Search

In light of fractional theory, this paper presents several new effective solitonic formulations for the Langmuir and ion sound wave equations. Prior to this study, no previous research has presented the comparision and obtained the generalized fractional soliton solutions of this kind with power law kernel and Mittag-Leffler kernel. The ion sound and Langmuir wave equations are essential in plasma physics, offering insights into the collective behavior of charged particles in plasmas and enabling diagnostics and control of these complex, ionized gas systems. The two distinct fractional order differential operators are substituted for the traditional order derivative to reshape the examined model. The Atangana-Baleanu non-singular and non-local operator and conformable fractional operator are the fractional-order operators that are used to create the fractional complex system equations for Langmuir waves and ion sound. A constructive approach new auxiliary equation method utilizes to obtain the exact analytical soliton solutions for ion sound and Langmuir wave equation. A wide range of soliton solutions is obtained, including mixed complex solitary shock solutions, singular solutions, mixed shock singular solutions, mixed trigonometric solutions, mixed singular solutions, exact solutions, mixed periodic solutions, and mixed hyperbolic solutions, dark soliton, bright soliton, trigonometric solutions, periodic results, and hyperbolic results. The solitons solution of the ion sound and Langmuir wave equations lies in their ability to maintain wave stability, their role in modeling wave propagation and nonlinear effects, their potential use as diagnostic tools, and their relevance in wave-particle interactions in plasma physics. The solitons provide a valuable framework for understanding the behavior of waves in plasmas and offer insights into the complex dynamics of these charged particle systems. A graphical comparison analysis of a few solutions is also shown here, taking into account appropriate parametric values through the use of the software package. Moreover, the results of this study have important implications for Hamilton's equations and generalized momentum, where solitons are employed in long-range interactions.

Ischaemic colitis is responsible for more than half of the presentations of gastrointestinal ischaemia and develops due to an interruption of intestinal blood flow. Risk factors include increasing age and conditions associated with decreased perfusion. Infrequently, ischaemic colitis may develop in young females prescribed oral contraceptives. Here, we present a case of ischaemic colitis secondary to oral contraceptives that resolved with medication discontinuation.

This work presents the development of a novel antifungal ternary approach that is eco-friendly, biocompatible, and cost-effective. It consists of Bryum argenteum extract, silver nanoparticles, and healing clay smectite. The research focuses on the green production of silver nanoparticles using an aqueous extract of Bryum argenteum as a stabilizing and reducing agent, as well as the synthesis of clay dispersion and plant extract. The silver nanoparticles were characterized by FTIR, SEM, UV–Vis spectroscopy, and XRD. Using a standard phytochemical screening procedure, the aqueous, ethanolic, and acetonic extracts of Bryum argenteum were subjected to phytochemical screening. Silver nanoparticles and plant extract were evaluated for their antioxidant properties using DPPH scavenging activity at 517 nm. Using the agar well diffusion method, a number of investigations have been conducted on the antifungal potential of the proposed innovative ternary approach against Rhizopus oryzae (R. oryzae) and Aspergillus Niger (A. Niger). The color shift validated the silver nanoparticle generation, and the maximum absorbance at 432.11 nm was observed employing UV–Vis spectroscopy. Several functional groups responsible for the synthesis of AgNPs were identified by Fourier transform infrared spectroscopy. The particles are spherical in shape, with the range of 10 nm to 50 nm in size. Both ethanolic and aqueous extracts of Bryum argenteum contain sterols, flavonoids, cardiac glycosides, and terpenoids. AgNPs have stronger antioxidant activity in comparison to the aqueous extract of Bryum argenteum. Out of all the individual components, AgNPs demonstrated the strongest antifungal activity, with clay and plant extract coming in second and third, respectively. Additionally, their binary composition exhibits a synergistic effect with each combination. However, the ternary combination consisting of smectite clay, Bryum argenteum mediated silver nanoparticles, and Bryum argenteum extract showed exceptional antifungal efficiency against the mentioned fungus species. In respect to the zone of inhibition, the maximal antifungal activity was correlated with concentration and pH. Conclusion: It is concluded here that the proposed ternary system has significant antifungal potential. Future technological and medicinal studies will find this new ternary system to be an invaluable tool.

This study explores the effect of silver nanoparticles on heat transfer and flow behavior within the context of the Ellis fluid model. It specifically considers electroosmotic forces in a nonuniform divergent channel with compliant walls. The analysis involves studying thermal transport in silver-blood nanofluid flow, using MATHEMATICA 13.2 software to obtain exact solutions for velocity and temperature distribution. Findings reveal that certain parameters, such as wall damping and wall elastic properties, increase skin friction, while compliant wall parameters generally reduce flow velocity. Additionally, wall rigidity and tension parameters lead to larger trapped boluses. Notably, a 1% concentration of nanoparticles enhances heat transfer by up to 13.75%, offering control over heat transfer rates. This research introduces a novel perspective by examining compliant wall impacts on heat transfer analysis in the context of electroosmotic flow within the Ellis fluid model, incorporating silver nanoparticles with potential therapeutic applications due to their antibacterial properties.

This work investigates the dynamics of solitary waves in a thin-film ferroelectric material model, an essential component of optical systems. The study recognizes the limitations of the inverse scattering transform in solving the Cauchy problem for this conformable thin-film ferroelectric material model and applies a new Kudryashov approach and Bernoulli’s equation technique to ordinary differential equations. We apply these methods to the present model and obtain closed form analytical solutions. A variety of traveling wave and soliton solutions are constructed, including kink, bell, bright, and dark soliton solutions. It is acknowledged that the nonlinear evolution equation can be transformed into an ordinary differential equation by applying traveling wave transformations. Suitable physical parameters are chosen to create 2D, 3D, and contour plots that graphically depict the graphical dispersion of obtained fractional soliton solutions. The impact of the conformable fractional parameter is further demonstrated by the graphical representation of solitons propagation. Furthermore, the study develops the Hamiltonian function of the dynamical system to discuss the system’s total energy in terms of momentum and position. While a chaos analysis describes chaotic, quasi-periodic, and periodic behaviors, a sensitivity analysis demonstrates how responsive the model is to various initial conditions. Due to their dual-purpose nature as nonlinear ferroelectric and dielectric materials, thin ferroelectric films are widely used in modern electrical devices.

In the present work, we utilize a new Sardar sub-equation approach, leading to the successful derivation of several exact solutions for the time-fractional Kudryashov’s equation, which describes the propagation pulses in optical fibers. These solutions encompass a range of categories, including singular, wave, bright, mixed dark-bright, and bell-shaped optical solutions. To effectively showcase these novel optical soliton solutions, we utilized contour plots, three-dimensional graphs, and three-dimensional surface plots. Through multiple graphical simulations, we provide a comprehensive demonstration of the dynamic behavior and physical significance of these optical solutions within the proposed model. Moreover, we investigate the magnitude of the time-fractional Kudryashov’s equation by analyzing the influence of the fractional order derivative and the impact of the time parameter on the newly constructed optical solutions. Our findings highlight the versatility of the presented method, as it can readily be applied to other differential equations in various fields, such as non-linear optics and plasma physics. The proposed technique is a generalized form that incorporates various methods, including the improved Sardar sub-equation method, the modified Kudryashov method, the tanh-function extension method, and others. To the best of our knowledge, these solutions are novel and have not been reported in the literature and have potential application in nonlinear optics.

The goal of the current paper is to create a novel model for the two-dimensional flow (TDF) of a second-grade fluid and the transfer of heat due to free convection. The second-grade fluid travels through the porous media and is electrically conducted. The governing equation for fluid velocity and temperature is formulated as a set of partial differential equations jointly. The model is developed in fractional form by applying the Caputo-Fabrizio (CF) fractional derivative approach. The two-dimensional flow problem is modeled in terms of one-sided coupled fractional partial differential equations with corresponding physical conditions imposed on the fluid flow and temperature. The problem is initially converted to a dimensionless form and then solved for the exact solutions by applying joint Fourier and Laplace transforms. Exact solutions are examined for fluid velocity and temperature and then in limiting cases are reduced to some well-known fluid motions. Some special cases are also obtained from the general solutions. For the numerical results, Mathcad-15 software is used and the results are plotted in various graphs. The temperature, and velocity profiles are discussed and highlighted for embedded flow parameters. The model obtained in this work is new and can be extended for other fluid models hence this article provides a base for future research.

In this study, the Lie point symmetries and optimal system have been established. We discuss the biofilm model’s soliton solutions. To examine a nonlinear dynamical biofilm system, which is simply a bistable Allen–Cahn equation with quartic potential, to determine solitary wave profiles using the considered equation, a new auxiliary equation technique is used. A suitable variable transformation is used to convert the governing equation into a nonlinear ordinary differential equation. The unified approach is utilized to evaluate periodic solutions, solitary and soliton solutions as well as several newly discovered exact solitary wave solutions, it can be accomplished via Mathematica (https://www.wolfram.com/mathematica/online/). The new auxiliary equation approach is an efficient method for creating unique wave profiles based on a variety of soliton families. Also, the results are graphically visualized, by using the appropriate parametric settings. The outcomes are shown graphically in two dimensions, three dimensions, and contour form. The Hamiltonian conditions are satisfied by the planer dynamical framework of equations to ensure as the system that was generated is a conservative Hamiltonian dynamical system which includes all traveling wave structures. A sensitivity evaluation is used to explore the governing model’s thoroughly dynamical properties. It is demonstrated that the model becomes more dependent on the beginning conditions than the variables. The strategy could be used to look for exact solutions to various nonlinear evolution equations. We believe that this study will have important applications in different areas of science.

Cadmium (Cd) pollution of soil and food crops is a widespread environmental issue caused by excessive industrialization, unsustainable urbanization, and intensive farming practices. Cd, a hazardous element, poses significant risks to agro-environmental sustainability, food safety, and human health. Using organic materials such as biochar and compost to stabilize Cd in contaminated soil is an environmentally benign and cost-effective strategy for remediating moderately to highly polluted soil. However, in response to the scarcity of comparative studies on biochar and compost efficacy, this research explores the impact of wheat-straw biochar and chicken waste compost on Cd-contaminated soil remediation. A greenhouse experiment using two application rates (1.5 % and 2.5 %) of biochar and compost in 10 mg kg−1 Cd-contaminated soil revealed significant (p≤0.05) effects. The 2.5 % compost application increased soil organic carbon (SOC) from 0.45 % to 0.85 %, while 2.5 % biochar enhanced soil pH from 7.1 to 7.7 and electrical conductivity (EC) from 0.33 to 0.44 dSm−1. Notably, 2.5 % biochar significantly reduced Cd bioavailability from 9.49 to 4.90 mg kg−1, root accumulation from 29.8 to 16.4 mg kg−1 and shoot translocation from 16.8 to 8.4 mg kg−1. This reduction was confirmed through translocation factor (51.5 %) and immobilization efficiency (48.4 %). Furthermore, 2.5 % biochar improved chlorophyll content (a, b, and total) and wheat morphological attributes under Cd stress in soil. Overall, higher rates of biochar (2.5 %) and compost (2.5 %) effectively mitigate Cd uptake, improve soil properties, and enhance physiological and morphological responses, suggesting their promise for sustainable soil management practices.

This study focuses on the variant Boussinesq equation, which is used to model waves in shallow water and electrical signals in telegraph lines based on tunnel diodes. The aim of this study is to find closed-form wave solutions using the extended direct algebraic method. By employing this method, a range of wave solutions with distinct shapes, including shock, mixed-complex solitary-shock, singular,mixed-singular, mixed trigonometric, periodic, mixed-shock singular, mixed-periodic, and mixed-hyperbolic solutions, are attained. To illustrate the propagation of selected exact solutions, graphical representations in 2D, contour, and 3D are provided with various parametric values. The equation is transformed into a planar dynamical structure through the Galilean transformation. By utilizing bifurcation theory, the potential phase portraits of nonlinear and super-nonlinear traveling wave solutions are investigated. The Hamiltonian function of the dynamical system of differential equations is established, revealing the system’s conservative nature over time. The graphical representation of energy levels offers valuable insights and demonstrates that the model has closed-form solutions.

In this paper, the main motive is to mathematical explore the thin-film ferroelectric material partial differential equation which addresses the Ferroelectrics, that are being examined as key materials for applications in piezoelectric, pyroelectric electrostrictive, linear, and nonlinear optical systems. Thin ferroelectric films are used in a variety of modern electrical devices because they are both nonlinear ferroelectric and dielectric materials. This article appropriates the fractional travelling wave transformation allowing the partial differential equation to be changed into an ordinary differential equation. The considered fractional model is explored through employing the combo of G′G2−expansion method and new extended direct algebraic methodology. As an outcome, numerous types of soliton solutions like, Periodic pattern with anti-peaked crests and anti-troughs, singular solution, mixed complex solitary shock solution, mixed singular solution, mixed shock singular solution, mixed trigonometric solution, mixed periodic, periodic solution and mixed hyperbolic solution obtain via Mathematica. In addition, the G′G2−expansion technique produces singular, trigonometric, and hyperbolic solutions with different soliton families. The revealed solution will improve the mathematical analysis of this model and the associated physical phenomenon's. In order to visualize the graphical propagation of the obtained fractional soliton solutions, 3D, 2D, and contour graphics are generated by choosing appropriate parametric values. The impact of fractional parameter β is also graphically displayed on the propagation of solitons.

The well-known Chaffee–Infante reaction hierarchy is examined in this article along with its reaction–diffusion coupling. It has numerous variety of applications in modern sciences, such as electromagnetic wave fields, fluid dynamics, high-energy physics, ion-acoustic waves in plasma physics, coastal engineering, and optical fibres. The physical processes of mass transfer and particle diffusion might be expressed in this way. The Lie invariance criteria is taken into consideration while we determine the symmetry generators. The suggested approach produces the six dimensional Lie algebra, where translation symmetries in space and time are associated to mass conservation and conservation of energy respectively, the other symmetries are scaling or dilation. Additionally, similarity reductions are performed, and the optimal system of the sub-algebra should be quantified. There are an enormous number of exact solutions can construct for the traveling waves when the governing system is transformed into ordinary differential equations using the similarity transformation technique. The power series approach is also utilized for ordinary differential equations to obtain closed-form analytical solutions for the proposed diffusive coupled system. The stability of the model under the limitations is ensured by the modulation instability analysis. The reaction diffusion hierarchy’s conserved vectors are calculated using multiplier methods using Lie Backlund symmetries. The acquired results are presented graphically in 2-D and 3-D to demonstrate the wave propagation behavior.

Objective: To determine the visual outcomes and prognostic factors associated with open globe-injuries in patients attending Sindh Institute of Ophthalmology and Visual Sciences (SIOVS), Hyderabad, Pakistan.Methods: A prospective cross-sectional study was conducted at Sindh Institute of Ophthalmology and Visual Sciences (SIOVS), Hyderabad from January 2022 to February 2023. All patients irrespective of age and gender attended the institute with open globe injury were enrolled. Visual outcomes of open-globe injury were recorded as length of wound and lens status. Complications associated with open-globe injury were also noted.Results: Of 336 patients, the mean age of the patients was 17.6 ± 15.6 years. There were 231 (68.7%) males and 105 (31.3%) females. The most common object of injury was stick/thorn and metal/iron i.e., 117 (34.8%) and 105 (31.3%) respectively. Center of cornea/visual axis involvement was observed in 207 (61.6%) patients. The mean length of the wound was 6.28 ± 3.65 mm. Status of the lens showed an intact lens in 140 (41.7%) patients and traumatic cataract with intact/rupture of capsule in 196 (58.3%) patients. A significant association between the length of the wound and the status of the lens was found with the object of injury (p-value

The study aims to explore the nonlinear Landau-Ginzburg-Higgs equation, which describes nonlinear waves with long-range and weak scattering interactions between tropical tropospheres and mid-latitude, as well as the exchange of mid-latitude Rossby and equatorial waves. We use the recently enhanced rising procedure to extract the important, applicable and further general solitary wave solutions to the formerly stated nonlinear wave model via the complex travelling wave transformation. Exact travelling wave solutions obtained include a singular wave, a periodic wave, bright, dark and kink-type wave peakon solutions using the generalized projective Riccati equation. The obtained findings are represented as trigonometric and hyperbolic functions. Graphical comparisons are provided for Landau-Ginzburg-Higgs equation model solutions, which are presented diagrammatically by adjusting the values of the embedded parameters in the Wolfram Mathematica program. The propagating behaviours of the obtained results display in 3-D, 2-D and contour visualization to investigate the impact of different involved parameters. The velocity of soliton has a stimulating effect on getting the desired aspects according to requirement. The sensitivity analysis is demonstrated for the designed dynamical structural system's wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. This study shows that the method utilized is effective and may be used to find appropriate closed-form solitary solitons to a variety of nonlinear evolution equations (NLEEs).

Combination therapy and multitarget drugs have recently attracted much attention as promising tools to fight against many challenging diseases and, thus, represent a new research focus area. The aim of the current project was to screen multitarget compounds and to study their individual and combined effects on acetaminophen-induced liver injury. In this study, 2 of the best hepatoprotective multitargeting compounds were selected from a pool of 40 major compounds present in Curcuma longa and Cinnamomum zeylanicum by using molecular docking, ADMET profiling, and Pfizer’s rule of five. The two selected compounds, quercetin and curcumin, showed a high binding affinity for the CYP2E1 enzyme, MAPK, and TLR4 receptors that contribute to liver injury. The candidates caused the decreased viability of cancer cell lines (HepG2 and Huh7) but showed no effect on a normal cell line (Vero). Examination of biochemical parameters (ALT, AST, ALP, and bilirubin) showed the hepatoprotective effect of the candidate drugs in comparison with the control group, which was confirmed by histological findings. Taken together, quercetin and curcumin not only satisfied the drug-like assessment criterion and proved to be multitargeting by preventing liver damage but also showed anticancer activities.

In this paper, the main motive is to mathematical explore the Kuralay equation, which find applications in various fields such as ferromagnetic materials, nonlinear optics, and optical fibers. The objective of this study is to investigate different types of soliton solutions and analyze the integrable motion of induced space curves. This article appropriates the traveling wave transformation allowing the partial differential equation to be changed into an ordinary differential equation. To establish these soliton solutions, the study employs the new auxiliary equation method. As an outcome, a numerous types of soliton solutions like, Periodic pattern with anti-peaked crests and anti-troughs, singular solution, mixed complex solitary shock solution, mixed singular solution, mixed shock singular solution, mixed trigonometric solution, mixed periodic, periodic solution and mixed hyperbolic solution obtain via Mathematica. In order to visualize the graphical propagation of the obtained soliton solutions, 3D, 2D, and contour graphics are generated by choosing appropriate parametric values. The impact of parameter w is also graphically displayed on the propagation of solitons.

The present study predicts the energy savings, carbon emissions reduction and economic benefits for Pakistan through energy efficiency improvements for room air conditioners under different policy scenarios. The simulation model assumes that room air conditioner stock will increase from 2.7 million for year 2020 to 4.9 million for year 2030. A market average energy efficiency ratio of 2.95 is assumed for year 2020. The impact of improvement in energy efficiency ratio is analyzed for business as usual and four other different scenarios: continuous improvement (5-years and 2-years cycles) and accelerated improvement (5-years and 2-years cycles). The model dynamically incorporates the retiring of old stock and addition of new stock every year. Our results show that annual national electricity consumption for this sector is projected to increase from 7.3 TWh in 2020 to 12.6 TWh in 2030 under the business as usual scenario. The cumulative energy consumption and carbon emissions are 103.5 TWh and 63.1 MtCO 2. However, implementing energy efficiency policies can result in electricity savings of 11.6 TWh over the ten years or savings nearly 7 million barrels of oil import. Policy recommendations aimed at promoting energy labeling, minimum energy performance standards, regulatory policies, and further country-specific studies for variety of appliances are provided.

The most recent advancements in algebra and graph theory enable us to ask a straightforward question: what practical use does this graph connected with a mathematical system have in the real world? With the use of algebraic approaches, we may now tackle a wide range of graph theory-related problems. We compute loop-involutions and nonself-loop-involutions of flexible weak inverse property loops. Importantly, diameter, radius, and eccentricity of this loop structure’s inverse graph have all been calculated in a broad manner. Some topological indices, as an application of inverse graph, are also given at the end of the paper.

The major motive of this study is to analyze the nonlinear integrable model which is generalized Kadomtsev–Petviashvili modified equal width-Burgers equation. It can be utilized extensively a weakly non-linear restoring forces, dispersion, small damping and nonlinear media with dissipation to narrate the long wave propagation in chemical theory. This article allocates the partial differential equation by traveling waves transformation into an ordinary differential equation. In order to acquire the analytical propagating structures, one of the generalized techniques, new extended direct algebraic methodology utilizers. As a consequence, we establish the mixed singular solution, singular solution, mixed shock-singular solution, mixed complex solitary-shock solution, mixed periodic results, mixed trigonometric results have been derived in the formation of a mixed periodic and periodic class, the mixed hyperbolic solution, plane solution, which is derived via Mathematica. The Chaos investigation is carried out to envision the dynamical insights of ocean wave integrable model. The sensitive analysis performed to verify the perceptiveness of model regarding parameters and initial conditions. Modulational instability gain spectrum developed and envisaged with appropriate parametric values and ensured the stability of the considered model. In addition, two-dimension, three-dimension, and contour surfaces are embellished to validate the physical properties of the derived solutions. The developed electro potential soliton structures can reveal the deep atomic insights. The dynamics of physical phenomenon can be controlled by fractional parameter.

Introduction:: The chemical oscillators are identified as open system that demonstrate periodic changes in the concentration of some reaction species as a result of intricate physico-chemical mechanisms which can lead to bi-stability, the occurrence of limit cycle attractors, the emergence of spiral waves and turing patterns, and finally, deterministic chaos. Objectives:: The main objective of this paper is to analyze the simple Noyes–Field governing system of differential equations for the nonlinear Belousov–Zhabotinsky reaction which delineates the non-linear oscillatory behavior of chemical systems that occurs in the homogeneous media. Methodology:: The Lie symmetry invariance analysis performed to extract the symmetries infinitesimal generators and the adjoint representation carried out to develop optimal system for the obtained Lie vectors. The significant power series approach applied to obtain the analytical solution. The modulation instability criteria ensured the stability of nonlinear oscillatory Belousov–Zhabotinsky reaction process. Results:: The one-dimensional Lie symmetry generators algebra of the mathematical Noyes–Field governing system for oscillatory reaction is established. Furthermore, similarity reductions are carried out as well as the development of an optimal system of the sub-algebras. The similarity transformation technique converted the controlling system to ordinary differential equations and generates the large quantity of analytical traveling wave solutions. Moreover, the closed-form analytical solution for the proposed homogeneous nonlinear oscillatory chemical process is secured. The (MI) gain spectrum graphically visualized with the suitable choice of arbitrary parameters. Conclusion:: The graphical performance of the Noyes–Field model solution at various settings reveals new perspectives and fascinating model phenomena. The attained outcomes have significant applications and have opened up innovative development areas for research across numerous scientific fields.

The aim of study is to investigate the Hirota equation which has a significant role in applied sciences, like maritime, coastal engineering, ocean, and the main source of the environmental action due to energy transportation on floating anatomical structures. The classical Hirota model has transformed into a fractional Hirota governing equation by using the space-time fractional Riemann-Liouville, time fractional Atangana-Baleanu and space-time fractional β differential operators. The most generalized new extended direct algebraic technique is applied to obtain the solitonic patterns. The utilized scheme provided a generalized class of analytical solutions, which is presented by the trigonometric, rational, exponential and hyperbolic functions. The analytical solutions which cover almost all types of soliton are obtained with Riemann-Liouville, Atangana-Baleanu and β fractional operator. The influence of the fractional-order parameter on the acquired solitary wave solutions is graphically studied. The two and three-dimensional graphical comparison between Riemann-Liouville, Atangana-Baleanu and β-fractional derivatives for the solutions of the Hirota equation is displayed by considering suitable involved parametric values with the aid of Mathematica.

Blockchain technology in recent years has become potentially pervasive in the cryptocurrency market, thus providing tamper-proof security to decentralized transaction management systems. Structurally, the design foundation is an ideal advancement of the distributed ledger technology that maintains a set of global states across nodes. As technology expands with a higher trend towards mobile computing, the development of new applications demands understanding the current progression, especially concerning performance, data management, and storage prospects. Here, we report the principle design structure of the blockchain technology combined with the state of the arts, thus characterizing their original topological contexts. We depart from the fundamental concepts of the technology and analyze performance of the Ethereum blockchain on two devices having different computing power. Our presentation is tailored to provide a systematic review of the technology, thus facilitating their possible adoption into the new application domains like the Internet of Things (IoT). Further, we developed Debug-Bench, the first VSCode (Visual Studio Code) extension that enables benchmarking and profiling of the blockchain applications. Finally, we demonstrate several critical challenges concerning the design space of the current blockchain platforms for their implementation over resource-constrained devices.

The theory of convex function has a lot of applications in the field of applied mathematics and engineering. The Caputo-Fabrizio non-singular operator is the most significant operator of fractional theory which permits to generalize the classical theory of differentiation. This study consider the well known Hermite-Hadamard type and associated inequalities to generalize further. To full fill this mileage, we use the exponential convexity and fractional-order differential operator and also apply some existing inequalities like Holder, power mean, and Holder-Iscan type inequalities for further extension. The generalized exponential type fractional integral Hermite-Hadamard type inequalities establish involving the global integral. The applications of the developed results are displayed to verify the applicability. The establish results of this paper can be considered an extension and generalization of the existing results of convex function and inequality in literature and we hope that will be more helpful for the researcher in future work.

Problem statement: The study offers theoretical formulations for high-viscosity particulate flows in inclined reservoirs, taking into account the presence of homogeneous spheroidal particles of various types to produce discrete two-phase suspensions. Purpose: The primary objective of this analytical and comparative study is to identify the most dependable nanoparticles among hafnium and crystal metals that are suspended in an Eyring–Powell fluid through an inclined channel while being subjected to external magnetic and gravitational forces. Solution methodology: The flow dynamics of multiphase flows are formulated utilizing the stress tensor of the base fluid. The regular perturbation method (RPM) is employed to attain a more closed-form solution. The perturbation method is frequently employed in engineering problems to obtain an approximated solution, even when demonstrating the convergence of the solution is challenging. The rough solution is also validated through a thorough parametric analysis that shows the role of relevant parameters that contribute to the multiphase flow. Results: A concise parametric study is carried out against some of the most pertinent parameters and reveals that additional particles have promising effects on the momentum of each multiphase flow, whereas Eyring–Powell multiphase suspensions lessen in momentum due to strong internal viscous forces. The velocity of fluid and particle phases diminish with Hartmann number M and Froude number Fr. The second-order material constant B and concentration of nanoparticles C boost the motion of the fluid. The velocities of the particulate phase are quicker than the fluid phase. The hafnium particle is more reliable than crystal particles. Solution benchmark: Numerical and graphical findings have also been compared with the existing literature for the limiting case and found to be fully in agreement. Applications: This study’s findings provide a wider understanding of subterranean flows, specifically within the petroleum sector, with a focus on multiphase flows. Originality: The current study represents the authors’ original work and has not been previously submitted or published elsewhere.

This paper explores the diverse social, cultural and scientific facets of coloning as an alternate means of human reproduction. We review the various types, and implications of coloning as practiced in the modern world, specifically as a means of child birth for infertile parents. We also present the Islamic injunctions and worldview on different types of cloning. We assert that although biological cloning can be an productive technological intervention to promote agriculture yield, however it’s application for human reproduction is inappropriate, and finds no support in Islamic injunctions. Therefore, our paper suggest that human cloning should be prohibited acknowledging its socioeconomic demerits.

Businesses are intended to generate profits for the investors by engaging in economic activities. However, the fairness and legitimacy of business activities in terms of their contractual arrangements, margins of profit, and the underlying asset of trade have been a subject of debate. Over 1.5 Billion Muslims across the world and 52 Muslim countries look towards Islamic injunctions as the ultimate truth, and divine guidance to define a framework for conceptualizing profit and loss generation in a business. This paper reviews four sources of Islamic knowledge i.e. (i) qur’anic verses, (ii) sayings and practices of the Prophet (PBUH), (iii) commercial contracts, trade arrangements, and transactions as practiced in the Prophets era, and (iv) religious opinion drew on the major school of thoughts. Finally, this paper examines the profit-creation in contemporary Islamic banking practices through the lens of Islamic knowledge to address the contesting views and criticism on the profit-making and sharing arrangements instituted in present-day Islamic Banks. The findings of this paper demarcate the guiding principles to steer general business & commerce activities and specifically the profit-making arrangements for businesses for operationalizing their role in driving the overarching socio-economic welfare in a society.

This paper deals with the Lakshmanan-Porsezian-Daniel equation which delineates the continuum isotropic bi-quadratic Heisenberg spin chain phenomenon. A new auxiliary equation method is exerted on the considered equation to find solitary wave profiles. It is a simple and powerful approach for developing innovative wave profiles based on diverse soliton families such as trigonometric functions, rational, hyperbolic trigonometric function and exponential function etc. As a result, the solitonic wave patterns attain such as dark, bright, dark-bright, singular, rational, periodic-singular, exponential, and periodic solitons etc. The deep dynamical aspects of the governing model study by performing the chaos and sensitivity analysis. The planer dynamical system of equation develop and satisfy the Hamiltonian criteria to assure that, the developed system is Hamiltonian dynamical system and contains all traveling wave structures and the system is conservative. The graphical explanation of energy levels presents the significant insights and the existence of closed-form solutions to the model. The periodic, quasi-periodic, and quasi-periodic-chaotic profiles are present to see the deep dynamics of the continuum isotropic bi-quadratic Heisenberg spin chain system. The graphically visualization for sensitivity analysis of the governing equation portraits by taking some initial values to verify its dependence. It is shown that, the model is more sensitive regarding to initial conditions rather then parameters. The graphical two dimensional, three dimensional, and contour visualization of the obtained results are presented to express the pulse propagation behavior by assuming the appropriate values of the involved parameters. The impact of fractional parameter is displayed in the graphical sense. The fractional order controls the soliton behaviour which means that, the prediction and precautions can be constructed about the physical phenomenon of the continuum isotropic bi-quadratic Heisenberg spin chain. As a results, the fractional order exhibits the states of distortion in continuum bi-quadratic magnetic system with non-zero vector on which the form evaluates to zero. The graphical two dimensional, three dimensional, and contour visualization of the obtained results are presented to express the pulse propagation behavior by assuming the appropriate values of the involved parameters.

Abstract Soil with heavy metals contamination, mainly lead (Pb), cadmium (Cd), and chromium (Cr) is a progressively worldwide alarming environmental problem. Recently, biochar has been used as a soil amendment to remediate contaminated soils, but little work has been done to compare with other organic amendments like compost. We investigated biochar and compost's comparative effect on Pb, Cd, and Cr immobilization in soil, photosynthesis, and growth of maize plants. Ten kg soil was placed in pots and were spiked with Pb, Cd, and Cr at concentrations 20, 10, 20 mg kg−1. The biochar and compost treatments included 0, 0.5, 1, 2, and 4% were separately applied to the soil. The crop from pots was harvested after 60 days. The results show that the highest reduction of AB-DTPA extractable Pb, Cd, and Cr in soil was 79%, 61% and 78% with 4% biochar, followed by 61%, 43% and 60% with 4% compost compared to the control, respectively. Similarly, the highest reduction in shoot Pb, Cd, and Cr concentration was 71%, 63% and 78%with 4% biochar, followed by 50%, 50% and 71% with 4% compost than the control, respectively. The maximum increase in shoot and dry root weight, total chlorophyll contents, and gas exchange characteristics were recorded with 4% biochar, followed by 4% compost than the control. The maximum increase in soil organic matter and total nitrogen (N) was recorded at 4% biochar application while available phosphorus and potassium in the soil at 4% compost application. It is concluded that both biochar and compost decreased heavy metals availability in the soil, reducing toxicity in the plant. However, biochar was most effective in reducing heavy metals content in soil and plant compared to compost. In the future, more low-cost, eco-friendly soil remediation methods should be developed for better soil health and plant productivity.

Businesses are intended to generate profits for the investors by engaging in economic activities. However, the fairness and legitimacy of business activities in terms of their contractual arrangements, margins of profit, and the underlying asset of trade have been a subject of debate. Over 1.5 Billion Muslims across the world and 52 Muslim countries look towards Islamic injunctions as the ultimate truth, and divine guidance to define a framework for conceptualizing profit and loss generation in a business. This paper reviews four sources of Islamic knowledge i.e. (i) qur’anic verses, (ii) sayings and practices of the Prophet (PBUH), (iii) commercial contracts, trade arrangements, and transactions as practiced in the Prophets era, and (iv) religious opinion drew on the major school of thoughts. Finally, this paper examines the profit-creation in contemporary Islamic banking practices through the lens of Islamic knowledge to address the contesting views and criticism on the profit-making and sharing arrangements instituted in present-day Islamic Banks. The findings of this paper demarcate the guiding principles to steer general business & commerce activities and specifically the profit-making arrangements for businesses for operationalizing their role in driving the overarching socio-economic welfare in a society.

This paper models and analyses the dynamic response of a synchronous generator driven off-grid micro hydro power system using Simulink tool of MATLAB software. The results are assessed from various perspectives including regulation through no load to full load and overload scenarios under normal and abnormal operating conditions. The investigation under the normal conditions of no load, linearly changing load and full load divulges that the system operates in a satisfactory manner as generator voltage and frequency remain approximately constant at 1 pu. However, at full load generator voltage and frequency drop 3% and 0.5% respectively from its nominal values but remain within prescribed standard IEC limits. The results also expose that the abnormal conditions produced by abrupt changes in load, system faults and severe overload, cause the unwonted variations in the magnitude of generator parameters. Moreover, the study reveals that the system stability significantly enhances when the system is run at full load because the regulation time to fix the variations in the generator parameters; except input mechanical power; decreases, e.g. from 4.1 sec to 0.8 sec for generator voltage, with the increase in the loading from quarter to full load respectively at unity power factor. Further, it is also observed that the regulation time rises, e.g. from 0.8 sec to 1.3 sec for generator voltage, with the reduction in load power factor from unity to 0.8, respectively. Thus, proper protection, to cater for increased fault current at full load and power factor correction must be provided to improve the system stability and protection. Furthermore, it is also concluded that the over loading in any case should be strongly avoided in this type of system and it should never be allowed to exceed 20% of the full load value to avoid system failure

The solution of partial differential equations has generally been one of the most-vital mathematical tools for describing physical phenomena in the different scientific disciplines. The previous studies performed with the classical derivative on this model cannot express the propagating behavior at heavy infinite tails. In order to address this problem, this study addressed the fractional regularized long-wave Burgers problem by using two different fractional operators, Beta and M-truncated, which are capable of predicting the behavior where the classical derivative is unable to show dynamical characteristics. This fractional equation is first transformed into an ordinary differential equation using the fractional traveling wave transformation. A new auxiliary equation approach was employed in order to discover new soliton solutions. As a result, bright, periodic, singular, mixed periodic, rational, combined dark–bright, and dark soliton solutions were found based on the constraint relation imposed on the auxiliary equation parameters. The graphical visualization of the obtained results is displayed by taking the suitable parametric values and predicting that the fractional order parameter is responsible for controlling the behavior of propagating solitary waves and also providing the comparison between fractional operators and the classical derivative. We are confident about the vital applications of this study in many scientific fields.

The generalized Calogero–Bogoyavlenskii–Schiff equation (GCBSE) is examined and analyzed in this paper. It has several applications in plasma physics and soliton theory, where it forecasts the soliton wave propagation profiles. In order to obtain the analytically exact solitons, the model under consideration is a nonlinear partial differential equation that is turned into an ordinary differential equation by using the next traveling wave transformation. The new extended direct algebraic technique and the modified auxiliary equation method are applied to the generalized Calogero–Bogoyavlenskii–Schiff equation to get new solitary wave profiles. As a result, novel and generalized analytical wave solutions are acquired in which singular solutions, mixed singular solutions, mixed complex solitary shock solutions, mixed shock singular solutions, mixed periodic solutions, mixed trigonometric solutions, mixed hyperbolic solutions, and periodic solutions are included with numerous soliton families. The propagation of the acquired soliton solution is graphically presented in contour, two- and three-dimensional visualization by selecting appropriate parametric values. It is graphically demonstrated how wave number impacts the obtained traveling wave structures.

The Delta and Omicron variants’ system was used in this research study to replicate the complex process of the SARS-CoV-2 outbreak. The generalised fractional system was designed and rigorously analysed in order to gain a comprehensive understanding of the transmission dynamics of both variants. The proposed dynamical system has heredity and memory effects, which greatly improved our ability to perceive the disease propagation dynamics. The non-singular Atangana–Baleanu fractional operator was used to forecast the current pandemic in order to meet this challenge. The Picard recursions approach can be used to ensure that the designed fractional system has at least one solution occupying the growth condition and memory function regardless of the initial conditions. The Hyers–Ulam–Rassias stability criteria were used to carry out the stability analysis of the fractional governing system of equations, and the fixed-point theory ensured the uniqueness of the solution. Additionally, the model exhibited global asymptotically stable behaviour in some conditions. The approximate behaviour of the fatal virus was investigated using an efficient and reliable fractional numerical Adams–Bashforth approach. The outcome demonstrated that there will be a significant decline in the population of those infected with the Omicron and Delta SARS-CoV-2 variants if the vaccination rate is increased (in both the symptomatic and symptomatic stages).

The motive of the study was to explore the nonlinear Riemann wave equation, which describes the tsunami and tidal waves in the sea and homogeneous and stationary media. This study establishes the framework for the analytical solutions to the Riemann wave equation using the new extended direct algebraic method. As a result, the soliton patterns of the Riemann wave equation have been successfully illustrated, with exact solutions offered by the plane solution, trigonometry solution, mixed hyperbolic solution, mixed periodic and periodic solutions, shock solution, mixed singular solution, mixed trigonometric solution, mixed shock single solution, complex soliton shock solution, singular solution, and shock wave solutions. Graphical visualization is provided of the results with suitable values of the involved parameters by Mathematica. It was visualized that the velocity of the soliton and the wave number controls the behavior of the soliton. We are confident that our research will assist physicists in predicting new notions in mathematical physics.

This work discusses the soliton solutions for the fractional complex Ginzburg–Landau equation in Kerr law media. It is a particularly fascinating model in this context as it is a dissipative variant of the Hamiltonian nonlinear Schrödinger equation with solutions that create localized singularities in finite time. The ϕ6-model technique is one of the generalized methodologies exerted on the fractional complex Ginzburg–Landau equation to find the new solitary wave profiles. As a result, solitonic wave patterns develop, including Jacobi elliptic function, periodic, dark, bright, single, dark-bright, exponential, trigonometric, and rational solitonic structures, among others. The assurance of the practicality of the solitary wave results is provided by the constraint condition corresponding to each achieved solution. The graphical 3D and contour depiction of the attained outcomes is shown to define the pulse propagation behaviors while imagining the pertinent data for the involved parameters. The sensitive analysis predicts the dependence of the considered model on initial conditions. It is a reliable and efficient technique used to generate generalized solitonic wave profiles with diverse soliton families. Furthermore, we ensure that all results are innovative and mark remarkable impacts on the prevailing solitary wave theory literature.

Every organization is moving towards new concepts and philosophies. Big Data is a growing broad concept and philosophy for many. A lot is need do on Big Data in context of IT world. In perspective of Human Resource and Big Data is at initial level where things are bit confusing and many HR Specialists still un-aware of this term. Big data is such kind of data, which resides and keep evolving to grow more day-by-day due to its dynamic nature. Big Data imbue numerous potential can be used in area of HRM. Big Data will caste new paradigm shift is HRM, where HR managers can easily decide and execute new HR strategies of future. Big Data will replace the old HR practices by ministering new techniques and policies by Technology, Analytics and Software inclination in every organization with time to come. Through analysis of literature and published research, we revealed that most of researchers are using the observational technique and data produced by algorithms and software as well as organizational process.

Electrical energy is the most efficient and the cleanest form of energy at the moment that is being transmitted and distributed amongst end-users. From its earlier days, the AC system was preferred as an economical solution for transmission and distribution. However, the development in the power electronics technology and the evolution of highly efficient power electronic converters have established the resurgence of DC power system. Furthermore, the trend is shifting towards DC loads as various energy efficient appliances, such as DC inverter air conditioners, operate on DC nowadays. This further advocates the shift towards the DC power system. This research works is an effort to perform the comparative analysis of AC Distribution System (ACDS) and DC Distribution System (DCDS), with regards to power quality and harmonic distortion in particular. The comparison is performed considering load profile and load variation on daily basis. Simulations are performed in MATLAB. It has been concluded at the end that ACDS is better than DCDS in terms of power quality as total harmonic distortion of the DCDS under the same loading and same load variation during the whole day was significantly higher than that of ACDS.

To overcome the problems associated with soil phosphorus (P) insolubility, soil inoculation with phosphate-solubilizing bacteria (PSB) can be used. In a field experiment, we evaluated the efficacy of PSB in enhancing mungbean P acquisition, nitrogen (N) fixation, and morphological and yield traits in alkaline-calcareous soil when added together with P as single superphosphate (SSP) or rock phosphate (RP) at 45 or 90 kg P2O5 ha−1. Coupling PSB with mineral P fertilizers (SSP & RP) improved P use efficiency, mungbean P acquisition, N2 fixation, nodulation, NP uptake, and the morphological and yield-related traits of mungbeans compared with non-fertilized controls and plots received P from mineral sources alone. Soil PSB inoculation with mineral P also improved post-harvest soil fertility relative to pre-harvest by improving soil organic matter from 0.61% to 0.70%, lowering pH from 7.74 to 7.68, and improving soil total N from 0.04 to 0.09%, ABDTPA-extractable P from 2.07 to 3.44 mg kg−1, and potassium (K) concentrations from 100.27 to 129.45 mg kg−1. When combined with PSB, RP generally performed better than SSP. Moreover, there was a significant correlation between soil N and plant N, while the correlation between soil P and plant P was non-significant. The correlation between soil organic matter content and NP uptake by mungbeans was also non-significant. Therefore, adding P as RP at 45–90 kg ha−1, together with PSB inoculation, can be recommended for improving mungbean P acquisition, use efficiency, optimum N2 fixation, and yield in alkaline-calcareous soils.

This data in brief article represents the data set associated with a research article published in Geoderma [1]. The data set represents figures showing the spatial distribution of selected macro and micronutrients, and their quantification in different crop or nutrient management systems practiced in the boreal ecosystem. Spatial distribution of nutrients was measured by laser ablation inductively coupled plasma mass spectrometry (LA‒ICP‒MS), using the new techniques we developed to visualize nutrient distribution in intact soil cores representative of the root rhizosphere. This data article supports the findings published in the main article [1]. This work also demonstrates that LA-ICP-MS is a valuable technique to image the spatial distribution of macro and micronutrients in intact soil cores as affected by different crop management practices.

The present study documented the first record of Euphlyctis kalasgramensis from Punjab, Pakistan. The specimens were collected during field visits from June through August 2018. Various morphometric measurements of E. kalasgramensis were taken and compared with Euphlyctis cyanophlyctis. Snout-vent length (SVL) was 38.11 ± 0.87 mm (n = 5), snout length was 3% of SVL, foot length was 55% of SVL, head length was 32% of SVL and weight was 8.01 ± 0.12 g (n = 5). A few specimens (n = 2) were euthanized and preserved for molecular analysis through mitochondrial 16S rRNA gene sequences. The newly obtained DNA sequences of E. kalasgramensis were submitted to GenBank and accession numbers were obtained (MK881165.1 and MK920114.1). The Maximum likelihood and Neighbor-joining trees based on Kimura 2-parameter distance resulted in similar phylogenetic trees. Euphlyctis kalasgramensis was out group in both phylogenetic trees. The interspecific divergence of E. kalasgramensis and E. cyanophlyctis was high ranging from 4% to 6% as compared to low intraspecific divergence 0% and 1%. The diversity and distribution ranges of many amphibians species are not well known in Pakistan due to lack of taxonomic information. In our recommendation, a large scale DNA barcoding is required to report more cryptic or new species from Pakistan.

Automatic news repository collection systems involve a news crawler that extracts news from different news portals, subsequently, these news need to be processed to figure out the category of a news article e.g. sports, politics, showbiz etc. In this process there are two main challenges first one is to place a news article under the right category of news, while the second one is to detect a duplicate news, i.e. when the news are being extracted from multiple sources, it is highly probable to get the same news from many different portals, resulting into duplicate news; failing to which may result into inconsistent statistics obtained after pre-processing the news text. This problem becomes more pertinent when we deal with human loss news involving crime, accident etc. related news articles. As the system may count the same news many times resulting into misleading statistics. In order to address these problems, this research presents the following contributions. Firstly, a news corpus comprising of human loss news of different categories has been developed by gathering data from different sources of well-known and authentic news websites. The corpus also includes a number of duplicate news. Secondly, a comparison of different classification approaches has been conducted to empirically find out the best suitable text classifier for the categorization of different sub-categories of human loss news. Lastly, methods have been proposed and compared to detect duplicate news from the corpus by involving different pre-processing techniques and widely used similarity measures, cosine similarity, and Jaccard's coefficient. The results show that conventional text classifiers are still relevant and perform well in text classification tasks as MNB has given 89.5% accurate results. While, Jaccard coefficient exhibits much better results than Cosine similarity for duplicate news detection with different pre-processing variations with an average accuracy of 83.16%.

This study is aimed to measure and compare the service quality of mobile app-based taxi service companies in Kuala Lumpur Malaysia. For mobility in Kuala Lumpur, there are multiple options, e.g., Meter taxi, Transportation Network Companies (TNC) like Grabe and public transportation services. The latest, most often used service in urban areas are mobile app-based taxi services. The newest cab service has multiple benefits over traditional taxi service, which mainly includes convenience and security. However, in literature, There are very few studies focused on service quality of these companies. Very few studies already conducted has used old service, quality models. the newest service quality models are least validated in the context of mobile app-based taxi service companies. Therefore , this study has selected EtailQ model to measure the service quality of the companies. An online questionnaire adapted from eTailQ provided was designed and shared with the user of the top two taxi service providers, Grabe, and My car. The study has investigated four quality parameters: website design, reliability, privacy/security, and customer service. The study contributes to academia to validate the ETailQ model. The practitioners of the industry will also find it useful to improve the essential parameters of service quality as per the expectations of their users.

Muhammad Ishfaq,1 Wei Zhang,1 Wanying Hu,1 Syed Waqas Ali Shah,2 Yuhao Liu,1 Jian Wang,1 Zhiyong Wu,1 Ijaz Ahmad,3 Jichang Li1 1Heilongjiang Key Laboratory for Animal Disease Control and Pharmaceutical Development, College of Veterinary Medicine, Northeast Agricultural University, Harbin 150030, People’s Republic of China; 2College of Animal Science and Technology, Northeast Agricultural University, Harbin 150030, People’s Republic of China; 3The University of Agriculture Peshawar, Peshawar, Khyber Pakhtunkhwa 25130, PakistanCorrespondence: Jichang LiNortheast Agricultural University, 600 Changjiang Road, Xiangfang District, Harbin 150030, People’s Republic of ChinaTel +86 451 5519 0674Fax +86 451 5519 1200Email lijichang@neau.edu.cnBackground: Baicalin possesses potential anti-inflammatory, anti-tumor and anti-oxidant activities. In the present study, we attempted to investigate the preventive effects of baicalin against Mycoplasma gallisepticum (MG)-induced inflammation, apoptosis and energy metabolism dysfunction in chicken lungs.Methods: Experimental chickens were randomly divided into 1) control group, 2) MG infection group, 3) MG-infected group treated with baicalin at a dose of 450 mg/kg and 4) baicalin alone treated group (450 mg/kg). After 7 days of post-treatment, serum and lung tissues were collected for different experimental analyses. The hallmarks of inflammation, apoptosis and energy metabolism dysfunction were detected by histological and ultrastructural examination, qRT-PCR, Western blotting and terminal deoxynucleotidyl transferase-mediated dUTP nick endlabeling (TUNEL) assay.Results: The level of serum inflammatory markers were increased with MG infection. Histological and ultrastructural analysis showed excessive inflammatory cells infiltrates, alveolar wall thickening, hemorrhages, mitochondrial and nuclear damage, including mitochondrial swelling and condensation of DNA in the lungs of chickens infected with MG. TUNEL assay positive-stained nuclei were significantly increased in MG infection group. In addition, the mRNA and protein expression level of energy metabolism-related genes and ATPase activities were significantly reduced. Meanwhile, MG-induced morphological and ultrastructural changes were partially disappeared with baicalin-treatment, and the level of serum inflammatory markers were significantly reduced. It has been noted that baicalin significantly attenuated MG-induced inflammation and apoptosis in the chicken lungs through the suppression of nuclear factor-kappa B and reduced extensive positive-stained apoptotic nuclei. More importantly, ATPase activities and mRNA and protein expression level of energy metabolism-related genes were significantly improved with baicalin-treatment in the lungs of chickens infected with MG.Conclusion: Conclusively, it has been suggested from these results that baicalin-treatment efficiently prevented MG-induced inflammation, apoptosis and energy metabolism dysfunction in the chicken lungs and provide basis for new therapeutic targets to control MG infection.Keywords: baicalin, inflammation, Mycoplasma gallisepticum, lungs, energy metabolism

This paper aims to study an improved perturbed Schrödinger equation (IPSE) with a kind of Kerr law non-linearity equation governing the propagation dynamics of soliton in optical fibers through the nano-optical fiber. The considered model predicts the influence of quantic non-linearity on the motion of ultrashort optical pulses. The integrability of the model is accompanied by the transformed rational function V-expansion method (for simplicity V=(G′G2)). This proposed method is a significant mathematical tool to obtain the exact travelings wave solutions of non-linear complex partial differential equations (PDEs). A bunch of soliton solutions like dark, dark singular, plane wave solution, and periodic are retrieved along with suitable parametric values. The graphical analysis is also presented for the description of propagation of waves expressed by rational functions, hyperbolic functions, and trigonometric functions.

The propagation of optical soliton profiles in plasma physics and atomic structures is represented by the (1+1)− dimensional Schrödinger dynamical equation, which is the subject of this study. New solitary wave profiles are discovered by using Nucci’s scheme and a new extended direct algebraic method. The new extended direct algebraic approach provides an easy and general mechanism for covering 37 solitonic wave solutions, which roughly corresponds to all soliton families, and Nucci’s direct reduction method is used to develop the first integral and the exact solution of partial differential equations. Thus, there are several new solitonic wave patterns that are obtained, including a plane solution, mixed hyperbolic solution, periodic and mixed periodic solutions, a mixed trigonometric solution, a trigonometric solution, a shock solution, a mixed shock singular solution, a mixed singular solution, a complex solitary shock solution, a singular solution, and shock wave solutions. The first integral of the considered model and the exact solution are obtained by utilizing Nucci’s scheme. We present 2-D, 3-D, and contour graphics of the results obtained to illustrate the pulse propagation characteristics while taking suitable values for the parameters involved, and we observed the influence of parameters on solitary waves. It is noticed that the wave number α and the soliton speed μ are responsible for controlling the amplitude and periodicity of the propagating wave solution.

This study examined the mediating role of corporate social responsibility practices and the nexus between the operational excellence of competitive strategies, and performance, for Islamic banks operating in Pakistan. Particularly, two competitive strategies, namely, the cost-sensitive strategy and the differentiation strategy were considered. This study employed a structured questionnaire to collect the data from 512 respondents (361 from fully-fledged Islamic banks, FFIBs, and 151 from Islamic window banks, IWBs). A partial least square–structural equation modeling approach was employed to test the hierarchal component model. As a robustness check, the Gaussian copula approach was used to address the endogeneity issue, and the Partial least square prediction-oriented segmentation approach was adopted to explore the unobserved heterogeneity. The findings showed evidence of complementary partial mediation between competitive strategies and bank performance, channeled through operational excellence. However, corporate social responsibility (CSR) practices partially mediated the relationship between cost-sensitive strategy and bank performance. This study is worthwhile for managers, policy makers and regulatory authorities concerned with religiously conscious corporations.

This study examines the Chen–Lee–Liu dynamical equation, which represents the propagation of optical pulses in optical fibers and plasma. A new extended direct algebraic technique and Nucci’s scheme are used to find new solitary wave profiles. The method covers thirty-seven solitonic wave profiles, including approximately all soliton families, in an efficient and generic manner. New solitonic wave patterns are obtained, including a plane solution, mixed hyperbolic solution, periodic and mixed periodic solutions, mixed trigonometric solution, trigonometric solution, shock solution, mixed shock singular solution, mixed singular solution, complex solitary shock solution, singular solution and shock wave solutions. The exact fractional solution is obtained using Nucci’s reduction approach. The impact of the fractional order parameter on the solution is considered using both mathematical expressions and graphical visualization. The fractional order parameter is responsible for controlling the singularity of the solution which is graphically displayed. A sensitivity analysis was used to predict the sensitivity of equations with respect to initial conditions. To demonstrate the pulse propagation characteristics, while taking suitable values for the parameters involved, 2-D, 3-D, and contour graphics of the outcomes achieved are presented. The influence of the fractional order ζ is shown graphically. A periodic-singular wave with lower amplitude and dark-singular behaviour is inferred from the graphical behaviour of the trigonometric function solution H1 and the rational function solution H34 from the obtained solutions, respectively.

A generalized (3 + 1)-dimensional nonlinear wave is investigated, which defines many nonlinear phenomena in liquid containing gas bubbles. Basic theories of the natural phenomenons are usually described by nonlinear evolution equations, for example, nonlinear sciences, marine engineering, fluid dynamics, scientific applications, and ocean plasma physics. The new extended algebraic method is applied to solve the model under consideration. Furthermore, the nonlinear model is converted into an ordinary differential equation through the next wave transformation. A well-known analytical approach is used to obtain more general solutions of different types with the help of Mathematica. Shock, singular, mixed-complex solitary-shock, mixed-singular, mixed-shock singular, mixed trigonometric, periodic, mixed-periodic, mixed-hyperbolic solutions are obtained. As a result, it is found that the energy-carrying capacity of liquid with gas bubbles and its propagation can be increased. The stability of the considered model is ensured by the modulation instability gain spectrum generated and proposed with acceptable constant values. Two-dimensional, three-dimensional, and contour surfaces are plotted to see the physical properties of the obtained solutions.