Some bounds for integrals with refinements of the Grüss inequality

Some integral bounds are obtained which provide refinements and extensions of the Grüss type inequalities. We also get an alternative formulation of the Grüss inequality.     

Effects on the bifurcation and chaos in forced Duffing oscillator due to nonlinear damping

In this communication, the two-well Duffing oscillator with non-linear damping term proportional to the power of velocity is considered. We mainly focus our attention on how the damping exponent affects the global dynamical behaviour of the oscillator. In particular, we obtain analytically the threshold condition for the occurrence of homoclinic bifurcation using Melnikov technique and compare the results with the computational results. We also identify the major route to chaos and the regions of the 2D parameter space (consists of external forcing amplitude and damping coefficient) corresponding to the various types of asymptotic dynamics under linear (viscous or friction like) and nonlinear (drag like) damping. We also attempt to analyze how the basins of attraction patterns change with the introduction of nonlinear damping. We also present our analysis for the physically less-interesting cases where damping is proportional to the 3rd and 4th power of velocity for the sake of generalizing our findings and establishing firm conclusion.     

A Robust numerical approach for singularly perturbed time delayed parabolic partial differential equations

We consider the numerical solution of a initial boundary value problem with a time delay. The problem under consideration is singularly perturbed from the mathematical perspective. Assuming that the coefficients of the differential equation are smooth, we construct and analyze the finite difference method whose solutions converge pointwise at all points of the domain independently of the singular perturbation parameter. The method permits its extension to the case of adaptive meshes, which may be used to improve the solution. Numerical examples are presented to demonstrate the effectiveness of the method. The convergence obtained in practice satisfies the theoretical predictions.     

CuFe2O4 nanomaterials: Current discoveries in synthesis,catalytic efficiency in coupling reactions,and their environmental applications

In the last few decades, there has been enormous growth in ferrite nanoparticles. Magnetic, optical, and electrical properties of ferrites gain consideration due to their use in various applications such as rechargeable lithium batteries, medical diagnostics, solar energy devices, and so forth. A vast increase in interest in ferrite nanoparticles has led them to be used as catalysts in various applications as they possess a large surface area-to-volume ratio. Furthermore, iron-based magnetic characteristics make it simple to retrieve catalysts by using an external magnet. Iron's catalytic potential, however, is far less than copper's. Therefore, the catalytic scope is substantially increased by substituting copper within the crystal lattice. Recently copper ferrite nanoparticles have caught the interest of numerous researchers due to low-cost magnetic material, stability under diverse conditions, and ease at which catalyst can be retrieved using an external magnetic field and utilized repeatedly. This review of data from year 2010 through 2022 emphasizes the synthesis method, structure, application in dyes degradation, catalytic potential in the number of coupling reactions, recyclability, and reusability of the magnetic catalyst.     

Laser-Patterned Carbon-Supported Graphitic Carbon Nitride Quantum Dots for Flexible Nanozyme-Based Fluoride Sensor

Graphitic carbon nitride quantum dots (g-CNQDs)-based colorimetric sensors are typically solution-based and hence incompatible with wearable electronics. Today's competitive technology demands safe and reliable, high-performance sensors suitable for integration with sophisticated electronics—all at a low cost. Herein, a flexible and reusable solid-state fluoride ion sensor manufactured by combining the intriguing surface properties of laser-patterned carbon (LP-C) with the sensitivity of g-CNQDs is reported. LP-C is obtained by direct IR-laser writing onto polyimide films, and g-CNQDs are synthesized via a solvent-free and zero-waste green process. The hybrid of LP-C and g-CNQDs (g-CNQDs/LP-C), mimics the natural enzyme horseradish peroxidase and oxidizes the chromogenic substrate 3,3’,5,5’-tetramethylbenzidine in the presence of H₂O₂ in acidic media. The highly selective and user-friendly nanozyme sensors feature a lower limit of detection of 0.568 ± 0.006  × 10⁻⁶ m (23.8 ± 1.5 µg L⁻¹) with linearity in the range of 0.5 × 10⁻⁶ to 100  × 10⁻⁶ m . A sensing mechanism based on the electronic transitions of g-CNQDs and LP-C, the two variants of nitrogen-containing carbon used in this work, is established. Finally, the device is tested for fluoride ion sensing in natural water samples collected from the Uhl river in Mandi, India.     

Opportunities for Mercuric Ion Spectrophotometric Determination based on Reduction of Gold Nanoparticles Aggregation by N-containing Cyclic Molecules

Journal of Analytical Chemistry - Methods for the determination of mercury are described using gold nanoparticles functionalized with nitrogen containing cyclic molecules. Detection methods are...     

On a family of elliptic curves of rank at least 2

Let C_m:y² = x³ ? m²x + p²q² be a family of elliptic curves over ?, where m is a positive integer and p, q are distinct odd primes. We study the torsion part and the rank of C_m(?). More specifically, we prove that the torsion subgroup of C_m(?) is trivial and the ?-rank of this family is at least 2, whenever m ? 0 (mod 3), m ? 0 (mod 4) and m ≡ 2 (mod 64) with neither p nor q dividing m.

     

Meticulous assessment of natural compounds from NPASS database for identifying analogue of GRL0617, the only known inhibitor for SARS-CoV2 papain-like protease (PLpro) using rigorous computational workflow

Molecular Diversity - The latest global outbreak of 2019 respiratory coronavirus disease (COVID-19) is triggered by the inception of novel coronavirus SARS-CoV2. If recent events are of any...     

Uranium: occurrence,distribution across India and its potential health effects

Journal of Radioanalytical and Nuclear Chemistry - Uranium contamination in the aquatic environment is an emerging concern worldwide. With the development of the global economy, uranium...     

Simultaneous high-performance thin-layer chromatography analysis of phytoconstituents and antioxidant potential of Inula grandiflora Willd. from India

JPC – Journal of Planar Chromatography – Modern TLC - The Inula genus has been used for the cure of pulmonary, heart diseases and also acts as a rejuvenator, immunomodulator in...