Contemporary Mathematics

Idealization of a Semigroup by Using Bruck-Reilly Monoids

2023-07-12T16:37:40+08:00

The aim of this paper is to create a new semigroup by defining a special idealization operation on semigroups. Additionally, by considering amalgamation, we will present novel distinguishing results on idealization over semigroups. Initially, we will combine the definitions of idealization and the Bruck-Reilly extension. Consequently, by integrating these two structures, we will provide a significant result on idealization in semigroups that will be crucial for future studies. Finally, we will conclude by discussing the ideal extension for the new semigroup structure, namely idealization.

A Comprehensive Flood Risk Inundation Mapping and Hybrid Model for Flood Forecasting in the Panam River Basin

2023-10-27T15:00:21+08:00

The forecasting of flooding plays a pivotal role in the field of hydrology and serves as an essential measure for preventing any possible flood damage. This study presents an analysis of the utilization of an Adaptive Neuro-Fuzzy Inference System (ANFIS) to prevent floods in river basins. ANFIS represents a hybrid approach that combines elements of neural networks and fuzzy logic methodologies for the purpose of analyzing and comparing input and output data. Performance evaluation of ANFIS is based on the ratio of Discrepancy Ratio (D) along with the determination coefficient (R²), Coefficient of correlation (R), and Root Mean Square Error (RMSE). Results: The best ANFIS model was the one that gave the best results during training. The RMSE was 622.43, with a correlation coefficient of 0.93 and an R² of 0.86. Nevertheless, its validation performance demonstrated slightly elevated RMSE figures and lower correlation and R² values, with RMSE at 2847.99, R at 0.91, and R² at 0.83. An Artificial Neural Network (ANN) model with three transfer functions (SIGMOID, HYPERBOLIC TANGENT, and LINEAR) is developed and evaluated based on R = correlation and MSE = mean squared error. Furthermore, the study also entails the development of a flood model for the research area, consisting of 38 cross profiles for a detailed analysis of the river’s profile and flood inundation. This analysis aims to provide precise recommendations for flood protection measures.

Fixed Point Results in Generalized Bi-2-metric Spaces Using θ-Type Contractions

2023-11-16T10:54:30+08:00

The main purpose of this manuscript is to provide a generalization of the concept of a 2-metric and prove some fixed point results for θ-type contractions. In this paper, we proved that a mapping T that is orbitally continuous, satisfying a θ-type contraction as a result of a relation between a pair of generalized 2-metrics and if one of the spaces is T-orbitally complete, then the mapping T has a fixed point.

Analysis of Humoral Immunity SARS-CoV-2 Infection Model with ACE2 Receptor and Latent Phase

2024-01-12T15:56:02+08:00

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is RNA virus which causes the coronavirus disease 2019 (COVID-19). SARS-CoV-2 infects the epithelial (target) cells by binding its spike protein, S, to the Angiotensin-Converting Enzyme 2 (ACE2) receptor on the surface of epithelial cells. ACE2 is an essential mediating factor in the SARS-CoV-2 infection pathway. In this study, we build a mathematical model for characterizing the dynamics of SARS-CoV-2 within the host while taking into account the impact of humoral immunity and the function of the ACE2 receptor. We incorporate the cells that are latently infected into the model. We consider three distributed delays: (i) delay in development of latently infected epithelial cells, (ii) delay in the latently infected epithelium cells’ activation, and (iii) delay in the maturation of recently released SARS-CoV-2 virions. We first address the fundamental properties of the delayed system, then find all possible equilibria. We demonstrate the existence and stability of the equilibria on the basis of two threshold parameters, namely basic reproduction number (ℜ₀) and humoral immune activation number (ℜ₁). By building appropriate Lyapunov functions and applying LaSalle’s invariance principle, we prove the global asymptotic stability for all equilibria. We do numerical simulations to demonstrate the theoretical conclusions. We do sensitivity analysis and determine the most vulnerable parameters. Discussion is had on how the dynamics of the SARS-CoV-2 are affected by ACE2 receptors, humoral immunity, latent phase and time delays. It is shown that vigorous activation of humoral immunity can suppress viral multiplication. We found that, ℜ₀ is influenced by the rates of ACE2 receptor growth and degradation, and this may offer valuable guidance for the creation of potential receptor-targeted vaccinations and medications. Further, it is shown that, increasing time delays can effectively decrease ℜ₀ and then inhibit the SARS-CoV-2 replication. Finally, we showed that, excluding the latently infected cells in the model would result in an overestimation of ℜ₀. Our findings may be useful in understanding the dynamics of SARS-CoV-2 infection in the host as well as in the development of novel therapies.

Inclusion Results on Hypergeometric Functions in a Class of Analytic Functions Associated with Linear Operators

2023-12-22T16:06:50+08:00

This study focuses on analyzing the inclusion properties of a certain subclass of analytic functions. This study examines the Hohlov integral transform, which is associated with the normalized Gaussian hypergeometric function, and the Komatu integral operator, which is associated with the generalized polylogarithm. The investigation utilizes Taylor coefficients to analyze these analytic functions. Various results are obtained for these operators for specific values of the parameters. The results presented here include several previously known results as their special cases.

Dominance of Fractional-Order Derivatives in the Transmission of the Chlamydia Disease Model

2023-02-11T17:30:07+08:00

In this article, we study a mathematical model of the chlamydia infection caused by sexual contact. To analyze this model, we combine the homotopy perturbation Laplace transform technique with the fractional order formulation in the Caputo sense. This article illustrates the increased degree of freedom that fractional derivative models allow to investigate disease dynamics for a given data set and to highlight memory effects. The existence, singularity, and consistency of the problem are also examined in the research. The unique parameter estimation for each value of the noninteger order makes this study more useful.

Highly Dispersive Optical Gap Solitons with Kundu-Eckhaus Equation Having Multiplicative White Noise

2024-02-04T11:56:51+08:00

This paper explores the dynamics of highly dispersive gap solitons within the framework of the Kundu-Eckhaus equation, augmented by the inclusion of multiplicative white noise in the Itô sense, a novel addition to the model. Two integration schemes, the extended simplest equation approach and the generalized Riccati equation mapping scheme, are employed to analyze and integrate the model. Despite yielding bright, singular, and dark-singular straddled solitons, both methods independently fail to capture dark optical solitons. Additionally, our investigation highlights that the influence of white noise predominantly affects the phase aspect of the solitons, with negligible impact on their amplitude. Further details regarding the specific physical system or optical medium under study would provide readers with context, aiding in the comprehension of the significance of our findings.

MHD Stagnation Point Radiative Flow of Hybrid Casson Nanofluid across a Stretching Surface

2023-07-10T16:57:56+08:00

This paper aims to investigate the hybrid stagnancy point in casson nanofluid on a transient elongation plane in accordance with impact of thermal heat. Resistive heating effect also considered in this study. Nano particles of assumed Cu and Al are utilized. Hence derived partial differential equations are broken down into nonlinear differential equations using suitable Transformations. Then succeeding results are worked out by employing Bvp4c Method. The obtained values for the analysis are indicated by indicating velocity and temperature graphs for distinct constants like radiation constant (Rd), Casson constant (β), magnetic variable (M), Prandtl constant (Pr), unsteady parameter (s). As well, the confined parameter, coefficient of skin friction is analysed. For continuing estimates of Casson parameter speed of liquid flow will be lessen. On intensifying Prandtl number of liquid shrink gradually. It is observed that for rapidly rised values of both Nano molecules velocity of the liquid lessens whereas reverse tendency is identified for temperature profile. Utilisation of hybrid nanoflows has a benifit of heat convertion improvement. The outcomes of current investigation are liquid is better within the congruence with comparision of subsist work.

An Imperfect Production Inventory Model for Instantaneous Deteriorating Items with Preservation Investment Under Inflation on Time Value of Money

2023-11-17T09:58:24+08:00

Effective inventory management is crucial for businesses dealing with deteriorating items, where demand is influenced not only by traditional factors but also dependent on the selling price. This research paper proposes a comprehensive inventory model that considers the dynamic nature of demand for deteriorating items and incorporates the impact of inflation on the time value of money, all within the context of an imperfect production and screening process. To reduce the waste of products, the proposed model uses a rework process to convert imperfect items into perfect ones. Additionally, this study incorporates preservation technology investment to alleviate the rate of deterioration under partially backlogged shortages. The incorporation of an imperfect production process further enhances the model’s practical applicability by addressing real-world scenarios where production may not always be flawless. The study employs mathematical modeling and optimization techniques to derive optimal ordering policies that balance the conflicting objectives of minimizing costs. To validate the model, numerical analysis has been performed, and the convexity of the total cost function has been shown graphically and analytically using MATHEMATICA software. Sensitivity analyses are conducted to assess the robustness of the proposed model under varying parameters, providing valuable insights for decision-makers.

Topological Indices and Properties of the Prime Ideal Graph of a Commutative Ring and its Line Graph

2023-10-13T16:12:31+08:00

Let R be a commutative ring with identity, and P be a prime ideal of R. The prime ideal graph, denoted by Γ_p, is the graph where the set of vertices is R/{0} and two vertices are joined by an edge if their product belongs to P. This paper will discuss topological indices and some properties of the prime ideal graph of a commutative ring and its line graph. Topological indices, such as the Wiener, first Zagreb, second Zagreb, Harary, Gutman, Schultz, and Harmonic indices, are related to the degree of vertices and the diameter of the graphs. In this paper, we also discuss the independence and domination numbers of the line graph.

Solution of the Space Fractional Diffusion Equation Using Quadratic B-Splines and Collocation on Finite Elements

2023-11-23T14:18:15+08:00

In this paper, we consider the solution of the space fractional diffusion equation using orthogonal collocation on finite elements (OCFE) with quadratic B-spline basis functions. The main advantage of quadratic B-splines is that they have good interpolating properties and can be easily adapted for solving problems on non-uniform grids. The method is unconditionally stable and its convergence is also discussed. It is of order (3 − α) for 1 < α < 2. We present various linear and nonlinear examples. The solutions compared favourably with previous results in the literature.

On Linearization Coefficients of Shifted Jacobi Polynomials

2024-02-01T10:47:33+08:00

Generalized Caputo Fractional Proportional Differential Equations and Inclusion Involving Slit-Strips and Riemann-Stieltjes Integral Boundary Conditions

2024-01-18T10:00:23+08:00

The main purpose of this study is to investigate the existence and uniqueness of solutions to a nonlocal boundary value problem. This newly defined class involves nonlinear fractional differential equations of general proportional fractional derivative and integral with respect to another function. Additionally, the inclusion case results associated to our problem are discussed. Our analysis relies on fixed point theorems and fractional calculus techniques. By giving examples, the obtained results are clearly illustrated.

Fuzzy Metric Spaces: Optimizing Coincidence and Proximity Points

2023-04-17T14:12:10+08:00

Our manuscript puts forward two novel fuzzy proximal contractive conditions. First, we present two variants of fuzzy α-proximal quasi-H-contractions and establish optimal coincidence point outcomes for these contractions in fuzzy metric space. This manuscript’s second part proposes the fuzzy ψ-contraction for a multivalued mapping equipped with fuzzy weak P-property and achieves the best proximity point outcome in strong fuzzy metric space. The findings of this study broaden and generalize some existing research results.

Extraction of Solitons in Optical Fibers for the (2+1)-Dimensional Perturbed Nonlinear Schrödinger Equation Via the Improved Modified Extended Tanh Function Technique

2024-01-31T14:24:38+08:00

The presented research investigates the (2+1)-dimensional perturbed nonlinear Schrödinger model. This model takes into account various effects such as fourth order dispersion, intermodal dispersion, nonlinear dispersion, group velocity dispersion, Kerr nonlinearity and self steepening effects. This model simulates the estimation of optical solitons and a variety of broadcasting networks’ transmission in nonlinear fiber optics. The proposed model is studied using the improved modified extended tanh function technique. For the proposed model, several solitons and other solutions are generated. These solutions including {bright, dark and singular} solitons, singular periodic and Jacobi elliptic solutions. By introducing the two- and three-dimensional graphs, the physical behavior of the retrieved solutions is displayed.

Hyperbolic 3-manifolds with Boundary Which are Side-pairings of Two Tetrahedra as Exteriors of Knotted Graphs in the 3-sphere

2023-06-25T10:46:40+08:00

In this paper, we give a generalization of Ivanšić’s method for hyperbolic 3-manifolds without boundary, which allows us to recognize if a hyperbolic 3-manifold with totally geodesic boundary, given by an isometric side-pairing of two hyperbolic truncated tetrahedra, is the exterior of a knotted graph; i.e., it is the complement of a 1-manifold with isolated singularities embedded in S³, in which case we get the corresponding diagram of the knotted isotopy class of its boundary. Otherwise, we obtain that the corresponding 3-manifold with boundary is the exterior of a knotted graph embedded in some lens space. Finally, we apply this method to a noncompact 3-manifold with a totally geodesic surface boundary of genus 2.

Two Indicators of Cross-Correlation for the Functions from Z_qⁿ to Z_2q

2023-09-12T10:23:42+08:00

Boolean functions play an important role in the design of secure cryptosystems and code division multiple access (CDMA) communication. Several possible generalizations of Boolean functions have been obtained in recent years. In this paper, we analyze the properties of functions from Z_qⁿ to Z₂_q in terms of their Walsh-Hadamard transform (WHT). We provide a relationship between cross-correlation and the WHT of these functions. Also, we present a necessary and sufficient condition for the functions to have complementary autocorrelation. The Parseval’s identity for the current setup of these functions is obtained. Further, we obtained the modulus indicator (MI) and the sum-ofsquares-modulus indicator (SSMI) of cross-correlation among two functions for the current setup.

The Relationship between Model Spaces and Invariant Subspaces of the Unilateral Shift Operator

2023-12-19T14:54:55+08:00

Application of Clifford Algebra on Group Theory

2023-12-13T17:29:33+08:00

The orthogonal operators defined as similarity transformations on Euclidean space E can also be considered as group actions on the Clifford Algebra. In this paper, we investigate the finite subgroup of Euclidian space E of Geometric Algebra over a finite dimension vector space E. The hierarchy of the finite subgroups of Clifford Algebra C(E) is depicted through the lattice structure and we discussed the group action of these subgroups on the vector space E. Further, we shall address the number of non-trivial finite subgroups, Normal subgroups, and subnormal series of the subgroup of Clifford Algebra C(E) constructed over the vector space E by performing group action over the subgroup of Clifford Algebra C(E).

Fast Two-Grid Finite Element Algorithm for a Fractional Klein- Gordon Equation

2023-12-18T11:01:07+08:00

In this article, we propose a spatial two-grid finite element algorithm combined with a shifted convolution quadrature (SCQ) formula for solving the fractional Klein-Gordon equation. The time direction at t_{n − θ} is approximated utilizing a second-order SCQ formula, where θ is an arbitrary constant. The spatial discretization is performed using a two-grid finite element method involving three steps: calculating the numerical solution by solving a nonlinear system iteratively on the coarse grid, obtaining the interpolation solution based on the computed solutions in the first step, and solving a linear finite element system on the fine grid. We present a numerical algorithm, validate the two-grid finite element method’s effectiveness, and demonstrate the computational efficiency for our method by the comparison of the computing results between the two-grid finite element method and the standard finite element method.

Artificial Intelligence Solution for Relaxation Oscillation Equation

2023-03-23T19:22:10+08:00

In this paper Artificial Intelligence Solution is given for Relaxation Oscillation Equation, which is one of the simplest Fractional Differential Equation.Artificial Intelligence solution has been identified as the best one for fractional differential equation. Sample for patterns of fractional different equation are extracted. The better performance of Machine Learning Models is compared with the Numerical solution of Successive Approximation Method and reported.

Co-Secure Domination in Zero-Divisor Graphs Γ(Z_n)

2024-03-01T10:59:52+08:00

Analyzing Observability of Fractional Dynamical Systems Employing ψ-Caputo Fractional Derivative

2023-08-03T12:01:18+08:00

In this present article, we inquire into the observability of linear and nonlinear fractional dynamical systems in terms of ψ-Caputo fractional derivative. The observability Grammian matrix, which is positive definite and expressed by the Mittag-Leffler functions, is used to obtain the necessary and sufficient conditions of observability of linear fractional dynamical systems, and Banach’s fixed point theorem is used to get the sufficient conditions for the observability of nonlinear fractional systems. Three numerical examples are given to demonstrate the applicability of theoretical results for linear and nonlinear cases.

Algorithm Optimizer in GA-LSTM for Stock Price Forecasting

2023-09-06T11:29:48+08:00

The training and success of deep learning is strongly influenced by the selection of hyperparameters. This research uses a hybrid method between the Genetic Algorithm (GA) and Long Short-Term Memory (LSTM) to find a suitable model for predicting stock prices. GAis used to optimize the architecture, such as the number of epochs, window size, and LSTM units in the hidden layer. Tuning optimizer is also carried out using several optimizers to achieve the best value. The method that has been applied shows that the method has a good level of accuracy with MAPE values below 10% in every optimizer used. A fairly stable and small value is generated by setting it using the Adam Optimizer.

A Dual Deflation Method for the Computation of Eigenmodes of Positive Definite Matrices

2023-12-06T11:29:17+08:00

In this paper we advocate a new method to compute the eigenmodes of real symmetric positive definite matrices. Our method involves the zeros of a quartic polynomial, shifted inverse iteration and deflation of two eigenmodes simultaneously.

Analyze the Eigenvalues of a Neutral Delay Differential Equation by Employing the Generalized Lambert W Function

2024-01-15T16:20:55+08:00

In this paper the authors discuss a class of differential equations known as neutral delay differential equations (NDDEs) in which the delay occurs in the derivative with the highest order. They are encountered in various fields of applied sciences and are essential for mathematically representing real-world phenomena. It was challenging to discover approximate analytical solutions for certain methods. In this study, the researchers utilized the generalized Lambert W function to derive the characteristic roots for a first-order neutral delay differential equation featuring random delays. Numerical examples were then utilized to validate the obtained results.

A New Model Making the Transition From Oil to Solar Energy

2024-01-08T15:37:51+08:00

Today, the use of renewable energy sources such as sun, wind and hot water to generate electricity is increasingly becoming a global priority. In this paper, we propose a deterministic dynamical system reporting the transition from oil to solar energy, in which we then add the randomness of this phenomenon. First, we study the positivity of the deterministic oil-solar model and show that there is a maximum solution of the deterministic model and that the system is controllable at any time T > 0 from an initial point. We also prove the existence of an equilibrium state, study its nature and prove that there is no limit cycle between the quantity of oil available and the solar production capacity installed. Secondly, we formulate the stochastic solar energy model from the deterministic model, for which we proved the existence of a unique solution. Finally, using a model extracted from the model performed and examining the transition from the amount of available oil to the installed solar generation capacity, we associate a linear optimal control problem, from which we prove that the optimal control components are of bang-bang type, and we characterize them.

An Efficient Technique to Study Time Fractional Extended Fisher-Kolmogorov Equation

2023-03-25T16:51:51+08:00

Reaction-diffusion partial differential equations are among the most widely used equations in applied mathematical modelling. In this study, we examine the solutions of one such equation, namely, the time-fractional extended Fisher-Kolmogorov equation. This equation is widely used in the study of population growth and wave propagation dynamics. The technique we consider is a combination of the natural transform and the Adomian decomposition method. Fractional derivatives are considered with singular and non-singular kernels. The existence and uniqueness of the solutions are presented. We analyse two different cases of the proposed problem to determine the validity and efficacy of the proposed scheme. Additionally, numerical simulation is shown, and the nature of the achieved solution is captured in terms of plots for various fractional orders. The outcome demonstrates that the method is straightforward, efficient, and dependable. The proposed method does not require any predetermined assumptions, linearization, perturbation, or discretization, and it prevents rounding errors. Therefore, the technique is ready to be implemented for a variety of nonlinear time fractional partial differential equations.

Optical Solitons with Dispersive Concatenation Model Having Multiplicative White Noise by the Enhanced Direct Algebraic Method

2024-02-22T15:10:34+08:00

This paper investigates the significance of the dispersive concatenation model, incorporating the Kerr law of self-phase modulation in the presence of white noise. Our methodology relies on the enhanced direct algebraic method for integration. We reveal that intermediate solutions are expressed in terms of Jacobi's elliptic functions, leading to soliton solutions as the modulus of ellipticity approaches unity. This discovery culminates in the emergence of a diverse range of optical solitons. Our findings contribute novelty to the existing literature by offering insights into the behavior of optical solitons within the dispersive concatenation model, presenting a significant advancement in understanding this complex phenomenon.

CSO-based Efficient Resource Management for Sustainable Cloud Computing

2023-04-25T19:41:49+08:00

The pervasive need for cloud-hosted application services has resulted from the widespread use of cloud data centers. Not only that, but there has been a dramatic increase in the resource demands of current applications, especially in data-intensive businesses. This has resulted in an increase in the number of cloud servers made available, which has increased energy usage and prompted environmental concerns. Only partially do the difficulties of scalability and adaptability in cloud resource management get addressed by conventional heuristics and reinforcement learning-based techniques. Many existing works overlook the interdependencies between host temperature, task resource usage, and scheduling decisions. Especially in contexts with fluctuating resource demands, this results in poor scalability and an upsurge in computing resource requirements. The study recommended a holistic resource management strategy based on resource scheduling for enduring cloud computing as a solution to these restrictions. Energy, thermal, and cooling models are all taken into account in the proposed model, which expresses the optimization of data center energy efficiency as a multi-objective scheduling issue. To generate optimal scheduling decisions and approximate the quality of service (QoS) for a given system state, the model employs cat-based swarm optimization as a surrogate model. Using the China Ocean Shipping Company (COSCO) framework, we conducted experiments that demonstrate cloud service orchestrator (CSO)’s superior performance compared to state-of-the-art baselines in terms of energy ingesting, makespan, and execution overhead in both simulated and real-world cloud environments.

Research on Green Production Factors by OFDI Along the Belt and Road Initiative

2024-04-07T16:47:28+08:00

To analyze the role of the Belt and Road Initiative in China’s OFDI by applying a double-difference model. To determine the accuracy of the model, using the skewed distribution matching method, and to determine the effect of OFDI in China’s coastal areas through practical tests. This paper adopts the DEA’s SBM model to study China’s green total factor productivity in 31 provinces; it evaluates China’s outward foreign direct investment (OFDI) through the use of three key indicators, including the currencies of the inflow countries, the currencies of the inward total, and exchange rate changes. The research in this paper considers various factors under the Belt and Road Initiative, including OFDI flows, reserves, and net flows. After an in-depth study, it is found that the Belt and Road policy significantly improves the mobility and sustainability of OFDI in the regions along the Belt and Road. This study may provide new perspectives for understanding the economic and social development patterns of provinces along the Belt and Road Initiative. Dissecting the complexity of regional development through the use of a "double split model" helps to recognize the different impacts of international projects on the local economy, and uniquely accounts for both spatial (geographic) and temporal (over time) variations in development, providing a robust framework for similar studies in other contexts.

Internally Disclosed Sets of a Real Space

2023-11-10T09:39:39+08:00

There is no single set in a real space, for which an exact mathematical definition would not exist by the mathematical symmetry laws. We discuss a theory in which a real number axis is defined at the new level, namely, at the level of real space allowing one to formulate and prove the theorem on the basis of its internal disclosure. This new theory of a set makes it possible to introduce a notion of the full compactness of sets of a real space, confirming their availability in the defined symmetry of elements of a definitely symmetrical line.

Some Orthogonal Combinations of Legendre Polynomials

2023-09-26T10:46:15+08:00

The principle objective of this article is to introduce and investigate a type of orthogonal polynomials that are written as combinations of Legendre polynomials. This kind of polynomials can be viewed as generalized Jacobi polynomials (GJPs), since they are written in terms of Jacobi polynomials (JPs) with certain negative parameters. The analytic and inversion formulas of these polynomials are established. New derivative expressions for these polynomials are derived in detail in terms of their original polynomials. Other derivative expressions for these polynomials are found but in terms of some orthogonal and non-orthogonal polynomials. Some product formulas with some other polynomials are also obtained. Certain definite and weighted definite integrals are obtained using the newly introduced connection and product formulas.

Dynamics of HIV-1 and HTLV-1 Coinfection with both CTL and Antibody Responses

2023-11-28T10:17:52+08:00

Human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type 1 (HTLV-1) coinfection models with simply an antibody response or a CTL response have been the subject of several recent investigations. Thus, the primary objective of this paper is to formulate and examine a mathematical framework for analyzing the intricate dynamics of coinfection between HIV-1 and HTLV-1. The model takes into account the role of antibody response against free HIV-1 particles and CTL response against HTLV-1-infected cells. We prove that the model is well-posed and it admits eight equilibria. The stability and existence of the equilibria are precisely controlled by eight threshold parameters ℜ_i, i = 1, 2, ..., 8. By formulating suitable Lyapunov functions and applying LaSalle's invariance principle, we show the global asymptotic stability for all equilibria. To demonstrate the theoretical results, we conduct numerical simulations. We look at how the antibody and CTL responses affect the dynamical behavior of HIV-1/HTLV-1 coinfection. Although the parameters of antibody and CTL responses have no effect on the basic reproduction ratio of HIV-1 single-infection (ℜ₁) and HTLV-1 single-infection (ℜ₂), it has been demonstrated that viral coinfection can be inhibited by immunological activation of antibody and CTL responses. This could potentially facilitate the advancement of therapeutic approaches for HIV-1 and HTLV-1, which have the capability to enhance the HIV-1-specific antibody and HTLV-1-specific CTL reactions.

Enhanced Energy Transfer Performance in an Inclined Magneto-Convective Sutterby Ternary Hybrid Nanoflow: Application for Nano Diesel

2023-12-13T14:29:35+08:00

This study investigates sodium alginate-based nano-lubricants with added copper and aluminum oxides. The thermal performance of nano (Al₂O₃), hybrid (Al₂O₃ + CuO) and ternary (Al₂O₃ + CuO + TiO₂) nanofluids is studied and compared in this article. Due to the significant impact of higher stream rates, the ternary nanofluid is crucial in domains such as petroleum engineering. A Sutterby nanoflow model past a stretching sheet embedded in permeable media is considered. In this fluid, the effects of thermal radiation, hotness source/sink, inclined magneto-convection under Stefan blowing, and chemical reaction are assumed. The highest-order nonlinear partial differential equation is handled by utilizing the similarity function, producing a new set of ordinary differential equations. The derived equations are then quantitatively analyzed using the bvp4c approach in MATLAB.Graphical representations of several features for specific non-dimensional variables, including heat transfer, Sherwood, drag coefficient, velocity, temperature, and concentration, are presented. An increase in the thermal curve is observed due to the heat source/sink parameter; however, the Nusselt number exhibits the opposite pattern. The participation of Nb and the thermophoresis force led to greater thermal radiation. For Sc and Kr, the mass transfer ratio of the ternary nanofluid is lower. The results show very good congruence when compared to the literature. Our results also prove that the ternary hybrid nanofluid transfers more heat from the system than the hybrid or nanofluid. With an increase in Stefan blowing, the rate of energy and mass transfer rises, while the local skin friction coefficients show a tendency in the opposite direction.

Cryptographic Signature Scheme for Mobile Edge Computing Using DLFP Over Semiring

2023-12-29T08:44:04+08:00

The Undeniable Signature Scheme (USS) was first introduced by chaum and van in 1989. The advantage of the (USS) scheme is the signer’s co-operation during the verification process. In this paper, the Discrete Logarithm Problem with Factor Problem (DLFP) is introduced. It’s security and complexity is analyzed. Then, based on (DLFP), a key exchange protocol is given. An undeniable signature scheme based on DLFP over semiring is proposed along with illustration we have also given application of the proposed USS in Mobile Edge Computing (MEC). Then the proposed scheme’s security and complexity is examined.

Simulink Methods to Simulate COVID-19 Outbreak Using Fractional Order Models

2023-03-17T19:28:29+08:00

The objective of this work is to solve a coronavirus transmission model using Simulink, a platform for model-based design that facilitates simulation and design at the system level. The simulation is divided into two sections: the first deals with setting up the parameters, and the second deals with computing the fractional derivatives. The fundamental susceptible-infected-removed (SIR), susceptible-exposed-infected-recovered (SEIR), susceptible-exposed-infected-isolated-recovered (SEIQR), and susceptible-exposed-infected-asymptotically infected-recovered-reservoir (SEIARM) models were used in this study. An effective, quick, easy, and visually appealing method is used to simulate pandemic outbreaks. To accurately follow the progress of the infection, we contrast the simulation findings with those acquired by MATLAB code. The applications can be used for research projects and as a teaching tool.

Dynamic Path-Planning Approach of Garbage Cleanup Oriented Unmanned Ship Based on Simplified Flow Velocity Prediction

2024-02-28T16:43:07+08:00

Research on artificial intelligence and robotics for the ecological protection and restoration of waters has increased in importance with the promotion of national green sustainable development strategies. Autonomous Surface Vessel for Water Cleanup (ASV) research has not yet considered the uncertainty of water surface float positioning under complex current fluctuation factors. The result is that ASV has low accuracy in planning water surface float cleaning paths and its efficiency cannot meet the practical application requirements. To solve the above problems, this paper proposes a dynamic path-planning method architecture based on UAV flow velocity prediction for narrow and shallow water environments such as urban rivers and lakes. We have developed a fusion algorithm based on the progressive optimal rapid random search tree (RRT*) algorithm, DWA dynamic window method, and artificial potential field, and we have realized multi-objective water surface floating under uncertain water flow fluctuations. The location prediction of objects and optimum cleaning paths are carried out, and the method verification is carried out through numerical simulations and prototype experiments. Based on simulation and experimental results, the unmanned surface trash cleaning boat is capable of dynamically predicting trash floaters on the water surface under different water flow environments and generating an optimal cleaning path in real-time. It has certain advantages over existing planning methods in terms of accuracy and timeliness and holds significant practical significance.