In this paper, the Lie symmetry analysis method has been proposed for finding similarity reduction and exact solutions of nonlinear evolution equation. Here for illustrating the effectiveness and ...accuracy of proposed method, we have taken (3+1) dimensional Yu–Toda–Sasa–Fukuyama (YTFS) equation. Also by using symmetry reduction method, we have reduced nonlinear partial differential equation (NPDE) to nonlinear ordinary differential equation, which has advantage to provide semi analytical solution. We have obtained infinitesimal generators, the entire geometric vector field, commutator table of Lie algebra and symmetry group by using Lie symmetry analysis method. Then, we have used tanh method for finding new analytical exact solutions of some reduced transform equations.
The Schamel-KdV equation plays a vital role in studying the effect of electron trapping on the nonlinear interaction of ion-acoustic waves in plasma and dusty plasma. This work presents a numerical ...scheme-based radial basis function-finite difference (RBF-FD) method to solve the time-fractional Schamel-KdV equation. The advantages of using this method are their meshfree nature and flexibility in dealing with complex geometries. In the discretization process, a finite difference (FD) technique is used to discretize the temporal derivative, while the multiquadric (MQ) RBF is used to approximate the spatial derivatives. The theoretical convergence and stability analysis of the time-discrete scheme are also established. In addition, numerical experiments are executed through some illustrated problems, and the obtained results are compared with that acquired by the tanh method and Kudryashov method solutions to show the high accuracy and plausibility of the proposed technique. Also, the graphical representations are given to demonstrate the physical interpretation of the resulting wave structures.
Zinc oxide (ZnO) nanoparticles (NPs) have been synthesized using
Hibiscus subdariffa
leaf extract. Temperature dependent synthesis and particle growth have been studied. Formation of NPs was ...confirmed by UV-visible (UV-VIS) spectroscopy, Fourier transform infrared (FTIR) spectroscopy and X-ray diffraction (XRD). Electron microscopy has been used to study the morphology and size distribution of the synthesized particles. The synthesized ZnO nanoparticles as potential anti-bacterial agents have been studied on
Escherichia coli
and
Staphylococcus aureus
. Another study has indicated that small sized ZnO NPs, stabilized by plant metabolites had better anti-diabetic effect on streptozotocin (STZ) induced diabetic mice than that of large sized ZnO particles. It has also been observed by enzyme linked immunosorbent assay (ELISA) and real time polymerase chain reaction (RT-PCR) that ZnO can induce the function of Th1, Th2 cells and expressions of insulin receptors and other genes of the pancreas associated with diabetes.
Particle size dependent anti-bacterial and anti-diabetic activities of green synthesized ZnO nanoparticles.
This paper describes a simulated annealing based multiobjective optimization algorithm that incorporates the concept of archive in order to provide a set of tradeoff solutions for the problem under ...consideration. To determine the acceptance probability of a new solution vis-a-vis the current solution, an elaborate procedure is followed that takes into account the domination status of the new solution with the current solution, as well as those in the archive. A measure of the amount of domination between two solutions is also used for this purpose. A complexity analysis of the proposed algorithm is provided. An extensive comparative study of the proposed algorithm with two other existing and well-known multiobjective evolutionary algorithms (MOEAs) demonstrate the effectiveness of the former with respect to five existing performance measures, and several test problems of varying degrees of difficulty. In particular, the proposed algorithm is found to be significantly superior for many objective test problems (e.g., 4, 5, 10, and 15 objective problems), while recent studies have indicated that the Pareto ranking-based MOEAs perform poorly for such problems. In a part of the investigation, comparison of the real-coded version of the proposed algorithm is conducted with a very recent multiobjective simulated annealing algorithm, where the performance of the former is found to be generally superior to that of the latter.
The growing prevalence of antibiotic resistance poses an increasingly serious threat to human health. Although an important driver of antibiotic resistance is the continuous exposure of bacteria to ...sublethal concentrations of antibiotics in natural environments, antibiotic pollutants are not currently tracked globally or systematically. This limits the international capacity to address the rise of antibiotic resistance at its source. To address this lack of data, the development of methods to measure antibiotic concentrations on-site is essential. These methods, ideally, must be sensitive to sublethal concentrations of antibiotics and require minimal technical expertise. Furthermore, factors such as cost, selectivity, biosafety and the ability to multiplex must be evaluated in the context of field use. Based on these criteria, we provide a critical review of current methods in antibiotic detection and evaluate their adaptability for use on-site. We categorize these methods into microbiological assays, physical and chemical assays, immunoassays, aptasensors and whole-cell biosensors. We recommend continued development of a dipstick or microfluidics approach with a bacterial promoter-based mechanism and colorimetric output. This technique would incorporate the advantageous aspects of existing methods, maximize shelf-life and ease-of-use, and require minimal resources to implement in the field.
Boron‐ and nitrogen‐doped graphenes are are prepared by the arc discharge between carbon electrodes or by the transformation of nanodiamond under appropriate atmospheres. Using a combination of ...experiment and theories based on first principles, systematic changes in the carrier‐concentration and electronic structure of the doped graphenes are demonstrated. Stiffening of the G‐band mode and intensification of the defect‐related D‐band in the Raman spectra are also observed.
In this paper, symmetry properties and conservation laws of the (3+1) dimensional time-fractional modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equation have been studied with Riemann–Liouville ...fractional derivative. Fractional Lie symmetry method has been used here for getting symmetry properties of (3+1) dimensional time-fractional mKdV–ZK equation. Here, the reduction of (3+1) dimensional time-fractional mKdV–ZK equation into fractional ordinary differential equation has been done by using Erdélyi–Kober fractional differential operator. Also, by using the new conservation theorem, the new conserved vectors for (3+1) dimensional time-fractional mKdV–ZK equation have been constructed with the help of formal Lagrangian with a detail derivation.
The time-fractional resonant nonlinear Schrödinger equation is studied in this paper using the modified auxiliary equation approach. This effort yields several innovative optical soliton solutions to ...the investigated problem. An equivalent nonlinear ordinary differential equation with integer-order has been obtained from the time-fractional RNLSE using the modified Riemann–Liouville derivative along with fractional complex transform, and then the emerged equations are solved using the most impressive direct method, the modified auxiliary equation method. As a consequence, novel optical soliton solutions have been successfully developed, with several 3-D graphs demonstrating their behaviour.
In this article dispersive optical soliton solutions that are governed by the time-fractional Schrödinger–Hirota equation have been presented. Some new soliton solutions of the time-fractional SH ...equations are obtained in this work. Using extended auxiliary equation method, optical soliton solutions are sought for the fractional SH equations with power law nonlinearity as well as Kerr law nonlinearity. Using fractional complex transform the time-fractional SH equation is converted into the nonlinear ordinary differential equation, and then, the resulting equation is solved using a novel analytical method viz. extended auxiliary equation method. As a result of this, some new optical soliton solutions have been successfully obtained. The obtained results show that the proposed method is a straightforward technique to find out new optical solutions of time-fractional SH equation.
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