formation of different lipid, protein-derived molecules, and depletion of vitamin-C level in vitreous behind the endothelial dysfunction-induced vascular endothelial growth factor secretion and pathogenesis of diabetic retinopathy (DR) in type 2 diabetes mellitus (T2DM). Fourteen T2DM patients with mild non-proliferative diabetic retinopathy (MNPDR), 11 patients without diabetic retinopathy (DNR), 17 T2 DM subjects with high-risk proliferative diabetic retinopathy (HRPDR), and 5 healthy individuals without DM underwent vitreous analysis for estimation NADPH oxidase, lipid peroxide like malondialdehyde (MDA), 4-Hydroxy-noneal (HNE) and advanced lipoxidation end product (ALE) like Hexanoyl-lysine (HLY), protein carbonyl compound (PCC), Vitamin-C and concentration of vascular endothelial growth factor (VEGF) secretion following standard spectrophotometric methods and enzyme-linked immunosorbent assay (ELISA). Vitreous concentration of NADPH-oxidase, different protein and lipid-derived molecule, and VEGF were found to be significantly elevated among DNR and of DR subjects with different grades compared to HC subjects whereasthe vitamin-C level was found to be decreased among different DR subjects and DNR subjects in comparison to healthy individuals. Oxidative stress-mediated lipid and protein-derived biomolecules not only add important mediators in the pathogenesis of DR, but also accelerate the progression and severity of microangiopathy

On the Extended Version of Krasnoselśkiĭ’s Theorem for Kannan-Type Equicontractive Mappings

The purpose of the paper is to establish a sufficient condition for the existence of a solution to the equation T(u,C(u))=u using Kannan-type equicontractive mappings, T:A×C(A)¯→Y, where C is a compact mapping, A is a bounded, closed and convex subset of a Banach space Y. To achieve this objective, the authors have presented Sadovskii’s theorem, which utilizes the measure of noncompactness. The relevance of the obtained results has been illustrated through the consideration of various initial value problems

Repeatability tests were performed to ensure the reproducibility of the results. The performance of the devices for different urea concentrations (1mM, 1µM, 1nm and 1pM) is reported in the supporting information from Non-invasive paper-based microfluidic device for ultra-low detection of urea through enzyme catalysis

Plots of current vs time performed to demonstrate the repeatability and reproducibility of the results of the paper fluidic devices in sensing ure

The analyte after being dispensed (A) flows through the paper channels and react with the test reagents in the ports (B) resulting in color change (C). The paper based devices are ultra-thin (D) and are highly flexible (E) that they are often the preferred candidates in point-of-care applications. from Non-invasive paper-based microfluidic device for ultra-low detection of urea through enzyme catalysis

Analyte flowing through the multi-channeled paper fluidic device

Gold-free contacts on Al x Ga 1-x N/GaN high electron mobility transistor structure grown on a 200-mm diameter Si(111) substrate

The authors report on the fabrication and characterization of low-temperature processed gold-free Ohmic contacts for AlxGa1−xN/GaN high electron mobility transistors (HEMTs). The HEMT structure grown on a 200-mm diameter Si(111) substrate is used in this study. Using the Ti/Al/NiV metal stack scheme, the source/drain Ohmic contact optimization is accomplished through the variation of Ti/Al thickness ratio and thermal annealing conditions. For an optimized Ti/Al stack thickness (20/200 nm) annealed at 500 °C for 30 s with smooth contact surface morphology, a specific contact resistivity of ∼6.3 × 10−6 Ω cm2 is achieved. Furthermore, with gold-free Ni/Al gates, the fabricated HEMTs exhibit ION/IOFF ratio of ∼109 and a subthreshold swing of ∼71 mV/dec. The demonstrated gold-free contact schemes thus provide a solution toward the implementation of GaN-based HEMT process on a Si foundry platform.ASTAR (Agency for Sci., Tech. and Research, S’pore)Published versio