Contemporary Mathematics

An extension of Nobel's multiplying factor method for solutions of dual and triple $q$-integral equations

Maryam Al-Towailb — 2024-06-19

In this paper, we convert certain dual q-integral equations involving third Jackson q-Bessel functions to the first and second kind Fredholm q-integral equations by extending the multiplying-factor method introduced by Nobel. We also apply these results to convert a certain triple q-integral equations to two simultaneous Fredholm q-integral equations

A Vertical Surface Flow Analysis of MHD Nanofluids Influenced by Radiation, Viscous Dissipation, and Joule Heating with Soret and Dufour Effects

S. Jayanthi — 2024-06-19

The purpose of this study is to investigate the effects of radiation and activation energy on mass transfer nanofluids flowing across an expanding sheet in a vertical direction, as well as joule heating, viscous dissipation, Soret and Dufour, and magnetohydrodynamic (MHD) flow. The boundary layer (BL) equations for nonlinear momentum, energy, solute, and nanoparticle volume fraction are reduced by using similarity transformations. After that, the shooting technique and bvp4c are used to numerically solve the boundary layer equations. Schmidt and Eckert’s numbers, along with Soret effects on velocity, temperature, and the volume percentage of nanoparticles, cause an increase in skin friction. Fluid temperature rises significantly with Eckert number. As the Dufour and Schmidt numbers rise, so does the local Nusselt number. A greater thermophoresis parameter, enhanced skin friction, and an increased Schmidt number.

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

R. A. Adetona — 2024-04-02

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.

A Couple of Fresh New Perspectives on the Concatenation Model with Power-Law of Self-Phase Modulation

Anwar Ja'afar Mohamad Jawad — 2024-05-06

In this paper, we have secured new optical solitons for the concatenation model with power-law nonlinearity. The traveling wave hypothesis serves as the starting point. To retrieve optical soliton solutions, we have implemented two powerful techniques into the model: the Sardar Sub-Equation Method (SSEM) and the Tanh-Coth method. For power-law nonlinearity, we derived through the balancing principle that solitons would exist for different values of the power-law parameter. Therefore, we have secured a large variety of new soliton solutions for the model. This paper derives dark, bright, and singular soliton solutions for the value of n, as the first case was already covered in a previous report dedicated to addressing the model with Kerr law nonlinearity. Lastly, all the parametric existence conditions of the solitons and all solutions have been constructed.

Information Asymmetric Cooperative Game with Agreements Implemented by a Third Party

Jeanpantz Chen — 2024-06-19

This paper introduces asymmetric information into the analysis of cooperative games with agreements implemented by a third party and establishes theoretical models of a one-time information asymmetric cooperative game with agreements implemented by a third party for the first time, using the methodology proposed in previously done research studying coalition formation and cooperative payoff distribution. In an information asymmetric cooperative game with agreements implemented by a third party, players may retain their own private information, and make decisions through their virtual games on the basis of their own information sets. This paper defines the virtual cooperative games of the players and demonstrates the equilibrium of the virtual cooperative game of a player; proposes the condition for the existence of the coalition equilibrium in an information asymmetric cooperative game with agreements implemented by a third party, defines and provides the existence proof of this coalition equilibrium when it does exist; defines the public choice game of a coalition on the strategic combination choice in a certain coalition situation, defines and provides the existence proof of the equilibrium of this game; examines the condition for the existence of the bargaining game on the distribution of the cooperative payoff of a coalition, defines and provides existence proof of the bargaining game, when the coalition members are allied or unallied in the bargaining game.

A Secure Key Exchange Protocol and a Public Key Cryptosystem for Healthcare Systems

Yuvasri R — 2024-05-23

Diffie-Hellman (DH) is the reason for the existence of a solution to the key distribution problem, where two parties can mutually set up a shared secret key over an insecure channel without any previous communication. In this study, a novel key exchange protocol based on the difficulty of the Discrete Logarithm Problem with Factor Problem (DLPFP) utilizing matrices in non-commutative semigroup over semiring is proposed. The security and complexity analyses of the protocol are discussed. Also, an ElGamal cryptosystem based on a group of invertible matrices and DLPFP over a semiring to encrypt the Sensitive Health Information (SHI) in healthcare systems is suggested.

Alleviated Shifted Gegenbauer Spectral Method for Ordinary and Fractional Differential Equations

S. M. Sayed — 2024-05-10

This article introduces two numerical methods to address boundary value problems associated with secondorder and fractional differential equations. These methods employ two parameters related to shifted Gegenbauer polynomials as their basis functions. The process involves establishing a differentiation operational matrix for the shifted Gegenbauer polynomials. Subsequently, the initial/boundary value problems for ordinary and fractional differential equations are transformed into a system of equations through the Galerkin, collocation, and tau methods. The convergence analysis is ensured by leveraging theorems pertaining to the shifted Gegenbauer polynomials. To validate the accuracy of the approach, numerous numerical examples are presented.

Embracing Sustainability in Green Supplier Evaluation: A Novel Integrated Multi-Criteria Decision-Making Framework

Nayeem Ahamed — 2024-06-19

Nowadays, industrial production is a critical issue for companies as public consciousness is rising because of environmental impacts. Like most other industries, the ready-made garment (RMG) industry faces immense pressure to be more competitive in this increasingly competitive market and proactively reduce waste and ecological footprint impacts. Besides, suppliers’ environmental performance and image have far more effect on a corporation’s environmental sustainability than the corporation’s internal environmental efforts. Moreover, there is a shortage of environmental consciousness in emerging economies; thus, green supply chain practices are lagging. Therefore, the green supplier evaluation criteria should be identified and focused on during sustainable procurement. This study analyses quantitative and qualitative factors and explores the relationship between green supplier preference principles using the combination of the Fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL) method and the Fuzzy Technique for Order Performance by Similarity to Ideal Solution (TOPSIS). Initially, the supplier’s green performance was measured by identifying the criteria from relevant literature. After that, the Fuzzy DEMATEL technique measures the related criteria weights, and the Fuzzy TOPSIS method utilizes these criteria weights to rank suppliers among alternative suppliers. The findings will guide policymakers to improve supplier quality, increase profitability through improved brand recognition, and attract consumers who prioritize environmentally friendly products.

Metaheuristic Cost Optimization of M^X/G₁,G₂/ 1 Queue with Service disruption, Working breakdown, Balking, Catastrophe and Extended Server Vacation with Bernoulli Schedule

Rani R — 2024-05-16

We presented a M^X/G₁, G₂/1 queueing system with a Bernoulli schedule that includes service disruption, working breakdown, balking, catastrophe and extended server vacations. All customers that arrive are served by a single server, with service time determined by general distribution. As soon as the system fails, the server keeps serving the current client at a reduced rate while repairs are made. It is believed that the vacation schedule is broad. Random disruptions to the server occur, with an exponential distribution in the length of the disruption. We assume that besides a Poisson stream of positive arrivals, there is a Poisson stream of negative arrivals, which we refer to as catastrophes. Using the supplementary variable technique, the Laplace transforms of the time-dependent probability of the system state are derived. We can infer steady-state outcomes from this. The average waiting time and queue size were also obtained. An additional topic of discussion is Adaptive Neuro-Fuzzy Inference system (ANFIS). Furthermore, this work uses Particle Swarm Optimisation (PSO), Artificial Bee Colonies (ABC), and Genetic Algorithms (GA) to swiftly find the system’s optimal cost. Additionally, we examined the convergence of several graph-optimisation strategies.

Optimal Power Flow of Power System with Unified Power Flow Controller Using Moth Flame Optimization with Locational Marginal Price

Trinadh Babu Kunapareddy — 2024-06-25

Consideration of transmission line capacity and the optimal power flow (OPF) determines the locational marginal price (LMP), which in turn determines the performance and profitability of a producing unit. Reducing the total cost of the generators can lead to a drop in the market price of electricity. It is recommended to use numerical and repetition-based approaches for solving power flow equations due to their nonlinear nature. In order to achieve the ideal power flow at an affordable price, this paper employs a Moth Flame Optimization (MFO) to solve the equations. We then enhance the MFO’s structure to make it more effective at performing the simultaneous calculations of power passing through transmission lines. Flexible AC transmission systems (FACTS) tool that has been utilized to overcome this problem is the Unified Power Flow Controller (UPFC). Lastly, the proposed MFO algorithm would include the following parameters in its output: bus voltages, line losses, generated power, total generating expenditures, and generator profits. In this work, the proposed method is tested on the IEEE 57-bus network also shows that it improves upon the OPF problem.

A Fixed Point Theorem for Time-Fractional Fornberg-Whitham Equation Arising in Atmospheric Science

Ashok Kumar Badsara — 2024-04-25

In this paper, we apply the Homotopy perturbation transform method of the time-fractional Fornberg-Whitham equation with Caputo-Fabrizio fractional derivative. We establish the existence and uniqueness solutions of the time-fractional Fornberg-Whitham equation using fixed point theory. The physical interpretation of the nonlinear models are also discussed through the semi analytical solutions, which demonstrate the effectiveness of the proposed method. Finally, 2D and 3D graphs of some derived solutions are depicted through suitable parameter values.

Some Orthogonal Combinations of Legendre Polynomials

W.M. Abd-Elhameed — 2024-04-15

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.

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

Elsayed M. E. Zayed — 2024-04-28

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.

Fekete-Szegö Inequality for a Subclass of Bi-Univalent Functions Linked to q-Ultraspherical Polynomials

Abdullah Alsoboh — 2024-05-23

In this study, we introduce a new class of bi-univalent functions using q-Ultraspherical polynomials. We derive the Fekete and Szegö functional problems for functions in this new subclass, as well as estimates for the Taylor-Maclaurin coefficients |α₂| and |α₃|. Furthermore, a collection of fresh outcomes is presented by customizing the parameters employed in our initial discoveries.

A Certain q-Sălăgean Differential Operator and Its Applications to Subclasses of Analytic and Bi-Univalent Functions Involving (p, q)-Chebyshev Polynomial

Musthafa Ibrahim — 2024-06-19

In the present investigation, we make use of the q- analogue of the Sălăgean differential operator and introduce a new subclass of analytic and bi-univalent functions S_Σ^η,^μ involving the (P, Q)-Chebyshev polynomials. Furthermore, we derive coefficient inequalities and obtain the Fekete-Szegö problem for this new function class f ∈ S_Σ^η,^μ of functions.

Theoretical Analysis of Pre-Steady State Behaviour of Non-Linear Double Intermediate Enzymatic Reaction

Reena A — 2024-06-21

This paper explores the mathematical modelling of a non-linear double intermediate enzymatic reaction, focusing on its pre-steady state behaviour. Using homotopy perturbation and Taylor's series methods, an approximate analytical solution is derived for the concentrations of substrate, the first enzyme-substrate complex, and the second enzyme-substrate complex. The model is applicable in scenarios where the initial substrate concentration dramatically exceeds that of the enzyme and when they are comparable. Comparisons between analytical and numerical solutions are made, highlighting the efficacy of the proposed model. Additionally, an improved understanding is achieved by comparing results obtained from Matlab simulations with analytical solutions. Moreover, sensitivity analysis on parameters affecting the concentrations is conducted. This mathematical model enhances comprehension of biochemical reactions in living organisms.

A Caputo-Type Fractional-Order Model for the Transmission of Chlamydia Disease

Jignesh P. Chauhan — 2024-04-26

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.

Application of Clifford Algebra on Group Theory

Farooqhusain Inamdar — 2024-03-22

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).

Highly Dispersive Optical Solitons with Quadratic-Cubic Nonlinear form of Self-Phase Modulation by Sardar Sub-Equation Approach

Anwar Ja’afar Mohamad Jawad — 2024-05-07

The highly dispersive optical solitons with a quadratic-cubic form of self-phase modulation structure are derived. The governing model was reduced to an ordinary differential equation by the traveling wave hypothesis. Subsequently, the Sardar sub-equation method and its modified version are used to locate the soliton solutions. A full spectrum of optical solitons is thus obtained.

CSO-based Efficient Resource Management for Sustainable Cloud Computing

K. Shanmugam — 2024-03-29

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.

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

Revathi R — 2024-04-17

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.

Idealization of a Semigroup by Using Bruck-Reilly Monoids

Suha Wazzan — 2024-04-09

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.

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

Manas Kumar Giri — 2024-04-18

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.

Group Classification of Second-Order Linear Neutral Differential Equations

Jervin Zen Lobo — 2024-06-19

In this paper, we shall extend the method of obtaining symmetries of ordinary differential equations to second-order non-homogeneous functional differential equations with variable coefficients. The existing research for delay differential equations defines a Lie-Bäcklund operator and uses the invariant manifold theorem to obtain the infinitesimal generators of the Lie group. However, we shall use a different approach that requires Taylor’s theorem for a function of several variables to obtain a Lie invariance condition and the determining equations for second-order functional differential equations. Certain standard results from the theory of ordinary differential equations have been employed to simplify the equation under study. The symmetry analysis of this equation was found to be non-trivial for arbitrary variable coefficients. In such cases, by selecting certain specific functions, arising in most practical models, we find the symmetries that are seen to be in terms of Bessel’s functions, Mathieu functions, etc. We then make a complete group classification of the second-order linear neutral differential equation, for which there is no existing literature.

Convergence Analysis of Resolvent Equation Technique for Co-Variational Inequality Problem in Banach Spaces

Haider Abbas Rizvi — 2024-06-03

In this work, a co-variational inequality problem and a co-resolvent equation problem are introduced and investigated. It is shown that the fixed point problem is equivalent to the problem of co-variational inequality. The co-variational inequality problem and the co-resolvent equation problem are equivalent due to this resemblance. The coresolvent equation problem is solved using an iterative approach that we provide at the final stage. Our findings may be seen as an enhancement of several established findings.

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

Wafa Shammakh — 2024-04-17

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.

Application of Network Reconstruction Algorithm to Compute Maximum Flow for Water Supply Network: A Case Study of the City of Bulawayo, Zimbabwe

Trust Tawanda — 2024-06-25

Determining the maximum flow value in Water Supply Networks (WSN) is a common problem that is being faced by many cities during and after designing of WSN. In this article, the network reconstruction (NR) algorithm is applied to compute the maximum flow value for the city’s WSN based on the actual data. The city of Bulawayo has been selected for the following reasons, availability of research data, the city is facing severe water shedding and several studies have focused only on other issues such as alternative water sources, leakage detection and demand forecasting. The goal of this study is to determine the maximum flow value from the sources to the reservoirs. The results have revealed that the computed maximum flow value is within the estimated range of 110,000 cubic meters to 190,000 cubic meters. Dam sensitivity analysis were considered to determine the sources to give maintenance priority before the rain season. Several recommendations were suggested to improve the water supply situation.

Palindromic Antimagic Labeling of Products of Paw and Banner Graph

P. Reka — 2024-06-19

This article presents a novel classification of Antimagic labeling referred to as Palindromic antimagic. Palindromic Antimagic labeling pertains to the assignment of palindromic numbers {℘₁, ℘₂, ℘₃ . . . ℘_q} to the set of edges of a graph G = (V, E), where G consists of p vertices and q edges. This labeling is characterized by being invertible, meaning that each edge is uniquely associated with a palindromic number. Additionally, it involves an injective mapping of vertex labeling, where the sum of incident edges for any given vertex is distinct from one another. In
this study, we examine the palindromic antimagic labeling of Cartesian and Tensor product of certain Tadpole graphs, such as the paw and banner graph.

Neutrosophic Semi β^F-Contra Continuity in a Neutrosophic Topological Space

K. Fayaz Ur Rahman — 2024-06-19

The main intention of this article is to propose the theory of a neutrosophic S_β^F contra continuous function, neutrosophic strongly S_β^F continuous function, neutrosophic strongly S_β^F contra continuous function and neutrosophic S_β^F contra irresolute function in neutrosophic topological spaces. Further several properties based on the above concepts have been studied. Many theorems based on the above ideas have been proved with the suitable illustration. Further the relationship connecting neutrosophic S_β^F contra continuous function, neutrosophic strongly S_β^F continuous function, neutrosophic strongly S_β^F contra continuous function and neutrosophic S_β^F contra irresolute function are studied and illustrated. Moreover, various theorems based on compositions of functions have been proved. In addition to this, the product of two neutrosophic sets is defined and related theorems have been proved.

Revisitation of “Implicit Quiescent Optical Solitons with Complex Ginzburg-Landau Equation Having Nonlinear Chromatic Dispersion“: Linear Temporal Evolution

Abdullahi Rashid Adem — 2024-05-13

The current paper revisits the retrieval of quiescent optical solitons for the complex Ginzburg-Landau equation with nonlinear chromatic dispersion and several forms of self-phase modulation. The results obtained in this work consist of explicit or implicit quiescent optical solitons, unlike the previous report, which were expressed in terms of quadratures. Additionally, this study addresses two additional forms of self-phase modulation: the saturating law and the exponential law. This exploration yields quiescent optical solitons expressed in terms of quadratures for the first time.

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

K. Sasikala — 2024-04-16

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.

Investigation of a Mathematical Model and Non-Linear Effects Based on Parallel-Substrates Biochemical Conversion

Nebiyal A — 2024-06-25

According to the broad applicability and advancements made in addressing complex non-linear problems, Researchers have been actively involved in addressing the accurate approaches to solve non-linear problems in fields such as chemical science, material science, and image processing. In this paper, the Amperometric response of catalase-peroxidase (parallel-substrates) conversion has been discussed. The Mathematical model relies on a set of non-linear differential equations that describe the reaction and diffusion of the system. The analytical methods were extended to derive the approximate solution of the non-linear reaction-diffusion equation. The straightforward and concise analytical expressions for the concentrations and current of the Biosensor are developed. This study includes the computational resolution of the problem by utilizing a MATLAB program. A comparison between analytical outcomes and those derived numerically has been conducted. The analytical findings presented are dependable and offer an effective comprehension of the behaviour of this system.

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

Srilekha R — 2024-03-29

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.

Analysis of Fuzzy Membership Function on Greenhouse Gas Emission Estimation by Triangular and Trapezoidal Membership Functions in Indian Smart Cities

Velmurugan S — 2024-05-29

This research aims to analyze the efficiency of triangular and trapezoidal membership functions in forecasting CO₂, N₂O, and CH₄ emissions in Indian smart cities. Over 10-years, emissions data for these gases were collected and used to determine membership values for both functions. The study evaluated the performance of the membership functions using Root Mean Square Error (RMSE) values and percentage error analysis. The results indicated that the trapezoidal membership function provided more accurate results for CO₂ and CH₄ emissions, while the triangular membership function was more accurate for N₂O emissions. These findings highlight the importance of selecting appropriate membership functions tailored to specific gases to enhance emission forecast accuracy. The study emphasizes the significance of such insights for decision-makers, urban planners, and environmental agencies involved in emissions reduction measures and smart city development. However, further research is recommended to validate these findings and explore additional factors that may influence the performance of membership functions in emission prediction in smart cities. In conclusion, this project offers a comprehensive analysis of triangular and trapezoidal membership functions’ accuracy in predicting emissions in Indian smart cities, emphasizing the crucial factors.

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

Jian Yang — 2024-04-18

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.

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

A. Panneer Selvam — 2024-04-02

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.

A New Model Making the Transition From Oil to Solar Energy

Séverine Bernard — 2024-04-25

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.

Internally Disclosed Sets of a Real Space

Rasulkhozha S. Sharafiddinov — 2024-04-09

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.

Cryptographic Signature Scheme for Mobile Edge Computing Using DLFP Over Semiring

Sethupathi S — 2024-04-25

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.

Algorithm Optimizer in GA-LSTM for Stock Price Forecasting

YL Sukestiyarno — 2024-01-05

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. GA is 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 mean absolute percentage error (MAPE) values below 10% in every optimizer used. A fairly stable and small value is generated by setting it using the Adam optimizer.

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

Abdul Gazir Syarifudin — 2024-04-26

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.

Sensitivity Analysis and Optimal Control of Cocoa Black Pod Disease Caused by Phytophora Margakarya

Adebayo Adeniran — 2024-05-14

To address the critical threat black pod disease poses to global cocoa production and farmer income, this study developed a novel mathematical model that utilizes a system of ordinary differential equations to capture the interactions between various stages of cocoa pods (susceptible cherelles, young/mature pods, ripe pods) and their disease state (exposed, infected). Additionally, the model incorporates the dynamics of the disease-causing pathogen population. Employing Pontryagin's Maximum Principle, the model optimizes control strategies that minimize disease impact. This optimization identifies the efficient allocation of resources, timing of interventions, and deployment of control measures like infected pod removal, fungicides, and sanitation practices. The finding of the study reveals that control measure u₃ which is rouging (pod removal) and any one of the remaining control measures is best for the treatment of cocoa black pod disease caused by Phytophora Megarkaya. These findings translate into valuable, data-driven recommendations for cocoa farmers and disease management professionals. By strategically combining infected pod removal, targeted fungicide use, and environmental management practices, farmers can significantly reduce disease severity, enhance cocoa production, and promote a more sustainable cocoa industry.

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

Safeer Hussain Khan — 2024-04-03

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.

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

Islam Samir — 2024-04-25

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.

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

Ahmed M. Elaiw — 2024-04-15

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.

Mathematical Analysis of Nonlinear Differential Equations in Polymer Coated Microelectrodes

Dorathy Cathrine A — 2024-06-24

A theoretical analysis is conducted on the electrochemical behaviour of micro disk electrodes coated with thin coatings of electroactive polymers. The main focus of efforts to characterize the planar diffusion chemical reaction within polymer-modified ultra-microelectrodes is the creation of a theoretical model that explicitly takes into account the potential for the polymer film to cover the inlaid micro disc support surface. Approximate formulae for the steady-state amperometric response and formulation of the boundary value problem are given. The impact of substrate concentration, mediator concentration and current responsiveness in the solution besides the polymer film is also investigated. Akbari-Ganji method (AGM) and differential transformation method (DTM), two adequate and widely available analytical methods, were utilized to determine the steady-state non-linear diffusion equation. The approximate analytical solution for the substrate concentration and mediator concentration and the current for the small experimental kinetic values and diffusion coefficients are presented. We additionally determine the problem’s numerical solution using the MATLAB tool. A satisfactory agreement can be seen when the numerical outcomes verify with the analytical findings.

Artificial Intelligence Solution for Relaxation Oscillation Equation

A. Kalaiyarasi — 2024-04-17

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.

Non-Markovian Feedback Retrial Queue with Two Types of Customers and Delayed Repair Under Bernoulli Working Vacation

Sundarapandiyan S — 2024-05-10

This paper deals with an M/G/1 feedback retrial G-queue and delayed repair incorporating Bernoulli working vacation. Arrivals of both favorable and unfavorable consumers are two independent Poisson processes. The server is subjected to breakdown during the regular busy period due to the arrival of unfavorable customers and then the server will be down for a short period of time. Further, the concept of delay time is also discussed. After the fulfillment of regular service, the dissatisfied consumer may re-join the orbit to receive another service as a feedback consumer. During the working vacation period, the server provides the service to consumers at a reduced rate. By applying the supplementary variable technique (SVT), we have analyzed the steady-state probability generating function (PGF) for the system size and orbit size. In addition, we have presented the system performance, reliability indicators, and stochastic decomposition property. Finally, we provided numerical examples to illustrate our model’s mathematical results.

Extended Newton-Traub Method of Order Six

Ioannis K. Argyros — 2024-05-30

In various scientific and engineering fields, many applications can be simplified as the task of solving equations or systems of equations within a carefully chosen abstract space. However, analytical solutions for such problems are often difficult or even impossible to find. As a result, iterative methods are widely employed to obtain the desired solutions. This article focuses on introducing a highly efficient three-step iterative method that exhibits sixth order convergence. The analysis presented here thoroughly explores the local and semi-local convergence properties, taking into account the continuity conditions imposed on the operators present in the method. The innovative methodology described in this article is not limited to specific methods but can be extended to a broader range of approaches that involve the utilization of inverse operations on linear operators or matrices.

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

Sandhya Rani — 2024-04-15

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.

On Linearization Coefficients of Shifted Jacobi Polynomials

H. M. Ahmed — 2024-04-25

Optical Solitons for the Dispersive Concatenation Model with Polarization Mode Dispersion by Sardar's Sub-Equation Approach

Anwar Ja'afar Mohamad Jawad — 2024-06-21

This paper recovers the spectrum of optical solitons for the dispersive concatenation model with the application of the Sardar sub-equation approach. The single soliton solutions that emerge from this scheme are bright, dark, and of singular type. The parameter constraints for the existence of such solitons are also included.

Hyperbolic 3-Manifolds with Boundary Which are Side-Pairings of Two Tetrahedra as Exteriors of Knotted Graphs in the 3-Sphere

Juan Pablo Díaz — 2024-04-26

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 sidepairing 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 3,, 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.

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

Jingwei Jia — 2024-04-08

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.

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

Surendra Vikram Singh Padiyar — 2024-04-09

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.

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

Deep Singh — 2024-03-27

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.

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

Ahmed H. Arnous — 2024-03-27

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.

Multi-Class Network Anomaly Detection Using Machine Learning Techniques

Satyanarayana Gunupusala — 2024-06-19

Computer networks rely on Intrusion Detection Systems (IDSs) and Intrusion Prevention Systems (IPSs) to ensure the security, reliability, and availability of an organization. In recent years, various approaches were developed and implemented to create effective IDSs and IPSs. This paper specifically focuses on IDSs that utilize Machine Learning (ML) techniques for improved accuracy. ML-based IDSs have verified to be successful in discovering network attacks. However, their performance tends to decline when dealing with high-dimensional data spaces. It is essential to develop a suitable feature extraction strategy that could identify and remove irrelevant features that do not significantly classification process to address this issue. Additionally, many ML-based IDSs exhibit high false positive rates and poor detection accuracy when trained on unbalanced datasets. In this study, we analyze the UNSW-NB15 IDS, which will serve as the training and testing data for our models. In order to reduce the feature space and improve the efficiency of our analysis, we leverage a filter-based feature reduction method utilizing the Pearson correlation coefficient algorithm. By identifying and selecting only the most relevant features, we are able to streamline our dataset and focus on the variables that have the highest impact on our analysis. This approach not only reduces computational complexity but also improves the interpretability of our results by eliminating unnecessary noise from the data. After applying the feature reduction technique, we proceed to implement a range of machine learning methods to perform our classification task. These include well-known algorithms such as Stacking, Extra Trees, Multi-Layer Perceptron, XGBoost, K-Nearest Neighbors, Logistic Regression, Naïve Bayes, Support Vector Machine, Random Forest, and Decision Tree. By employing a diverse set of algorithms, we are able to explore different modeling approaches and evaluate their effectiveness in accurately classifying the various types of assaults. In order to assess the performance of our classification models, we utilize a range of specialized evaluation metrics such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), R2-Score, Mean Squared Error (MSE), Precision, F1-Score, Recall, and Accuracy. These metrics provide us with a comprehensive understanding of how well our models are performing across different dimensions, including the accuracy of predictions, the level of precision in classifying different assault types, and the overall goodness-of-fit of our models. By considering multiple evaluation metrics, we are able to gain a more nuanced understanding of the strengths and weaknesses of each algorithm and make informed decisions about their suitability for our classification task. These metrics deliver a complete evaluation of the classifiers’ effectiveness in detecting community intrusions.

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

A. Mohamed Ali — 2024-04-12

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

Xiaoyuan Yang — 2024-04-03

A Hybrid Fuzzy Extension and Its Application in Multi-Attribute Decision Making

AN. Surya — 2024-06-07

The hypersoft set theory is an extension of soft set theory. The complex non-linear diophantine fuzzy set is a hybrid fuzzy extension that serves as a generalization of the q-rung linear diophantine fuzzy set and the complex linear diophantine fuzzy set. In this paper, to tackle multi-sub-attributed real-world situations under complex non-linear diophantine fuzzy ambiance, the concept of complex q-rung linear diophantine fuzzy hypersoft set is proposed along with its score and accuracy function. Also, the idea of lattice ordered complex q-rung linear diophantine fuzzy hypersoft set is proposed in this paper, along with some of its basic algebraic operations. Furthermore, a highly effective algorithm using lattice ordered complex q-rung linear diophantine fuzzy hypersoft set is provided for handling multi-attributed decision-making issues exquisitely, along with an illustrative example in the field of vertical farming. Then, a comparative analysis between the proposed and current notions is provided to demonstrate the superiority and benefits of the suggested concepts over the current ones.

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

K. Pavani — 2024-04-08

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.

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

Ahmed M. Elaiw — 2024-04-15

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.

Mirror Symmetry, Zeta Functions and Mackey Functors

Mohammad Reza Rahmati — 2024-06-19

We present two alternative and new proofs for the duality between orbifold zeta functions of Berglund-Hubsch dual invertible polynomials. We re-prove the following theorem; Assume W and W^T are dual invertible polynomials in n + 2 variables. Denote by (X_W, G) and (X_W_^T ; G^T) the corresponding Berglund-Hubsch dual hypersurfaces in Pⁿ⁺¹, where G and G^T stands for their group of symmetries. The orbifold L-series of X_W and X_W_^T satisfy: (*) L_orb(X_W, s) = L_orb(X_W_^T, s)^(-1)n. We present two proofs of the above identity (*). Our methods of proof are different. The first proof uses cohomological Mackey functors on Mackey systems. The second proof is independent and uses a formula for the orbifold zeta functions. For an orbifold (X, G) we consider a Mackey system of subgroups of G and cohomological Mackey functors on this Mackey system. We investigate the relation between the above L-series of orbifolds and the Mackey functors. We show the orbifold cohomology H^*_orb(X, C) is an End_CG[⊕_gCG/C(g)]-module, that means; the orbifold cohomology defines a cohomological Mackey functor on the Mackey system of conjugacy classes in G. This leads one to split the zeta function according to properties of G-cohomological Mackey functors. This method allows obtaining identities on orbifold zeta functions from identities in a Grothendick group associated with subgroup quotients of G. In this context, the relation (1) is a consequence of cohomological mirror symmetry and Mackey structure. In other words, we obtain the identity (1) from Mackey type of identities in a Grothendieck group followed by a multiplicative homomorphism constructed from zeta functions of a Galois representation. The second proof uses a duality between age functions ι: G→Z, and ι^T: G^T→Z, of the dual invertible polynomials. It is known that G^T is the character group of G. We show that these age functions are Fourier transforms of each other with respect to a unitary representation obtained from the natural pairing between G and G^T. Using a formula of the orbifold zeta function in terms of the age functions, we deduce a comparison of zeta functions for the two dual invertible polynomials as given in the above.

Fuzzy Metric Spaces: Optimizing Coincidence and Proximity Points

Koon Sang Wong — 2024-03-28

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.

ANFIS-Enhanced M/M/2 Queueing Model Investigation in Heterogeneous Server Systems with Catastrophe and Restoration

Indumathi P — 2024-06-14

Exploring the Elzaki Transform: Unveiling Solutions to Reaction-Diffusion Equations with Generalized Composite Fractional Derivatives

Mohd Khalid — 2024-06-25

This article investigates the use of the Elzaki transform on a generalized composite fractional derivative. To establish the framework for this inquiry, numerous essential lemmas about the Elzaki transform are presented. We successfully extract the solution to the reaction-diffusion problem using both the Elzaki and Fourier transforms, which include a generalized composite fractional derivative. We also look at special examples of the generalized equation, which helps us understand its applications and consequences better. The results show that the Elzaki transform is successful in dealing with complicated fractional differential equations, introducing new analytical approaches and solutions to the subject of fractional calculus and its applications in reaction-diffusion systems.

Vector Fixed Point Approach to Control of Kolmogorov Differential Systems

Alexandru Hofman — 2024-04-29

The paper presents a vector approach to control problems for systems of equations. The method is described in the case of Kolmogorov systems which arise frequently in the dynamics of populations. Three types of problems are discussed: problems with control of both per capita growth rates, problems with control parameters acting on the growth rates, and problems which combine the first two types. The controllability is obtained via a vector approach based on the Perov fixed point theorem and matrices which are convergent to zero. Four concrete illustrative examples are added.

Normalized Laplacian Energy and Distance Based Energy for Cross Monic Zero Divisor Graphs Associated with Commutative Ring

R. Sarathy — 2024-05-07

Computing Certain Topological Indices of Silicate Triangle Fractal Network Modeled by the Sierpiński Triangle Network

Gayathiri V — 2024-05-10

The study of Sierpiński triangle network and extended Sierpiński graph is quite interesting in the field of fractal networks. In nature, fractal networks (FN) and silicate structure networks (Sio₄) play vital roles and in architecture to analyze the dimension of the above-mentioned FN and Sio₄ networks it is necessary to identify the number of copies of the network. In this paper, we introduced a silicate triangle fractal network (Si_n) which is a planar fractal and it is created using a related sequence of graphs named (Si_n)_n≥0, where n is the n^thlevel of silicate triangle fractal network. We analyze the topological indices (TI) of the silicate triangle fractal network Si_ngraph and compare the calculated topological indices to the number of copies of silicate structure (Sio₄) in each iteration of Si_nfor a sequence of a graph.

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

Monal Patel — 2024-04-12

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.

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

Pravin Singh — 2024-04-17

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.

Heuristic Incident Edge Path Algorithm for Interval-Valued Neutrosophic Transportation Network

Kanchana M — 2024-05-22

Neutrosophic Set is an extension of Fuzzy set theory dealts with uncertain environments in Transportation, Decision-making etc. Finding the shortest path for an uncertain environment is one of the most challenging tasks, many heuristic algorithms play a vital role in releasing this task. This research article an heuristic algorithmic approach using graph theoretical methods helps the researcher to crack the challenge and which type of algorithm can use the type of score functions are discussed. Especially, the interval-valued Neutrosophic transportation problem (IVNTP) is considered for finding the shortest path which is a real-world decision-making problem in an ambiguous (uncertain) environment. Providing the shortest and finest way to address this ambiguity leads to the success of researcher to the organization. The algorithm used has been introduced for determination of interval-valued Neutrosophic shortest path (IVNSP) from the origin node to all other nodes by de-neutrosophicated edges using score functions. An illustrative Interval-valued neutrosophic transportation problem explains the algorithm’s efficacy and authenticity to find optimum result; this research article discusses about the nature of score functions, and some score function were taken into consideration. Further, the heuristic algorithm used is applicable for both positive and negative weighted edges; it was elaborated and compared with existing algorithm results, and it also provided all pair of shortest path. Future study and brief study of this article was disclosed in conclusion.

Optimal Control Model of University-PhD-Postdoc-Industry (UPPI) Migration and Unemployment

Adeniji AA — 2024-06-19

This study explores the impact of the movement of PhD graduates and postdoctoral research fellows between academia and industry on unemployment within the academic and industry sectors. To achieve this, an optimal control model is analyzed which was developed for the population of the university, PhDs holders, postdocs, and industry compartments. The study discovered that, by offering incentives to PhD graduates and postdocs who choose to stay in academia rather than transition to industry, unemployment in the university sector can be reduced. Based on the findings, the authors advise for the governments to concentrate on offering these incentives to PhD holders and postdocs to persuade them to stay in academia. Policymakers can lower unemployment rates in both the academic and industrial sectors by putting in place measures that promote the retention of PhD holders and postdocs in academics and control their migration to the industry.

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

Ziyi Huang — 2024-04-16

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.

Regularity of Initial Ideal of Binomial Edge Ideals in Degree 2 and Their Powers

Bakhtyar Mahmood Rahim — 2024-06-19

In this paper, we study the Castelnuovo-Mumford regularity of the initial ideal of binomial edge ideals in degree 2 ([in_<(J_G)]₂), and their powers for some classes of graphs. Also, we obtain a lower bound for the regularity of powers of binomial edge ideal associated to complete bipartite graphs.

Review on Jacobi-Galerkin Spectral Method for Linear PDEs in Applied Mathematics

R. M. Hafez — 2024-06-13

This study explores the spectral Galerkin approach to solving the space-time Schrödinger, wave, Airy, and beam equations. In order to facilitate the creation of a semi-analytical approximation solution, it uses polynomial bases that are formed from a linear combination of Jacobi polynomials (JPs) in both spatial and temporal dimensions. By using these polynomials to expand the exact solution, the paper hopes to satisfy the homogeneous starting and Dirichlet boundary requirements. Notably, the Jacobi Galerkin (JG) method exhibits exponential convergence rates if the solution is sufficiently smooth. This result emphasizes the JG approach' s potential as an effective numerical solution method, which has promise for a variety of applications in other domains where these equations occur, such as quantum mechanics, acoustics, optics, and structural mechanics.