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In this paper, we utilized a hybrid method for the unsteady flow of the non-Newtonian third-grade fluid that combines the finite difference with the asymptotic interpolation method. This hybrid method is used to satisfy the semiunbound domain condition of the fluid flow’s length approaching infinity. The primary issue with this research is how much of the hybrid approach’s error may be accepted to guarantee that the method is significant. This paper discussed theoretical error analysis for numerical solutions, including the range and norm of error. The perturbation method’s concept is used to assess the hybrid method’s error. It is discovered that the hybrid approach’s relative error norm is lower than that of the finite difference method. In terms of the error standard, the hybrid approach is more consistent. Error analysis is performed to check for the accuracy as well as the platform for variable mesh size finite difference method in the future research.

Parameter estimation is a growing area of interest in statistical signal processing. Some parameters in real-life applications vary in space as opposed to those that are static. Most common methods in estimating parameters involve solving an optimization problem where the cost function is assembled variously, for example, maximum likelihood and maximum a posteriori methods. However, these methods do not have exact solutions to most real-life problems. It is for this reason that Monte Carlo methods are preferred. In this paper, we treat the estimation of parameters which vary with space. We use the Metropolis-Hastings algorithm as a selection criterion for the maximum filter likelihood. Comparisons are made with the use of joint estimation of both the spatially varying parameters and the state. We illustrate the procedures employed in this paper by means of two hyperbolic SPDEs: the advection and the wave equation. The Metropolis-Hastings procedure registers better estimates.

Edge detection consists of a set of mathematical methods which identifies the points in a digital image where image brightness changes sharply. In the traditional edge detection methods such as the first-order derivative filters, it is easy to lose image information details and the second-order derivative filters are more sensitive to noise. To overcome these problems, the methods based on the fractional differential-order filters have been proposed in the literature. This paper presents the construction and implementation of the Prewitt fractional differential filter in the Asumu definition sense for SARS-COV2 image edge detection. The experiments show that these filters can avoid noise and detect rich edge details. The experimental comparison show that the proposed method outperforms some edge detection methods. In the next paper, we are planning to improve and combine the proposed filters with artificial intelligence algorithm in order to program a training system for SARS-COV2 image classification with the aim of having a supplemental medical diagnostic.

In this paper, a high security color image encryption algorithm is proposed by 2D Sin-Cos-Hénon (2D-SCH) system. A new two-dimensional chaotic system which is 2D-SCH. This system is hyperchaotic. The use of the 2D-SCH, a color image encryption algorithm based on random scrambling and localization diffusion, is proposed. First, the secret key is generated by SHA512 through plaintext. As the initial value of the 2D-SCH system, the secret key is used to generate chaotic sequences. Then, the random scrambling is designed based on chaotic sequences. Finally, a pair of initial points is generated by the secret key; the image diffuses around this point. The ciphertext is obtained by a double encryption. Different from the traditional encryption algorithm, this paper encrypts three channels of color image simultaneously, which greatly improves the security of the algorithm. Simulation results show that the algorithm can resist various attacks.

In this paper, by the use of a new fixed point theorem and the Green function of BVPs, the existence of at least one positive solution for the third-order boundary value problem with the integral boundary conditions is considered,where there is a nonnegative continuous function. Finally, an example which to illustrate the main conclusions of this paper is given.

Let G be a finite simple graph with Laplacian polynomial ψG,λ=∑k=0n−1n−kckλk. In an earlier paper, the coefficients cn−4 and cn−5 for forests with respect to some degree-based graph invariants were computed. The aim of this paper is to continue this work by giving an exact formula for the coefficient cn−6.

In this paper, the population dynamics of rabies-infected dogs are studied. The mathematical model is constructed by dividing the dog population into two categories: stray dogs and domestic dogs. On the other hand, the rabies virus is likely to spread in both populations. In the current model, disease-controlling strategies such as vaccination and culling are applied, and their impact is studied. Both subpopulations of susceptible individuals are vaccinated to control disease spread. The current study assumes that stray dogs can transmit rabies to domestic dogs but not the other way around. Because domestic dogs are under the control of their owners, they are well vaccinated. The model is medically and analytically correct because the findings are idealistic and limited. The next-generation matrix technique is used to compute the effective reproductive amount, and also, each parameter is subjected to sensitivity analysis. The equilibrium point free from disease is discovered, demonstrating that it was asymptotically steady locally and globally. A conditionally global asymptotically stable point of endemic equilibrium is also discovered using the Lyapunov function method. The numerical simulation, which makes use of approximations for parameter values, shows that the most efficient method for avoiding rabies transmission is a combination of vaccination and the culling of infected stray dogs. Using MATLAB’s ode45, this numerical simulation investigation was carried out. Our early findings indicated that the annual dog birth rate is a critical factor in influencing the occurrence of rabies. In the body of the paper, the findings and discussion are organized logically.

In this paper, we investigate the transmission dynamics of onchocerciasis with asymptomatic infected humans using a mathematical model. The model incorporates interventions for treatment and vector control to evaluate the impact of these strategies. We analyse the model to determine the existence and stability of equilibrium points. Our results reveal that for the disease to persist in the community, the infection rate must exceed the sum of the treatment rate and the per capita death rate due to the disease. Sensitivity analysis highlights the critical role of the blackfly vector’s average daily biting rate in disease transmission. Numerical simulations indicate that administering highly effective drugs to infected individuals significantly reduces the number of cases. Therefore, in addition to vector control, the use of highly efficient drugs is crucial for controlling the transmission of river blindness.

This paper introduces a new idea to obtain a better order of approximation for the Baskakov operator. We conclude two new operators from orders one and two of the Baskakov type. Also, we prove some directed results concerning the rate of convergence of these operators. We apply the Maple software to demonstrate how the operators converge to a specific function.

In this paper, we developed a mathematical model for the dynamics of coronavirus disease (COVID-19) transmission. The model embraces the notion of contact tracing and contaminated surfaces which are vital for disease control and contribute to disease transmission, respectively. We analyzed the model properties such as the positivity of the solution, invariant region, existence, and stability nature of equilibria. Besides, we computed the basic reproduction number R0. The local stability and the global stability of disease-free equilibrium (DFE) points are proved by using the Routh–Hurwitz criteria and the Castillo-Chavez and Song approach, respectively. LaSalle’s invariant principle is applied to prove the stability of an endemic equilibrium (EE) point. The possibility of bifurcation is discussed using the center manifold theory. We used real data on the spread and control of COVID-19 disease in Ethiopia. Based on the data reported, we estimated the values of the parameters using the least squares method together with the fmin function in the MATLAB optimization toolbox. The sensitivity analysis of the model is explored numerically to illustrate the impact of the parameters on disease transmission. The study addressed that contact tracing is especially important because COVID-19 often has asymptomatic carriers, and there are many asymptomatic individuals unaware in Ethiopia. The new infections would decrease in the communities by detecting and isolating COVID-19 cases before they could spread the virus to others. Moreover, the study endorsed that the contaminated surface has contributed to disease transmission. The sensitivity analysis shows that if the rate of disinfected contaminated objects (ϕ) rises, then the transmission of the disease is reduced. Consequently, this study will aid in the fight against COVID-19 policymakers and NGOs. It can also be used as a policy input for different countries under this crisis. Because of the mathematical modeling of this global pandemic, there is another point of view rather than public health research outputs. Additionally, with the concept of contact tracing and contaminated surfaces incorporated into the model, the result provides insight for disease prevention.

In this paper, we applied an efficient integrative method called the fractional Picard method to find the approximate solution to a system of fractional algebraic differential equations (SFADEs). By comparing the results with the exact solution, it was found that this method is highly efficient for finding solutions. Also, a genetic algorithm (GA) was used to speed up the approximate solutions when choosing the best values for the fractional derivative, which increased the efficiency of Picard’s fractional integral method in finding the best solutions. The MATLAB program was used to find approximate solutions.

Many real-world applications can be modelled as graphs or networks, including social networks and biological networks. The theory of algebraic combinatorics provides tools to analyze the functioning of these networks, and it also contributes to the understanding of complex systems and their dynamics. Algebraic methods help uncover hidden patterns and properties that may not be immediately apparent in a visual representation of a graph. In this paper, we introduce left and right inverse graphs associated with finite loop structures and two mappings, P-edge labeling and V-edge labeling, of Latin squares. Moreover, this work includes some structural and graphical results of the commutator subloop, nucleus, and loop isotopes of inverse property quasigroups.

The Pareto dominance-based evolutionary algorithms can effectively address multiobjective optimization problems (MOPs). However, when dealing with many-objective optimization problems with more than three objectives (MaOPs), the Pareto dominance relationships cannot effectively distinguish the nondominated solutions in high-dimensional spaces. With the increase of the number of objectives, the proportion of dominance-resistant solutions (DRSs) in the population rapidly increases, which leads to insufficient selection pressure. In this paper, to address the challenges on MaOPs, a knee point-driven many-objective evolutionary algorithm with adaptive switching mechanism (KPEA) is proposed. In KPEA, the knee points determined by an adaptive strategy are introduced for not only mating selection but also environmental selection, which increases the probability of generating excellent offspring. In addition, to remove dominance-resistant solutions (DRSs) in the population, an interquartile range method is adopted, which enhances the selection pressure. Moreover, a novel adaptive switching mechanism between angle-based selection and penalty for selecting solutions is proposed, which is aimed at achieving a balance between convergence and diversity. To validate the performance of KPEA, it is compared with five state-of-the-art many-objective evolutionary algorithms. All algorithms are evaluated on 20 benchmark problems, i.e., WFG1-9, MaF1, and MaF4-13 with 3, 5, 8, and 10 objectives. The experimental results demonstrate that KPEA outperforms the compared algorithms in terms of HV and IGD in most of the test instances.

This paper investigates the steady and fully developed magnetohydrodynamic (MHD) flow of two nonmiscible Jeffrey fluids in a horizontal cylinder filled with a homogenous porous medium. A constant pressure gradient drives the flow in both regions, and a uniform magnetic field is applied transversely to the flow direction. Instead of the usual no-slip condition, the linear Navier slip is used as a boundary condition on the cylinder’s surface, whereas the usual continuity conditions of velocity and shear stress are presumed at the fluid–fluid interface. The equations describing the problem under consideration are mathematically formulated and transformed into nondimensional forms with the proper choice of nondimensional variables. Analytical solutions have been obtained by solving the transformed equations of motion. The effects of different nondimensional parameters involved in the flow problem, including the magnetic number, Jeffrey parameter, Darcy number, ratio of viscosities, Reynolds number, slip parameter, and pressure gradient, on the velocity in each region are studied, and the results are exhibited graphically. In addition, numerical values for stress at the wall and volume flow rates are calculated for various fluid parameters and shown in tables. It is noticed that an increase in the values of the magnetic number and viscosity ratio reduces the velocity of the fluid, whereas increasing the Jeffrey parameters, Darcy number, Reynolds number, slip parameter, and pressure gradient enhances fluid velocity. Furthermore, the most favorable agreement was observed between the results of this study and the results of the previous studies.

In this paper, the sequential conformable Langevin-type differential equation is studied. A representation of a solution consisting of the newly defined conformable bivariate Mittag-Leffler function to its nonhomogeneous and linear version is obtained via the conformable Laplace transforms’ technique. Also, existence and uniqueness of a global solution to its nonlinear version are obtained. The existence and uniqueness of solutions are shown with respect to the weighted norm defined in compliance with (conformable) exponential function. The concept of the Ulam–Hyers stability of solutions is debated based on the fixed-point approach. The LRC electrical circuits are presented as an application to the described system. Simulated and numerical instances are offered to instantiate our abstract findings.

In this paper, we develop the theoretical provisions of symmetric cryptographic algorithms based on the polynomial residue number system for the first time. The main feature of the proposed approach is that when reconstructing the polynomial based on the method of undetermined coefficients, multiplication is performed not on the found base numbers but on arbitrarily selected polynomials. The latter, together with pairwise coprime residues of the residue class system, serve as the keys of the cryptographic algorithm. Schemes and examples of the implementation of the developed polynomial symmetric encryption algorithm are presented. The analytical expressions of the cryptographic strength estimation are constructed, and their graphical dependence on the number of modules and polynomial powers is presented. Our studies show that the cryptanalysis of the proposed algorithm requires combinatorial complexity, which leads to an NP-complete problem.

Gumboro disease is a viral poultry disease that causes immune suppression on the infected birds leading to poor production, mortality, and exposure to secondary infections, hence a major threat in the poultry industry worldwide. A mathematical model of the transmission dynamics of Gumboro disease is developed in this paper having four compartments of chicken population and one compartment of Gumboro pathogen population. The basic reproduction number Rog is derived, and the dynamical behaviors of both the disease-free equilibrium (DFE) and endemic equilibrium are analyzed using the ordinary differential equation theory. From the analysis, we found that the system exhibits an asymptotic stable DFE whenever Rog1. The numerical simulation to verify the theoretical results was carried out using MATLAB ode45 solver, and the results were found to be consistent with the theoretical findings.

In this paper, we study asymptotic model change detection in multivariate linear regression by using the Kolmogorov–Smirnov function of the partial sum process of recursive residuals. We approximate the rejection region and also the power function of the test by establishing a functional central limit theorem for the sequence of the partial sum processes of the recursive residuals of the observations. When the assumed model is true, the limit process is given by the standard multivariate Brownian motion which does not depend on the regression functions. However, when the assumed model is not true (some models change), the limit process is represented by a vector of deterministic trend plus the standard multivariate Brownian motion. The finite sample size rejection region and the power of the test are investigated by means of Monte Carlo simulation. The simulation study shows evidence that the proposed test is consistent in the sense that it attains the power larger than the size of the test when the hypothesis is not true. We also demonstrate the application of the proposed test method to Indonesian economic growth data in which we test the adequacy of three-variate low-order polynomial model. The test result shows that the growth of the Indonesian economy is neither simultaneously constant nor linear. The test has successfully detect the appearance of a change in the model which is mainly caused by the COVID-19 pandemic in 2020.

Lymphatic filariasis is a leading cause of chronic and irreversible damage to human immunity. This paper presents deterministic and continuous-time Markov chain (CTMC) stochastic models regarding lymphatic filariasis dynamics. To account for randomness and uncertainties in dynamics, the CTMC model was formulated based on deterministic model possible events. A deterministic model’s outputs suggest that disease extinction is feasible when the secondary threshold infection number is below one, while persistence becomes likely when the opposite holds true. Furthermore, the significant contribution of asymptomatic carriers was identified. Results indicate that persistence is more likely to occur when the infection results from asymptomatic, acutely infected, or infectious mosquitoes. Consequently, the CTMC stochastic model is essential in capturing variabilities, randomness, associated probabilities, and validity across different scales, whereas oversimplification and unpredictability of inherent may not be featured in a deterministic model.

This paper introduces a novel approach for solving first-order stiff initial value problems through the development of a one-step family of three optimized second-derivative hybrid block methods. The optimization process was integrated into the derivation of the methods to achieve maximal accuracy. Through a rigorous analysis, it was determined that the methods exhibit properties of consistency, zero-stability, convergence, and A-stability. The proposed methods were implemented using the waveform relaxation technique, and the computed results demonstrated the superiority of these schemes over certain existing methods investigated in the study.

This paper presents a study on the numerical solutions of the Burgers’ equation with forcing effects. The article proposes three hybrid methods that combine two-point, three-point, and four-point discretization in time with the Galerkin finite element method in space (TDFEM2, TDFEM3, and TDFEM4). These methods use backward finite difference in time and the finite element method in space to solve the Burgers’ equation. The resulting system of the nonlinear ordinary differential equations is then solved using MATLAB computer codes at each time step. To check the efficiency and accuracy, a comparison between the three methods is carried out by considering the three Burgers’ problems. The accuracy of the methods is expressed in terms of the error norms. The combined methods are advantageous for small viscosity and can produce highly accurate solutions in a shorter time compared to existing numerical schemes in the literature. In contrast to many existing numerical schemes in the literature developed to solve Burgers’ equation, the methods can exhibit the correct physical behavior for very small values of viscosity. It has been demonstrated that the TDFEM2, TDFEM3, and TDFEM4 can be competitive numerical methods for addressing Burgers-type parabolic partial differential equations arising in various fields of science and engineering.

This paper focuses on the impact of mosquito biting bias on the success of malaria intervention strategies. The initial model is developed considering the existence of symptomatic and asymptomatic humans, as well as vector bias. The model is then analyzed to demonstrate how the malaria-endemic equilibrium always exists and is globally asymptotically stable if the basic reproduction number is larger than one. On the other hand, malaria will always go extinct in the population if the basic reproduction number is less than one. For intervention analysis, the model is extended by considering mosquito repellent and hospitalization as control strategies. The control reproduction number is shown analytically. Using the Pontryagin maximum principle, we characterize our optimal control problem. Several scenarios are conducted to observe the dynamics of control variables under different circumstances. We found that the intervention of mosquito repellent and hospitalization together is the most cost-effective strategy to reduce the spread of malaria. Furthermore, we have shown that the more biased the vector attracted to infected individuals, the higher the cost needed to implement the control strategy.

The KdV-Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. In this paper, we reformulate this problem in the sense of Caputo fractional derivative, whose physical meanings, in this case, are very evident by describing the whole time domain of physical processing. The main aim of this work is to present the analytical approximate series for the nonlinear Caputo fractional KdV-Burgers equation by applying the Laplace residual power series method. The main tools of this method are the Laplace transform, Laurent series, and residual function. Moreover, four attractive and satisfying applications are given and solved to elucidate the mechanism of our proposed method. The analytical approximate series solution via this sweet technique shows excellent agreement with the solution obtained from other methods in simple and understandable steps. Finally, graphical and numerical comparison results at different values of α are provided with residual and relative errors to illustrate the behaviors of the approximate results and the effectiveness of the proposed method.

Cryptography has recently become a critical area to research and advance in order to transmit information safely and securely among various entities, especially when the transmitted data is classified as crucial or important. This is due to the increase in the use of the Internet and other novel communication technology. Many businesses now outsource sensitive data to a third party because of the rise of cloud computing and storage. Currently, the key problem is to encrypt the data such that it may be stored on an unreliable server without sacrificing the ability to use it effectively. In this paper, we propose a graph encryption scheme by using cryptography and steganography. Data is encrypted using association schemes over finite abelian groups and then hiding the encrypted data behind randomly chosen cover image. We implemented and evaluated the efficiency of our constructions experimentally. We provide experimental results, statistical analysis, error analysis, and key analysis that demonstrates the appropriateness and efficiency of the proposed technique.

In this paper, an efficient new technique is used for solving nonlinear fractional problems that satisfy specific criteria. This technique is referred to as the double conformable fractional Laplace-Elzaki decomposition method (DCFLEDM). This approach combines the double Laplace-Elzaki transform method with the Adomian decomposition method. The fundamental concepts and findings of the recently suggested transformation are presented. For the purpose of assessing the accuracy of our approach, we provide three examples and introduce the series solutions of these equations using DCLEDM. The results show that the proposed strategy is a very effective, reliable, and efficient approach for addressing nonlinear fractional problems using the conformable derivative.

Given that the Crimean and Congo hemorrhagic fever is one of the deadly viral diseases that occur seasonally due to the activity of the carrier “tick,” studying and developing a mathematical model simulating this illness are crucial. Due to the delay in the disease’s incubation time in the sick individual, the paper involved the development of a mathematical model modeling the transmission of the disease from the carrier to humans and its spread among them. The major objective is to comprehend the dynamics of illness transmission so that it may be controlled, as well as how time delay affects this. The discussion of every one of the solution’s qualitative attributes is included. According to the established basic reproduction number, the stability analysis of the endemic equilibrium point and the disease-free equilibrium point is examined for the presence or absence of delay. Hopf bifurcation’s triggering circumstance is identified. Using the center manifold theorem and the normal form, the direction and stability of the bifurcating Hopf bifurcation are explored. The next step is sensitivity analysis, which explains the set of control settings that have an impact on how the system behaves. Finally, to further comprehend the model’s dynamical behavior and validate the discovered analytical conclusions, numerical simulation has been used.

This paper uses an augmented Lagrangian method based on an inexact exponential penalty function to solve constrained multiobjective optimization problems. Two algorithms have been proposed in this study. The first algorithm uses a projected gradient, while the second uses the steepest descent method. By these algorithms, we have been able to generate a set of nondominated points that approximate the Pareto optimal solutions of the initial problem. Some proofs of theoretical convergence are also proposed for two different criteria for the set of generated stationary Pareto points. In addition, we compared our method with the NSGA-II and augmented the Lagrangian cone method on some test problems from the literature. A numerical analysis of the obtained solutions indicates that our method is competitive with regard to the test problems used for the comparison.

Giardiasis is among the ignored zoonotic illnesses accorded by the World Health Organization that is caused by Giardia duodenalis. The disease is ignored regardless of the harm it causes to people and other creatures. In this paper, a mathematical model for giardiasis illness transmission is formed, which considers sickness carriers and control measures such as screening, treatment, and sanitation of the environment around people. In the assessment, the basic reproduction number, R0, which is used for analyzing the local stability of the equilibria is determined using the state-of-the-art next-generation matrix, while the Metzler constancy speculation is used to show the overall adequacy of the global stability of the equilibrium point free from the disease. In addition, a Lyapunov function has been used to study the stability of the endemic equilibrium point. The assessment of parameters is performed to explore the limits that significantly influence the transmission components of the disease disorders using the normalizing sensitivity index method. The result revealed that the recruitment rate is the most sensitive limit to the reproduction number. The environment-human interaction parameter is the second influential factor in the transmission of giardiasis in the community. In the same manner, the outcomes recommend that carriers assume an expected part in the rate of giardiasis subsequently; disregarding them could risk endeavors to control the pestilence. Besides, the mathematical recreation of the model shows that a mix of each of the three interventions fundamentally affects the control of giardiasis. In this way, we advise implementing the strategies simultaneously in endemic areas to effectively stop the spread of the giardiasis disease in humans.

Automatic production system scheduling problem under a just-in-time environment is researched in this paper. The automatic production system is composed of many tanks and one robotic, the tank of the researched problem is responsible for processing the job, and the robotic moves the job from one tank to the other tank. The difference between the researched problem and the classic shop scheduling problem is that the former must consider job scheduling and the robotic move sequence, but the latter considers only job scheduling. For optimizing simultaneously job scheduling and robotic move sequence in the proposed problem and minimizing total earliness/tardiness, an improved NEH (Nawaz-Enscore-Ham) and variable search (INEH-VNS) algorithm are developed. In the proposed method, firstly, to obtain initial solution, an improved NEH is shown. Secondly, for computing value of the objective function, the double procedure method is constructed. Thirdly, according to the properties of the proposed problem, three neighborhood structures, adjacent exchange, random insertion, and job exchange, are investigated. To test the performance of the INEH-VNS, 100 instances are randomly generated. When the run time is the same, compared with CPLEX 12.5, the INEH-VNS algorithm can find high-quality approximate optimal solution, a special big scale. Compared with the G-VNS algorithm, the average improvement rate of the approximate optimal solution is 45.9%, and the average stability rate of the INEH-VNS algorithm enhances 75.04%. That is to say, the INEH-VNS algorithm is outstanding and more effective.

Graph theory (GT) is a mathematical field that involves the study of graphs or diagrams that contain points and lines to represent the representation of mathematical truth in a diagrammatic format. From simple graphs, complex network architectures can be built using graph operations. Topological indices (TI) are graph invariants that correlate the physicochemical and interesting properties of different graphs. TI deal with many properties of molecular structure as well. It is important to compute the TI of complex structures. The corona product (CP) of two graphs G and H gives us a new graph obtained by taking one copy of G and VG copies of H and joining the ith vertex of G to every vertex in the ith copy of H. In this paper, based on various CP graphs composed of paths, cycles, and complete graphs, the geometric index (GA) and atom bond connectivity (ABC) index are investigated. Particularly, we discussed the corona products Ps⨀Pt, Ct⨀Cs, Kt⊙Ks, Kt⊙Ps, and Ps⊙Kt and GA and ABC index. Moreover, a few molecular graphs and physicochemical features may be predicted by considering relevant mathematical findings supported by proofs.

This paper investigates the dynamics of systemic risk in banking networks by analyzing equilibrium points and stability conditions. The focus is on a model that incorporates interactions among distressed and undistressed banks. The equilibrium points are determined by solving a reduced system of equations, considering both homogeneous and heterogeneous scenarios. Local and global stability analyses reveal conditions under which equilibrium points are stable or unstable. Numerical simulations further illustrate the dynamics of systemic risk, while the theoretical findings offer insights into the behavior of distressed banks under varying conditions. Overall, the model enhances our understanding of systemic financial risk and offers valuable insights for risk management and policymaking in the banking sector.

The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation xn+1=αxnxn−1xn−2/βxn−12+γxn−22, where the initial conditions x−2,x−1,x0 are nonzero real numbers and α,β,γ are positive constants such that α≤β+γ. Visual examples supporting solutions are given at the end of the study. The figures are found with the help of MATLAB.

Image restoration is an interesting ill-posed problem. It plays a critical role in the concept of image processing. We are looking for an image that is as near to the original as possible among images that have been skewed by Gaussian and additive noise. Image deconstruction is a technique for restoring a noisy image after it has been captured. The numerical results achieved by the prox-penalty method and the split Bregman algorithm for anisotropic and isotropic TV denoising problems in terms of image quality, convergence, and signal noise rate (SNR) are compared in this paper. It should be mentioned that isotropic TV denoising is faster than anisotropic. Experimental results indicate that the prox algorithm produces the best high-quality output (clean, not smooth, and textures are preserved). In particular, we obtained (21.4, 21) the SNR of the denoising image by the prox for sigma 0.08 and 0.501, such as we obtained (10.0884, 10.1155) the SNR of the denoising image by the anisotropic TV and the isotropic TV for sigma 0.08 and (-1.4635, -1.4733) for sigma 0.501.

Coffee berry disease (CBD) is a fungal disease caused by Colletotrichum kahawae. CBD is a major constraint to coffee production to Kenya and Africa at large. In this research paper, we formulate a mathematical model of the dynamics of the coffee berry disease. The model consists of coffee plant population in a plantation and Colletotrichum kahawae pathogen population. We derived the basic reproduction number Rk0, and analyzed the dynamical behaviors of both disease-free equilibrium and endemic equilibrium by the theory of ordinary differential equations. Using the MATLAB ode45 solver, we carried out numerical simulation, and the findings are consistent with the theoretical results.

A picture in a group presentation is a geometric configuration with an arrangement of discs and arcs within a boundary disc. The drawing of this picture does not have to follow a particular rule, only using the generator as discs and the relation as arcs. It will form a picture label pattern if drawn with a particular rule. This paper discusses the label pattern of a picture in the presentation of direct product groups. Direct product presentation is used with two cyclic groups, ℤp and ℤq where p,q∈ℤ+ and p,q≥2. The method for forming a picture label pattern is to arrange the first generator in the initial arrangement, compile a second generator, and add a number of commutators. Furthermore, the pattern is used to calculate the length of the label on the picture. It is obtained that the picture’s label is aq−1bnabq−n and the length of the label is p+2n−q, where n is the number of commutator discs.

The purpose of this paper is to investigate the valuation of equity-linked death benefit contracts and the multiple life insurance on two heads based on a joint survival model. Using the exponential Wiener process assumption for the stock price process and a Kn distribution for the time until death, we provide explicit formulas for the expectation of the discounted payment of the guaranteed minimum death benefit products, and we derive closed expressions for some options and numerical illustrations. We investigate multiple life insurance based on a joint survival using the bivariate Sarmanov distribution with Kn (i.e., the Laplace transform of their density function is a ratio of two polynomials of degree at most) marginal distributions. We present analytical results of the joint-life status.

This paper is mainly concerned with the existence of mild solutions and exact controllability for a class of fractional semilinear system of order q∈1,2 with instantaneous and noninstantaneous impulses. First, combining the Kuratowski measure of noncompactness and the Mönch fixed point theorem, we investigated the existence result for the considered system. It is remarkable that our assumptions for impulses and the nonlinear term are weaker than the Lipschitz conditions. Next, on this basis, the exact controllability for the considered system is determined. In the end, an example is provided to support the main findings.

The novel coronavirus is a recently discovered member of one of the largest families of viruses with symptoms ranging from a simple cold to excruciating respiratory agony. In the present paper, a deterministic mathematical model is formulated to estimate the transmission dynamics of COVID-19 with the inclusion of control strategies like (i) double-dose vaccination, (ii) prevention, and (iii) treatment. In addition, instead of considering all infectious humans as one unit, we separate them into symptomatic and asymptomatic groups, and the impact is analyzed. This separation is meaningful because various reports indicate that the asymptomatic cases will spread the disease more than the symptomatic cases. The model is proved to be mathematically well-posed and biologically meaningful by showing positivity and boundedness of the solution using the appropriate initial conditions. For the reproduction number, a parametric formula is constructed, and also the associated numerical value is calculated from the reported real data in Ethiopia. Moreover, disease-free and endemic equilibria are determined, and their local and global stabilities are discussed using the Lyapunov function technique. These equilibria are found to be locally asymptotically stable if R01, respectively. Following the model fitting and estimation of the parameter values, sensitivity analysis was performed in order to analyze the impact of each parameter on transmission dynamics. In other words, this study can be used to evaluate how major model parameters affect transmission dynamics and control. Utilizing Pontryagin’s maximal principle, the best control measures are implemented with the aim of lowering the burdens associated with infection, prevention, and treatment. To comprehend and visualize the impact of control techniques on the development of the disease and to illustrate the analytical findings generated in this study, numerical simulation studies are conducted. Finally, the output of the study illustrates that adhering to all the control strategies has a big impact on minimizing the transmission of the disease in society. Which means that if the control strategies are well managed by the concerned body, then the burden of the disease is reduced quickly in the Ethiopian population.

Lung cancer is the biggest cause of cancer mortality worldwide and a major impediment to extending life expectancy. In comparison to other cancers, it has a relatively poor survival rate. In this paper, we have developed a mathematical model for lung cancer based on biological phenomena using nonlinear ordinary differential equations and analyzed it both analytically and numerically. According to the findings, CD8+ T cells and dendritic cells have a role in tumor cell variety. Surgery and chemotherapy have been used as treatment options, and we have observed that three doses of chemotherapy after surgery had the greatest results after examining several treatment options. During the treatment period, the cycle of each chemotherapy has been taken every 4 weeks, and the first dose has been taken after 28 days of surgery. Finally, we have evaluated the various starting dates for the best treatment choice and discovered that the patient who begins treatment sooner has a better probability of surviving.

This paper provides asymptotic expansions for large values of n of tangent Tnμz and Apostol-tangent Tnμz;λ polynomials of complex order. The derivation is done using contour integration with the contour avoiding branch cuts.

Deep learning with specific network topologies has been successfully applied in many fields. However, what is primarily called into question by people is its lack of theoretical foundation investigations, especially for structured neural networks. This paper theoretically studies the multichannel deep convolutional neural networks equipped with the downsampling operator, which is frequently used in applications. The results show that the proposed networks have outstanding approximation and generalization ability of functions from ridge class and Sobolev space. Not only does it answer an open and crucial question of why multichannel deep convolutional neural networks are universal in learning theory, but it also reveals the convergence rates.

In this study, the steady hydromagnetic flow of two immiscible couple stress fluids through a uniform porous medium in a cylindrical pipe with slip effect is investigated analytically. Essentially, the flow system is divided into two regions, region I and region II, which occupy the core and periphery of the system, respectively. The flow is driven by a constant pressure gradient applied in a direction parallel to the cylinder’s axis, and an external uniform magnetic field is applied in the direction perpendicular to the direction of fluid motion. Instead of the classical no-slip condition, the slip velocity along with vanishing couple stress boundary conditions is taken on the surface of the rigid cylinder, and continuity conditions of velocity, vorticity, shear stress, and couple stress are imposed at the fluid-fluid interface. The governing equations are modeled using the fully developed flow conditions. The resulting differential equations governing the flow in the two regions are converted to nondimensional forms using appropriate dimensionless variables. The nondimensional equations are solved analytically, and closed-form expressions for the flow velocity, flow rate, and stresses are derived in terms of the Bessel functions. The impacts of several parameters pertaining to the flow such as the magnetic number, couple stress parameters, Darcy number, viscosity ratio, Reynolds number, and slip parameter on the velocities in respective regions are examined and illustrated through graphs. The flow rate’s numerical values are also calculated for different fluid parameters and displayed in tabular form. It is found that increasing the magnetic number, viscosity ratio, Reynolds number, and slip parameters decreases the velocities of the fluids whereas increasing the couple stress parameter, Darcy number, and pressure gradient increases fluid velocities. The results obtained in this paper show an excellent agreement with the already existing results in the literature as limiting cases.

In this paper, we consider a multivariate statistical model of accident frequencies having a variable number of parameters and whose parameters are dependent and subject to box constraints and linear equality constraints. We design a minorization-maximization (MM) algorithm and an accelerated MM algorithm to compute the maximum likelihood estimates of the parameters. We illustrate, through simulations, the performance of our proposed MM algorithm and its accelerated version by comparing them to Newton-Raphson (NR) and quasi-Newton algorithms. The results suggest that the MM algorithm and its accelerated version are better in terms of convergence proportion and, as the number of parameters increases, they are also better in terms of computation time.

In this paper, we introduce a new generalized inverse, called the G-MPCEP inverse of a complex matrix. We investigate some characterizations, representations, and properties of this new inverse. Cramer’s rule for the solution of a singular equation Ax=B is also presented. Moreover, the determinantal representations for the G-MPCEP inverse are studied. Finally, the G-MPCEP inverse being used in solving appropriate systems of linear equations is established.

The objective of this paper is to study the antidamage ability of beam column joints in complex steel structures under external forces and to improve the safety of such structures. In this study, a three-dimensional model of complex steel structure based on BIM technology is proposed by analyzing and calculating the ultimate strength of complex steel structure for mine protection. The vibration control algorithm of complex steel structure for mine protection is designed, and the boundary elastic constraint conditions are determined. According to the constraint conditions, the vibration characteristics of complex steel structures for mining are analyzed. The experimental results show that the maximum displacement of the design model is reduced by half compared with that before optimization, which can meet the design requirements.

Crime is one among the most challenging problems in most developing countries in which unemployment is among the causes. Not all kind of crimes can be eradicated indeed; this paper is intended to contribute on eradication of unemployment-related crimes in the developing countries by proposing a deterministic mathematical model of unemployment-crime dynamics including vocational training and employment as control measures for crime. The study adopts the epidemiological model concepts on model formulation and model analysis while considering unemployment as main driver of crime. The basic properties of the model are analyzed, and well-posed of the model is established by using the Lipschitz condition. The next-generation matrix is used to obtain the criminal reproduction number which help to derive the conditions for local and global stability of the model. Moreover, the existence of backward and forward bifurcation when the crime reproduction number is equal to one was analyzed by center manifold theory. Simulations of the model are carried out to validate the theoretical part of the model and demonstrate vocational training, and employment strategies are more effective in combating crime when applied simultaneously. The findings suggest that unemployment problem should be addressed in order to reduce the number of unemployed individuals in joining the criminal activities.

In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcation by using normal form theory and center manifold theorem are identified. Additionally, using numerical simulations and a hypothetical dataset, various dynamic characteristics are discovered, including stability switches, chaos, and Hopf bifurcation scenarios.

This paper deals with the solution of a third kind mixed integro-differential equation (MIDE) in displacement type in space L2−1,1×C0,T,T

Mathematical models have been widely used to explain the system originating from human-nature interaction, investigate the impacts of various components, and forecast system behaviour. This paper provides a profound reference to the current state of the art regarding the application of mathematical models to study the impact of human population and population pressure on forest biomass and forest-dependent wildlife. The review focused on two aspects, namely, model formulation and model analysis. In model formulation, the review revealed that socioeconomic status influences forest resource consumption patterns, thus, stratification of the human population based on economic status is a critical phenomenon in modelling human-nature interactions; however, this component has not been featured in the reviewed models. Regarding model analysis, in most of the reviewed work, single parameter approach was utilized to perform uncertainty quantification of the model parameter; this approach has been proven to be inadequate in measuring the uncertainty and sensitivity of the parameter. Thus, the use of correlation or variance based methods, which are multidimensional parameter space methods are of significant importance. Generally, despite the limitations of many assumptions in mathematical modelling, it is revealed that mathematical models demonstrate the ability to handle complex systems originating from interactions between humans and nature.