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Abstract In this paper, we investigate the optimal conditions to the boundaries where the unique existence of the solutions to an advection-diffusion-reaction equation is secured by applying the contraction mapping theorem from the study of fixed points. Also, we extract, traveling wave solutions of the underlying equation. To this purpose, a new extended direct algebraic method with traveling wave transformation has been used. Achieved soliton solutions are different functions which are hyperbolic, trigonometric, exponential, and some mixed trigonometric functions. These functions show the nature of solitons. Two and three-dimensional plots are drawn using different values of parameters and coefficients for the comparison and behavior of solitons as combined bright-dark, dark, and bright solitons.

Abstract This work examines the (2+1)-dimensional Boiti–Leon–Pempinelli model, which finds its use in hydrodynamics. This model explains how water waves vary over time in hydrodynamics. We provide new explicit solutions to the generalized (2+1)-dimensional Boiti–Leon–Pempinelli equation by applying the Sardar sub-equation technique. This method is shown to be a reliable and practical tool for solving nonlinear wave equations. Furthermore, different types of solitary wave solutions are constructed: w-shaped, breather waved, chirped, dark, bright, kink, unique, periodic, and more. The results obtained with the variable coefficient Boiti–Leon–Pempinelli equation are stable and different from previous methods. As compared to their constant-coefficient counterparts, the variable-coefficient models are more general here. In the current work, the problem is solved using the Sardar Sub-problem Technique to produce distinct soliton solutions with parameters. Plotting these graphs of the solutions will help you better comprehend the model. The outcomes demonstrate how well the method works to solve nonlinear partial differential equations, which are common in mathematical physics.With the help of this method, we may examine a variety of solutions from significant physical perspectives.

Abstract This study introduces a fractional order model to investigate the dynamics of polio disease spread, focusing on its significance, unique results, and conclusions. We emphasize the importance of understanding polio transmission dynamics and propose a novel approach using a fractional order model with an exponential decay kernel. Through rigorous analysis, including existence and stability assessment applying the Caputo Fabrizio fractional operator, we derive key insights into the disease dynamics. Our findings reveal distinct disease-free equilibrium (DFE) and endemic equilibrium (EE) points, shedding light on the disease’s stability. Furthermore, graphical representations and numerical simulations demonstrate the behavior of the disease under various parameter values, enhancing our understanding of polio transmission dynamics. In conclusion, this study offers valuable insights into the spread of polio and contributes to the broader understanding of infectious disease dynamics.

The stochastic dynamical ϕ4 equation is obtained by adding a multiplicative noise term to the classical ϕ4 equation. The noise term represents the random fluctuations that are present in the system and is modeled by a Wiener process. The stochastic dynamical ϕ4 equation is a powerful tool for modeling the behavior of complex systems that exhibit randomness and nonlinearity. It has a wide range of applications in physics, chemistry, biology, and finance. Our goal of this paper is to use the new extended direct algebraic method to find the stochastic traveling wave solutions of the dynamical ϕ4 equation. We explore the new trigonometric, hyperbolic, and rational functions using the new extended direct algebraic method. Furthermore, we use Matlab to plot 3D surfaces of exact solutions to show how multiplicative noise affects the solutions to the stochastic dynamical ϕ4 equation.

With the advent of smart grids, advanced information infrastructures, advanced metering facilities, bidirectional exchange of information, and battery storage home area networks have all transformed the electricity consumption and energy efficiency. There is a significant shift in the energy management structure from the traditional centralized infrastructure to the flexible demand side driven cyber-physical power systems with clean energy and energy storage system. These changes have significantly evolved the home energy management (HEM) space. Consequently, stakeholders must define their responsibilities, create efficient regulatory frameworks, and test out novel commercial strategies. P2P energy trading appears to be a feasible solution in these circumstances, allowing users to trade electricity with one another before becoming completely reliant on the utility. P2P energy trading offers a more stable platform for energy trade by facilitating the exchange of energy between prosumers and consumers. This research proposes a novel demand and generation prediction techniques of P2P HEMS for optimal energy using the Multi-Objective Optimization model. An enhanced Wild Horse Optimization technique was first used to summarize historical records' qualities. Then, the Bi-LSTM is used to predict the demand and generation values. Furthermore, a Grasshopper optimization (GHO) approach is employed to fine-tune the model's hyperparameters. The P2P HEMS demand and generation prediction framework is offered with a probabilistic and fault evaluation that upholds load flow balance between need and supply for continuous operations. It results in an intelligent community transforming cities into smart ones, opening new avenues for scientific research in terms of technological developments.

Abstract Solitary wave solutions are of great interest to bio-mathematicians and other scientists because they provide a basic description of nonlinear phenomena with many practical applications. They provide a strong foundation for the development of novel biological and medical models and therapies because of their remarkable behavior and persistence. They have the potential to improve our comprehension of intricate biological systems and help us create novel therapeutic approaches, which is something that researchers are actively investigating. In this study, solitary wave solutions of the nonlinear Murray equation will be discovered using a modified extended direct algebraic method. These solutions represent a uniform variation in blood vessel shape and diameter that can be used to stimulate blood flow in patients with cardiovascular disease. These solutions are newly in the literature, and give researchers an important tool for grasping complex biological systems. To see how the solitary wave solutions behave, graphs are displayed using Matlab.

Abstract In this manuscript, the well-known stochastic Burgers’ equation in under investigation numerically and analytically. The stochastic Burgers’ equation plays an important role in the fields of applied mathematics such as fluid dynamics, gas dynamics, traffic flow, and nonlinear acoustics. This study is presented the existence, approximate, and exact stochastic solitary wave results. The existence of results is shown by the help of Schauder fixed point theorem. For the approximate results the proposed stochastic finite difference scheme is constructed. The analysis of the proposed scheme is analyzed by presented the consistency and stability of scheme. The consistency is checked under the mean square sense while the stability condition is gained by the help of Von-Neumann criteria. Meanwhile, the stochastic exact solutions are constructed by using the generalized exponential rational function method. These exact stochastic solutions are obtained in the form of hyperbolic, trigonometric and exponential functions. Mainly, the comparison of both numerical and exact solutions are analyzed via simulations. The unique physical problems are constructed from the newly constructed soliton solutions to compare the numerical results with exact solutions under the presence of randomness. The 3D and line plots are dispatched that are shown the similar behavior by choosing the different values of parameters. These results are the main innovation of this study under the noise effects.

Multilevel inverters (MLIs) have remained a promising contribution to research in the modern era, especially in the area of energy conversion. Their popularity, nominal and optimal operations have merged them into low, medium, and high-power applications. Their use in advanced and wide range of applications have proved them as innovative solutions to many issues. Advanced MLIs structure tackle high-profile total harmonic distortion (THD) issues, maximum switching losses, low fault tolerance, low-quality output voltage, high rating of devices, low switching frequency, and frequency interfacing. Such factors classify them into various categories, which specify their operations in multiple applications. The existing literature lacks proper control strategies, design mechanisms, mathematical and application analysis. The aforementioned strategies help to investigate switching losses, configuration complexity, cost analysis, load management, input and output voltage categorization and many other prominent features of MLIs. Therefore, this paper provides a detailed review study and investigates various MLI topologies based on their structure, synthesis, mathematical explanations, control strategies, design mechanisms and utilization in various applications. The evolution of MLIs their classification, advantages, disadvantages, design mechanisms, control strategies, load vs input voltage interfacing and applications based utilization are tabulated to highlight their importance in various sectors. The proposed review study is compared with other prominent review studies and have covered a wide range of MLI topologies based on their evolutional development, mathematical representations, generic utilization and design methodologies.

In this paper, discover exact solutions of the space–time shifted nonlocal stochastic Sasa–Satsuma equations using the enhanced modified extended tanh-expansion method. This method is a sophisticated mathematical approach for analytical and approximate solution of a nonlinear partial differential equations. The space–time shifted nonlocal stochastic Sasa–Satsuma equations define the behavior of two complex-valued functions, u and v, in a nonlinear system. These equations are complicated to solve analytically because they contain a number of components that describe space–time shifting, nonlocal interactions, and stochastic problems. To increase reliability and effectiveness of the solutions, this method couples the extended tanh-function method with an enhanced method. In order to demonstrate how white noise affects the solutions to the space–time shifted nonlocal stochastic Sasa–Satsuma equations, we also use Matlab to create 3D surfaces and contour graphs of exact solutions.

Abstract In this study, the Lengyel-Epstein system is under investigation analytically. This is the reaction–diffusion system leading to the concentration of the inhibitor chlorite and the activator iodide, respectively. These concentrations of the inhibitor chlorite and the activator iodide are shown in the form of wave solutions. This is a reaction†“diffusion model which considered for the first time analytically to explore the different abundant families of solitary wave structures. These exact solitary wave solutions are obtained by applying the generalized Riccati equation mapping method. The single and combined wave solutions are observed in shock, complex solitary-shock, shock singular, and periodic-singular forms. The rational solutions also emerged during the derivation. In the Lengyel-Epstein system, solitary waves can propagate at various rates. The harmony of the system’s diffusive and reactive effects frequently governs the speed of a single wave. Solitary waves can move at a variety of speeds depending on the factors and reaction kinetics. To show their physical behavior, the 3D and their corresponding contour plots are drawn for the different values of constants.

An essential stage in the spread of cancer is the entry of malignant cells into the bloodstream. The fundamental mechanism of cancer cell intravasation is still completely unclear, despite substantial advancements in observing tumor cell mobility in vivo. By creating therapeutic methods in conjunction with control engineering or by using the models for simulations and treatment process evaluation, tumor growth models have established themselves as a crucial instrument for producing an engineering backdrop for cancer therapy. Because tumor growth is a highly complex process, mathematical modeling has been essential for describing it because a carefully crafted tumor growth model constantly describes the measurements and the physiological processes of the tumors. This article discusses the exact and solitary wave behavior of a tumor cell with a three-dimensional linear-quadratic model. Exact solutions have been discussed in detail using the newly extended direct algebraic method, which presents a variety of answers to this issue based on the conditions applied. This article also illustrates its graphical behavior with surface and contour plots of several solitons.

This study deals with a stochastic reaction–diffusion biofilm model under quorum sensing. Quorum sensing is a process of communication between cells that permits bacterial communication about cell density and alterations in gene expression. This model produces two results: the bacterial concentration, which over time demonstrates the development and decomposition of the biofilm, and the biofilm bacteria collaboration, which demonstrates the potency of resistance and defense against environmental stimuli. In this study, we investigate numerical solutions and exact solitary wave solutions with the presence of randomness. The finite difference scheme is proposed for the sake of numerical solutions while the generalized Riccati equation mapping method is applied to construct exact solitary wave solutions. The numerical scheme is analyzed by checking consistency and stability. The consistency of the scheme is gained under the mean square sense while the stability condition is gained by the help of the Von Neumann criteria. Exact stochastic solitary wave solutions are constructed in the form of hyperbolic, trigonometric, and rational forms. Some solutions are plots in 3D and 2D form to show dark, bright and solitary wave solutions and the effects of noise as well. Mainly, the numerical results are compared with the exact solitary wave solutions with the help of unique physical problems. The comparison plots are dispatched in three dimensions and line representations as well as by selecting different values of parameters.

The reaction-nonlinear diffusion model is analyze analytically, under both logistic and bistable growth regularization. These regularization techniques have been widely apply and employ in models of chemical phase separation. In this study, we mainly focus on construct the different wave structures are with the help of the generalized Riccati equation mapping method. This method is provided us the different hyperbolic, trigonometric, and rational solutions. These solutions help for the dynamic study of the reaction-nonlinear diffusion model. Moreover, for the physical significance, we construct the 3D and their corresponding contour by choosing the different values of the parameters. Additionally for the computational interests of the readers stability and consistency analysis were proved.

In this review paper, the anti-surge control (ASC) of the compressors and fault-tolerant control (FTC) systems are described from the perspective of integration for reliability enhancement against faults in the system components. It explains the phenomenon of a surge in the compressors, surge precursors, and the potential damage caused by this surge. The explanation of surge avoidance methods in compressors incorporated with modern surge control systems is described along with their applications. The sizing of the system components and valves, particularly methodologies for appropriately estimating acceptable upstream pipe sizes, are elaborated. The existing surge protection techniques for compressors are analyzed to highlight the advantages and disadvantages and from a future perspective, new approaches for detecting system changes and surges, are included. In the end, the concept of fault tolerance and its advanced applications concerning the anti-surge control for compressors are explained. This study contributes to the young researchers in the field of anti-surge control systems for compressors with the integration of fault tolerance to increase the reliability of the system.

This article investigates the transmission of polio-virus disease in the human population. The classical model is considered for studying fatal disease. First of all, the model is converted into the fractal fractional epidemic model. Then, the existence of the solution for the said model is ensured with the help of the fixed point theory. Points of equilibria for the model are worked out. The basic reproduction number is described and its role in the disease communication and stability of the model is examined by some standard results. Simulated graphs are also plotted to support the pre-results and claims. Lastly, the findings of the study are presented.

The concept of smart grids has enabled the addition of renewable energy resources in the utility grids. This integration is possible after energy conversion and energy conversion causes the degradation in the quality of electric power. The power quality can be enhanced by reducing the total harmonic distortion (THD) in energy conversion. In this paper, we have presented an improved artificial neural network (ANN) based approach that can be useful to reduce the THD levels in a cascaded H-bridge (CHB) multilevel inverter (MLI). The proposed ANN architecture consists of only one hidden layer with ten neurons and can generate accurate results in both overfitting and underfitting conditions. Due to a smaller number of neurons, the proposed architecture is less complex and can produce results relatively faster as compared to other ANN architectures available in the literature. The proposed ANN architecture is tested on an asymmetrical CHB MLI, and the results are compared with the recent state-of-the-art (SOTA) techniques. The CHB MLI under test had three DC voltage sources with 1:2:4 and inductive loads. The simulations are performed in MATLAB and Simulink environment and the switching angles are optimized by using the ANN architecture. The results have shown a 71.95% improvement in current THDs and a 13.91% improvement in voltage THDs as compared to the SOTA technique. The proposed configuration is 89.6% efficient on inductive load and uses a smaller number of switches. Finally, an experimental setup is created, and the simulation results are validated through various experiments.

In this study, the acoustic nonlinear equation namely the confirmable time-fractional Westervelt equation is under consideration analytically. This equation is applicable in the wave propagation of sound and high amplitude in medical imaging and therapy. The different types of wave structures are constructed for the confirmable time-fractional Westervelt equation by using two different techniques namely as, the modified exponential rational functional method and the modified G′/G2-model expansion method. With the help of these two techniques, we gain the different hyperbolic, exponential, periodic, and plane wave function solutions. Additionally, to show the graphical behavior of the wave structure, the 3D, 2D, and their corresponding contour representations are drawn by the different choices of parameters.

The current study deals with the stochastic Nizhnik–Novikov–Veselov (SNNV) system analytically under the multiplicative noise effect. The Nizhnik–Novikov–Veselov equation is an extension of the KdV equation with applications in shallow-water waves, ionic acoustic waves in plasma, long internal waves in density-stratified oceans, and sound waves on crystal networks. The stochastic wave structures are constructed with the help of the Sardar subequation method. The different solutions are extracted which are in the form of solitons and solitary wave structures in the noise effect. Additionally, the stochastic behavior appears in the 3-dim, 2-dim, and their corresponding contour representations by the various selection of parameters.

In this paper, the examination of soliton solutions of the biofilm model with the help of a new extended direct algebraic method is expressed. Besides the exact solutions, the existence of these solutions is also discussed with the help of the Schauder fixed point theorem. The nonlinear dynamical biofilm model which we consider in this paper is basically the bistable Allen–Cahn equation with quartic potential. For more physical understanding, the 3D plots of the solutions are presented. The different types of hyperbolic, trigonometric, and rational soliton solutions are gained. In the biofilm model, different parameters belong to certain spaces and give the exact solutions by applying the technique of new extended direct algebraic method. Exact solutions of the biofilm model are highlighted along with their restriction.

In this study, we construct the abundant families of soliton solutions for the generalized (2+1)-dimensional Camassa–Holm–KP equation. This equation is used in tiny amplitude shallow water waves. The solutions are obtained in the form of Jacobi elliptic function solutions which are the soliton and solitary wave solutions. They are observed in the form of shock, bright, combined complex shock, singular and periodic waves, as well as rational solutions. Some techniques are applied to obtain the solutions with the help of Mathematica namely as; ϕ6-model expansion and a new modified extended direct algebraic method. In nonlinear dynamics, the acquired results are particularly helpful for studying and confirming the analytical solutions with numerical and experimental work. Additionally, the contour diagrams and three- and two-dimensional representations of the solutions are drawn for the various parameter values.

In this article, we investigate existence and the exact solutions of the extended Fisher-Kolmogorov (EFK) equation. This equation is used in the population growth dynamics and wave propagation. The fourth-order term in this model describes the phase transitions near critical points which are also known as Lipschitz points. He's variational method is adopted to construct the soliton solutions as well as the periodic wave solutions successfully for the extended (higher-order) EFK equation. This approach is simple and has the greatest advantages because it can reduce the order of our equation and make the equation more simple. So, the results that are obtained by this approach are very simple and straightforward. The graphics behavior of these solutions are also sketched in 3D, 2D, and corresponding contour representations by the different choices of parameters.

In this article, we have introduced the diarrhea disease dynamics in a varying population. For this purpose, a classical model of the viral disease is converted into the fractional-order model by using Atangana-Baleanu fractional-order derivatives in the Caputo sense. The existence and uniqueness of the solutions are investigated by using the contraction mapping principle. Two types of equilibrium points i.e., disease-free and endemic equilibrium are also worked out. The important parameters and the basic reproduction number are also described. Some standard results are established to prove that the disease-free equilibrium state is locally and globally asymptotically stable for the underlying continuous system. It is also shown that the system is locally asymptotically stable at the endemic equilibrium point. The current model is solved by the Mittag-Leffler kernel. The study is closed with constraints on the basic reproduction number $ R_{0} $ and some concluding remarks.

In this paper, we investigate the soliton solutions of the time–space fractional order nonclassical Sobolev-type (TSFNST) equation. Sobolev equations are used in thermodynamics, the flow of fluid through fractured rock, and other fields. There are certain significant partial differential equations having a third-order mixed derivative with regard to time and space that are now being used in real-world applications. The study aims to analyze the TSFNST equation analytically by employing the ϕ6-model expansion and modified G′/G2 expansion techniques respectively. The solution is obtained successfully in the Jacobi elliptic function solutions that will prove to us the hyperbolic, trigonometric, and rational solutions. Additionally, we select some unique physical problems of the solution. Lastly, the 3-dimensional and their corresponding contour plots are drawn by choosing the different values of constants

The current research deals with the exact solutions of the nonlinear partial differential equations having two important difficulties, that is, the coefficient singularities and the stochastic function (white noise). There are four major contributions to contemporary research. One is the mathematical analysis where the explicit a priori estimates for the existence of solutions are constructed by Schauder’s fixed point theorem. Secondly, the control of the solution behavior subject to the singular parameter ϵ when ϵ → 0. Thirdly, the impact of noise that is present in the differential equation has been successfully handled in exact solutions. The final contribution is to simulate the exact solutions and explain the plots.

This article deals with the stochastic Gross–Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation (SSE) and modified exponential rational functional (MERF) techniques. The exact solutions are constructed in the form of exponential, hyperbolic, and trigonometric forms. Finally, the comparison of the exact solutions with numerical solutions is drawn in the 3D and line plots for the different values of parameters.

This paper investigates the analytical solutions of the autocatalytic reaction–diffusion Selkov–Schnakenberg system of coupled nonlinear PDEs mathematical perspective. This is a simple chemical reaction system that admits periodic solutions. The new families of exact solutions are derived which represent the autocatalyst and reactant of chemical concentrations. These exact solutions are obtained by using the technique namely as ϕ6-model expansion. Furthermore, the existence of these solutions is also discussed under different constraint conditions and variables of concentrations that are represented in hyperbolic, trigonometric, and rational forms. These results are new and effective in the physical phenomena of autocatalytic chemical reactions. For a better understanding of the physical interpretation of the solutions, the 3D and 2D graphs of some reported solutions are dispatched below for the different choices of parameters. Hence the physical description of our results may fruitful tool for investigating the further results for nonlinear wave problems in applied science.

Internal Combustion (IC) engines are commonly used in the process industry, and proper Air-Fuel Ratio (AFR) regulation in their fuel system is essential for improved engine performance, fuel efficiency, and environmental protection. Since faults in the sensors of the AFR system cause the engine to shut down, fault tolerance is essentially required for them. In this paper, an advanced Active Fault-Tolerant Control System (AFTCS) for AFR control of an IC engine is proposed to prevent the engine shutdown. For analytical redundancy, the proposed AFTCS uses the Genetic Algorithm (GA) based observer model in the Fault Detection and Isolation (FDI) unit to generate estimated value for the faulty sensors using the values of other healthy sensors. The proposed framework was simulated in the MATLAB/Simulink environment to verify its effectiveness. In comparison to previous literature works, the results show that the AFR control system has superior fault tolerance output for sensor faults, especially for the MAP sensor, in terms of less oscillatory response. Finally, a comparison of the proposed GA-based AFTCS was carried out with the existing literature works and its superior performance was elaborated.

In the recent article, a reaction-advection-diffusion model of the hepatitis-B virus (HBV) is studied. Existence and uniqueness of the optimal solution for the proposed model in function spaces is analyzed. The advection and diffusion terms make the model more generic than the simple model. So, the numerical investigation plays a vital role to understand the behavior of the solutions. To find the existence and uniqueness of the optimal solutions, a closed and convex subset (closed ball) of the Banach space is considered. The explicit estimates regarding the solution of the system for the admissible auxiliary data is computed. On the other hand, for the numerical approximation of the solution, an elegant numerical technique is devised to find the approximate solutions. After constructing the discrete model, some fundamental properties must necessarily be possessed by the proposed numerical scheme. For instance, consistency, stability, and positivity of the solutions. These properties are carefully studied in the current article. To prove the positivity of the proposed scheme, M-matrix theory is used. All the above mentioned properties are verified by sketching the graph via simulations. Furthermore, these plots are helpful to understand the true behavior of the solutions. For this purpose, a fruitful discussion is included about the simulations to justify our results.

In this paper, nonlinear fractional order Ebola virus mathematical model is discussed for the complex transmission of the epidemic problems. We developed the fractional order Ebola virus transmission model for the treatment and control to reduce its effect on a population which play an important role for public health. Qualitative analysis has been made to verify the the steady state and uniqueness of the system is also developed for reliable results. Caputo fractional derivative operator φ i ∈ (0,1] works to achieve the fractional differential equations. Laplace with Adomian Decomposition Method successfully solved the fractional differential equations. Ultimately, numerical simulations are also developed to evaluate the effects of the device parameter on spread of disease and effect of fractional parameter φ i on obtained solution which can also be assessed by tabulated results.

Abstract Background Plant height (PH) and fruit branch number (FBN) are important traits for improving yield and mechanical harvesting of cotton. In order to identify genes of PH and FBN in cotton germplasms to develop superior cultivars, quantitative trait loci (QTLs) for these traits were detected based on the phenotypic evaluation data in nine environments across four locations and 4 years and a previously reported genetic linkage map of an recombinant inbred line (RIL) population of upland cotton. Results In total, 53 QTLs of PH and FBN, were identified on 21 chromosomes of the cotton genome except chromosomes c02, c09-c11, and c22. For PH, 27 QTLs explaining 3.81%–8.54% proportions of phenotypic variance were identified on 18 chromosomes except c02, c08-c12, c15, and c22. For FBN, 26 QTLs explaining 3.23%–11.00% proportions of phenotypic variance were identified on 16 chromosomes except c02-c03, c06, c09-c11, c17, c22-c23, and c25. Eight QTLs were simultaneously identified in at least two environments. Three QTL clusters containing seven QTLs were identified on three chromosomes (c01, c18 and c21). Eleven QTLs were the same as previously reported ones, while the rest were newly identified. Conclusions The QTLs and QTL clusters identified in the current study will be helpful to further understand the genetic mechanism of PH and FBN development of cotton and will enhance the development of excellent cultivars for mechanical managements in cotton production.

Internal Combustion (IC) engines are prevalent in the process sector, and maintaining sufficient Air-Fuel Ratio (AFR) regulation in their fuel system is crucial for enhanced engine performance, fuel economy, and environmental safety. Faults in the AFR system's sensors cause the engine to shut down, hence, fault tolerance is essential. In order to avoid engine shutdown, this paper offers a novel Active Fault-Tolerant Control System (AFTCS) for air-fuel ratio control of an Internal Combustion (IC) engine in a process plant. In the Fault Detection and Isolation (FDI) unit, the proposed AFTCS uses a nonlinear regression-based observer model for analytical redundancy. The suggested system was simulated in the MATLAB / Simulink environment. The proposed system was tested at two different speeds (300 r/min and 600 r/min) and the results show that the system's response is within the acceptable bound without compromising the stability. The findings also demonstrate the higher fault tolerance capability for sensor defects of the AFR control system, particularly for the MAP sensor (at 300 r/min) in terms of reduced oscillatory response in comparison to the current literature. Compared to the linear regression-based and Genetic Algorithm (GA) based model, the nonlinear regression-based model results in a more accurate estimation of the faulty sensors. The proposed model is also efficient in terms of computation power and response time.

In this article, the transmission dynamical model of the deadly infectious disease named Ebola is investigated. This disease identified in the Democratic Republic of Congo (DRC) and Sudan (now South Sudan) and was identified in 1976. The novelty of the model under discussion is the inclusion of advection and diffusion in each compartmental equation. The addition of these two terms makes the model more general. Similar to a simple population dynamic system, the prescribed model also has two equilibrium points and an important threshold, known as the basic reproductive number. The current work comprises the existence and uniqueness of the solution, the numerical analysis of the model, and finally, the graphical simulations. In the section on the existence and uniqueness of the solutions, the optimal existence is assessed in a closed and convex subset of function space. For the numerical study, a nonstandard finite difference (NSFD) scheme is adopted to approximate the solution of the continuous mathematical model. The main reason for the adoption of this technique is delineated in the form of the positivity of the state variables, which is necessary for any population model. The positivity of the applied scheme is verified by the concept of M-matrices. Since the numerical method gives a discrete system of difference equations corresponding to a continuous system, some other relevant properties are also needed to describe it. In this respect, the consistency and stability of the designed technique are corroborated by using Taylor’s series expansion and Von Neumann’s stability criteria, respectively. To authenticate the proposed NSFD method, two other illustrious techniques are applied for the sake of comparison. In the end, numerical simulations are also performed that show the efficiency of the prescribed technique, while the existing techniques fail to do so.

The study of A-genome Asian cotton as a potential fiber donor in Gossypium species may offer an enhanced understanding of complex genetics and novel players related to fiber quality traits. Assessment of individual fibers providing classified fiber quality information to the textile industry is Advanced Fiber Information System (AFIS) in the recent technological era. Keeping the scenario, a diverse collection of 215 Asiatic cotton accessions were evaluated across three agro-ecological zones of China. Genome-Wide Association Studies (GWAS) was performed to detect association signals related to 17 AFIS fiber quality traits grouped into four categories viz: NEPs, fiber length, maturity, and fineness. Significant correlations were found within as well as among different categories of various traits related to fiber quality. Fiber fineness has shown a strong correlation to all other categories, whereas these categories are shown interrelationships via fiber-fineness. A total of 7,429 SNPs were found in association with 17 investigated traits, of which 177 were selected as lead SNPs. In the vicinity of these lead SNPs, 56 differentially expressed genes in various tissues/development stages were identified as candidate genes. This compendium connecting trait-SNP-genes may allow further prioritization of genes in GWAS loci to enable mechanistic studies. These identified quantitative trait nucleotides (QTNs) may prove helpful in fiber quality improvement in Asian cotton through marker-assisted breeding as well as in reviving eroded genetic factors of G. hirsutum via introgression breeding.

In this article, a nonlinear autocatalytic chemical reaction glycolysis model with the appearance of advection and diffusion is proposed. The occurrence and unicity of the solutions in Banach spaces are investigated. The solutions to these types of models are obtained by the optimization of the closed and convex subsets of the function space. Explicit estimates of the solutions for the admissible auxiliary data are formulated. An elegant numerical scheme is designed for an autocatalytic chemical reaction model, that is, the glycolysis model. The fundamental traits of the prescribed numerical method, for instance, the positivity, consistency, stability, etc., are also verified. The authenticity of the proposed scheme is ensured by comparing it with two extensively used numerical techniques. A numerical example is presented to observe the graphical behavior of the continuous system by constructing the numerical algorithm. The comparison depicts that the projected numerical design is more productive as compared to the other two schemes, as it holds all the important properties of the continuous model.

In this article, an implicit numerical design is formulated for finding the numerical solution of spatiotemporal nonlinear dynamical system with advection. Such type of problems arise in many fields of life sciences, mathematics, physics and engineering. The epidemic model describes the population densities that have some special types of features. These features should be maintained by the numerical design. The proposed scheme, not only solves the nonlinear physical system but also preserves the structure of the state variables. Von-Neumann criteria, M-matrix theory and Taylor’s expansion are used for proving some standard results. Basic reproduction number is evaluated and its key role in deciding the stability at the equilibrium points is also investigated. Graphical solutions are also presented against the test problem.

This article deals with the study of ultrasound propagation, which propagates the mechanical vibration of the molecules or of the particles of a material. It measures the speed of sound in air. For this reason, the third-order non-linear model of the Westervelt equation was chosen to be studied, as the solutions to such problems have much importance for physical purposes. In this article, we discuss the exact solitary wave solutions of the third-order non-linear model of the Westervelt equation for an acoustic pressure p representing the equation of ultrasound with high intensity, as used in acoustic tomography. Moreover, the non-linear coefficient B/A (being a part of space-dependent coefficient K), has also been investigated in this literature. This problem is solved using the Generalized Kudryashov method along with a comparison of the Modified Kudryashov method. All of the solutions have been discussed with both surface and contour plots, which shows the behavior of the solution. The images are prepared in a well-established way, showing the production of tissues inside the human body.

In this article, three distinct strategies for designing an Active Fault-Tolerant Control System (AFTCS) for Air-Fuel Ratio (AFR) control of an Internal Combustion (IC) engine in a process plant to avoid engine shutdown, are presented. The proposed AFTCS employs a Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and a Nonlinear Regression (NLR)-based observer model in the Fault Detection and Isolation (FDI) unit for analytical redundancy. A comparison between these three proposed techniques is carried out to determine the least expensive and most accurate approach. The results show that the nonlinear regression produces highly accurate results by consuming very low computational power, and its response time is also very low as compared to GA and PSO. The results obtained show that NLR requires 99.6% and 93.1% less computational time for throttle and MAP estimation, respectively, by reducing the estimation error to as low as 0.01. The simulation of the proposed system is carried out in the MATLAB/Simulink environment. The results prove the superior fault tolerance performance for sensor faults of the AFR control system, especially for the Manifold Absolute Pressure (MAP) sensor in terms of less oscillatory response as compared to that reported in existing literature.

For about a century, plant breeding has widely exploited the heterosis phenomenon–often considered as hybrid vigor–to increase agricultural productivity. The ensuing F1 hybrids can substantially outperform their progenitors due to heterozygous combinations that mitigate deleterious mutations occurring in each genome. However, only fragmented knowledge is available concerning the underlying genes and processes that foster heterosis. Although cotton is among the highly valued crops, its improvement programs that involve the exploitation of heterosis are still limited in terms of significant accomplishments to make it broadly applicable in different agro-ecological zones. Here, F1 hybrids were derived from mating a diverse Upland Cotton germplasm with commercially valuable cultivars in the Line × Tester fashion and evaluated across multiple environments for 10 measurable traits. These traits were dissected into five different heterosis types and specific combining ability (SCA). Subsequent genome-wide predictions along-with association analyses uncovered a set of 298 highly significant key single nucleotide polymorphisms (SNPs)/Quantitative Trait Nucleotides (QTNs) and 271 heterotic Quantitative Trait Nucleotides (hQTNs) related to agronomic and fiber quality traits. The integration of a genome wide association study with RNA-sequence analysis yielded 275 candidate genes in the vicinity of key SNPs/QTNs. Fiber micronaire (MIC) and lint percentage (LP) had the maximum number of associated genes, i.e., each with 45 related to QTNs/hQTNs. A total of 54 putative candidate genes were identified in association with HETEROSIS of quoted traits. The novel players in the heterosis mechanism highlighted in this study may prove to be scientifically and biologically important for cotton biologists, and for those breeders engaged in cotton fiber and yield improvement programs.

The article studies the extraction of electromagnetic wave structures in a spin ladder anti-ferromagnetic medium with a coupled generalized non-linear Schrodinger model. The direct algebraic technique is used to extract the wave solutions. The solutions are obtained in the form of dark, singular, kink, and dark-singular under different constraint conditions. Moreover, the dynamic behavior of the structures have depicted in 3D graphs and their corresponding counterplots. The results are helpful for the understanding of wave propagation study and are also vital for numerical and experimental verifications in the field of electromagnetic wave theory.

Abstract Background Heterosis, a multigenic complex trait extrapolated as sum total of many phenotypic features, is widely utilized phenomenon in agricultural crops for about a century. It is mainly focused on establishing vigorous cultivars with the fact that its deployment in crops necessitates the perspective of genomic impressions on prior selection for metric traits. In spite of extensive investigations, the actual mysterious genetic basis of heterosis is yet to unravel. Contemporary crop breeding is aimed at enhanced crop production overcoming former achievements. Leading cotton improvement programs remained handicapped to attain significant accomplishments. Results In mentioned context, a comprehensive project was designed involving a large collection of cotton accessions including 284 lines, 5 testers along with their respective F1 hybrids derived from Line × Tester mating design were evaluated under 10 diverse environments. Heterosis, GCA and SCA were estimated from morphological and fiber quality traits by L × T analysis. For the exploration of elite marker alleles related to heterosis and to provide the material carrying such multiple alleles the mentioned three dependent variables along with trait phenotype values were executed for association study aided by microsatellites in mixed linear model based on population structure and linkage disequilibrium analysis. Highly significant 46 microsatellites were discovered in association with the fiber and yield related traits under study. It was observed that two-thirds of the highly significant associated microsatellites related to fiber quality were distributed on D sub-genome, including some with pleiotropic effect. Newly discovered 32 hQTLs related to fiber quality traits are one of prominent findings from current study. A set of 96 exclusively favorable alleles were discovered and C tester (A971Bt) posited a major contributor of these alleles primarily associated with fiber quality. Conclusions Hence, to uncover hidden facts lying within heterosis phenomenon, discovery of additional hQTLs is required to improve fibre quality. To grab prominent improvement in influenced fiber quality and yield traits, we suggest the A971 Bt cotton cultivar as fundamental element in advance breeding programs as a parent of choice.

Diversifying available natural resources to cope with abrupt climatic changes and the necessity to equalize rising agricultural production with improved ability to endure environmental influence is the dire need of the day. Inherent allelic variability regarding significant economic traits featuring both enhanced productivity and environmental adaptability is one such prominent need. To address this requirement, a series of analyses were conducted in this study for exploring natural diploid wheat germplasm resources. The current study involved 98 Recombinant Inbred Lines (RILs) populations developed by crossing two diploid ‘A’ sub-genome wheat species, Triticummonococcum and Triticum boeoticum, enriched with valuable alleles controlling, in particular, biotic and abiotic stresses tolerance. Their 12 phenotypic traits were explored to reveal germplasm value. All traits exhibited vast diversity among parents and RILs via multivariate analysis. Most of the investigated traits depicted significant (p < 0.05) positive correlations enlightening spikelet per spike, total biomass, seed weight per spike, number of seeds per spike, plant height, and days to heading as considerably focused traits for improving hexaploid wheat. Principal component analysis (PCA) exhibited 61.513% of total variation with three PCs for 12 traits. Clustering of genotypes happened in three clades, and the two parents were separated into two extreme clusters, validating their enrichment of diversity. This study provided beneficial aspects of parental resources rich in diverse alleles. They can be efficiently exploited in wheat improvement programs focusing on introgression breeding and the recovery of eroded genetic factors in currently available commercial wheat cultivars to sustain calamities of environmental fluctuations.

Wireless charging has become an emerging challenge to reduce the cost of a conventional plug-in charging system in electric vehicles especially for supercapacitors that are utilized for quick charging and low-energy demands. In this article, the design of an efficient wireless power transfer system has been presented using resonant inductive coupling technique for supercapacitor-based electric vehicle. Mathematical analysis, simulation, and experimental implementation of the proposed charging system have been carried out. Simulations of various parts of the systems are carried out in two different software, ANSYS MAXWELL and MATLAB. ANSYS MAXWELL has been used to calculate the various parameters for the transmitter and receiver coils such as self-inductance ( L ), mutual inductance ( M ), coupling coefficient ( K ), and magnetic flux magnitude ( B ). MATLAB has been utilized to calculate output power and efficiency of the proposed system using the mathematical relationships of these parameters. The experimental setup is made with supercapacitor banks, electric vehicle, wattmeters, controller, and frequency generator to verify the simulation results. The results show that the proposed technique has better power transfer efficiency of more than 75% and higher power transfer density using a smaller coil size with a bigger gap of 4–24 cm.

The present study aimed to characterize the simple sequence repeat markers in cotton using the cotton expressed sequence tags. A total of 111 EST-SSR polymorphic molecular markers with trinucleotide motifs were used to evaluate the 79 accessions of Gossypium L., (G. darwinii, 59 and G. barbadense, 20) collected from the Galapagos Islands. The allele number ranged from one to seven, with an average value of 2.85 alleles per locus, while polymorphism information content values varied from 0.008 to 0.995, with an average of 0.520. The discrimination power ranks high for the majority of the SSRs, with an average value of 0.98. Among 111 pairs of EST-SSRs and gSSRs, a total of 49 markers, comprising nine DPLs, one each of MonCGR, MUCS0064, and NAU1028, and 37 SWUs (D-genome), were found to be the best matched hits, similar to the 155 genes identified by BLASTx in the reference genome of G. barbadense, G. arboreum L., and G. raimondii Ulbr. Related genes GOBAR_DD21902, GOBAR_DD15579, GOBAR_DD27526, and GOBAR_AA04676 revealed highly significant expression 10, 15, 18, 21, and 28 days post-anthesis of fiber development. The identified EST-SSR and gSSR markers can be effectively used for mapping functional genes of segregating cotton populations, QTL identification, and marker-assisted selection in cotton breeding programs.

This study evaluated the genetic diversity and population structures in a novel cotton germplasm collection comprising 132 diploids, including Glossypium klotzschianum and allotetraploid cotton accessions, including Glossypium barbadense, Glossypium darwinii, Glossypium tomentosum, Glossypium ekmanianum, and Glossypium stephensii, from Santa Cruz, Isabella, San Cristobal, Hawaiian, Dominican Republic, and Wake Atoll islands. A total of 111 expressed sequence tag (EST) and genomic simple sequence repeat (gSSR) markers produced 382 polymorphic loci with an average of 3.44 polymorphic alleles per SSR marker. Polymorphism information content values counted 0.08 to 0.82 with an average of 0.56. Analysis of a genetic distance matrix revealed values of 0.003 to 0.53 with an average of 0.33 in the wild cotton collection. Phylogenetic analysis supported the subgroups identified by STRUCTURE and corresponds well with the results of principal coordinate analysis with a cumulative variation of 45.65%. A total of 123 unique alleles were observed among all accessions and 31 identified only in G. ekmanianum. Analysis of molecular variance revealed highly significant variation between the six groups identified by structure analysis with 49% of the total variation and 51% of the variation was due to diversity within the groups. The highest genetic differentiation among tetraploid populations was observed between accessions from the Hawaiian and Santa Cruz regions with a pairwise FST of 0.752 (p < 0.001). DUF819 containing an uncharacterized gene named yjcL linked to genomic markers has been found to be highly related to tryptophan-aspartic acid (W-D) repeats in a superfamily of genes. The RNA sequence expression data of the yjcL-linked gene Gh_A09G2500 was found to be upregulated under drought and salt stress conditions. The existence of genetic diversity, characterization of genes and variation in novel germplasm collection will be a landmark addition to the genetic study of cotton germplasm.