International Journal of Analysis and Applications

Mathematical Analysis for a Zika Virus Dynamics in a Seasonal Environment

2024-03-06T01:29:44+08:00

We propose a mathematical model for the Zika virus (ZIKV) spread under the influence of a seasonal environment. The basic reproduction number R₀ was calculated for both cases, the fixed and seasonal environment permitting the characterisation of the extinction and the persistence of the disease for both cases. We proved that the virus-free steady state is globally asymptotically stable if R₀≤1, while the disease will be persist if R₀>1. Finally, extensive numerical simulations are given to confirm the theoretical findings.

Perfect Quadratic Forms Connected With a Lattice and Cubature Formulas

2024-02-01T20:44:33+08:00

In the present work, a new improved Voronoi algorithm is proposed for calculating the Voronoi neighborhood of a perfect form in many variables, and using this algorithm, all non-equivalent adjacent perfect forms in five variables are calculated.

Global Properties of a Discrete SARS-CoV-2/HIV Co-Dynamics Model

2024-02-17T08:10:39+08:00

Coronavirus disease 2019 (COVID-19), which is caused by the virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is a respiratory disease. In this paper, we analyze the global stability of a discrete SARS-CoV-2/HIV co-dynamics model. We create the discrete model by applying a nonstandard finite difference (NSFD) method. We demonstrate that NSFD retains essential solution properties, including positivity and boundedness. We determine the fixed points and identify their existence conditions. We investigate the global stability of these fixed points through the application of the Lyapunov method. To complement our analytical findings, we present numerical simulations.

Multiple and Singular Soliton Solutions for Space–Time Fractional Coupled Modified Korteweg–De Vries Equations

2024-03-07T04:59:02+08:00

The focus of this paper is on the nonlinear coupled evolution equations, specifically within the context of the fractional coupled modified Korteweg–de Vries (mKdV) equation, employing the conformable fractional derivative (CFD) approach. The primary objective of this paper is to thoroughly investigate the applicability of the Hirota bilinear method for deriving analytical solutions to the fractional mKdV equations. A range of exact analytical solutions for the fractional coupled mKdV equations is obtained. The findings in general indicate that the Hirota bilinear method is an effective approach for resolving the complexities associated with the fractional coupled mKdV equations.

Identifying the Severity of Criminal Activity in Society Using Picture Fuzzy Baire Space

2024-02-27T16:44:01+08:00

In this paper, the idea of picture fuzzy Baire space is explored and its properties are examined. The features of picture fuzzy semi-closed and semi-open sets, picture fuzzy nowhere dense sets, picture fuzzy first and second category sets, picture fuzzy residual sets, picture fuzzy submaximal spaces, picture fuzzy strongly irresolvable spaces, picture fuzzy G_δ set, picture fuzzy F_σ set, and picture fuzzy regular closed sets are analyzed. To understand the concepts, some examples are provided. An algorithm using picture fuzzy Baire space is developed to address real-world scenarios. This method is more effective in assessing criminal activity as it identifies an individual who has committed a more serious offense. This algorithmic approach proves its effectiveness in navigating the complexities of practical examples, showcasing its potential for real-world applications.

F-Modular b-Metric Spaces and Some Analogies of Classical Fixed Point Theorems

2024-01-11T16:59:54+08:00

The main aim of this study is to provide a novel concept of F-modular b-metric spaces. Within this comprehensive framework, we establish three well-known fixed point theorems for self-maps. The results we have obtained broaden and enrich prior findings in the field of fixed point theory. To support our arguments, we provide four concrete examples along with graphical representations.

Adomian Decomposition Method With Inverse Differential Operator and Orthogonal Polynomials for Nonlinear Models

2024-02-08T19:00:27+08:00

A proficient Adomian decomposition method is proposed amidst the presence of inverse differential operator and orthogonal polynomials for solving nonlinear differential models. The method is indeed a reformation of the standard Adomian method thereby improving the rapidity of the solution's convergence rate. A generalized recurrent scheme for a general nonlinear model was derived and further utilized to solve certain nonlinear test models. Lastly, numerical results are reported in comparative tables, demonstrating absolute error differences between the exact and approximate solutions with regards to various employed orthogonal polynomials.

New Auxiliary Principle Technique for General Harmonic Directional Variational Inequalities

2024-02-26T04:19:01+08:00

This paper explores the utilisation of harmonic variational inequalities to establish the minimum value among two locally Lipschitz continuous harmonic convex functions. This investigation introduces novel classes of harmonic directed variational inequalities, particularly focusing on scenarios like harmonic complementarity and related optimization challenges. The study proposes and analyses various inertial iterative strategies for addressing harmonic directed variational inequalities through the auxiliary principle technique. It examines convergence criteria under specific weak conditions, emphasising the simplicity of the approach compared to other methodologies. The findings presented herein have broad applicability in the context of harmonic variational inequalities and optimization problems, though they are limited to theoretical exploration. Further research is required to implement these strategies numerically.

A Study on Degree Based Topological Indices of Harary Subdivision Graphs With Application

2023-10-25T02:24:33+08:00

Combinatorial design theory and graph decompositions play a critical role in the exploration of combinatorial design theory and are essential in mathematical sciences. The process of graph decomposition involves partitioning the set of edges in a graph G. An n-sun graph, characterized by a cycle with an edge connecting each vertex to a terminating vertex of degree one, is introduced in this study. The concept of n-sun decomposition is applied to certain even-order graphs. The indices covered in this study include the general connectivity index of the harary graphs, Zagreb indices, symmetric division degree indices and randic indices.

Paley Wiener Theorem on a Reductive Lie Group

2024-02-04T00:40:53+08:00

Let G be a locally compact group, K a maximal compact subgroup of G and δ on arbitrary class of irreducible unitary representations of K. The spherical Grassmannian G_p,δ is an equivalence class of spherical functions of type δ−positive of height p. In this work, we give an extension of orbital integral with respect to δ, when G is reductive Lie group. Moreover, if the discret serie is not empty, we give an extension of Paley-Wiener theorem using a compact Cartan subgroup of G.

Approximation of Periodic Functions by Wavelet Fourier Series

2023-10-13T22:49:00+08:00

This paper aims to examine the expansion of periodic functions using wavelet bases. M. Skopina [8] obtained a Wavelet analog of the classical Jackson’s theorem for trigonometric approximation. Our result generalizes the result of M. Skopina [8] and V. Karanjgaokar et al. [15].

Geometrical Aspect of Pointwise Semi-Slant Conformal Submersions

2024-02-16T17:13:31+08:00

The aim of this paper is to define pointwise semi-slant conformal submersions from locally product Riemannian manifolds onto Riemannian manifolds. We investigated the conditions under which the distributions are integrable and the leaves of the distributions defines totally geodesic foliation. Additionally, we examined the concept of pluriharmonicity of pointwise semi-slant conformal submersions. In support of the results we obtained, we present non-trivial examples.

Fuzzy (Almost, δ) Ideal Continuous Mappings

2024-01-17T23:18:14+08:00

In this paper, we introduce the concept of fuzzy δ-ideal continuous, fuzzy θ-ideal continuous, fuzzy strongly δ-ideal continuous and fuzzy almost ideal continuous mappings in fuzzy ideal topological spaces given the definition of Sostak. In addition, we study some properties between them.

A Study on Quotient Structures of Bipolar Fuzzy Finite State Machines

2023-11-21T10:16:17+08:00

This article introduces different congruence relations on the bipolar fuzzy set associated with the bipolar fuzzy finite state machine. Each congruence relation associates a semigroup with the bipolar fuzzy finite automata. We also discuss characterizing a bipolar fuzzy finite state machine by defining an admissible relation.

On KU-Modules Over KU-Algebras

2024-01-31T05:38:05+08:00

The paper introduces the concept of modules for KU-algebras, named as KU-modules. It presents basic isomorphism theorems for KU-modules and explores their applications, particularly concerning chains of KU-modules. Additionally, it defines and examines exact sequences of KU-modules. The paper discusses various properties of chains of KU-modules and establishes the butterfly lemma in the context of KU-modules.

Common Fixed Point Theorems for Mappings Satisfying (E.A)-Property on Cone Normed B-Metric Spaces

2023-08-04T20:06:23+08:00

In this article, we demonstrate the conditions for the existence of common fixed points (CFP)theorems for four self-maps satisfying the common limit range (E.A)-property on cone normed B-metric spaces (CNBMS). Furthermore, we have an unique common fixed point for two weakly compatible (WC) pairings.

Estimations with Step-Stress Partially Accelerated Life Tests for Ailamujia Distribution under Type-I Censored Data

2024-01-21T04:51:22+08:00

This paper addresses the problem of estimating parameters in partial accelerated life tests following the Ailamujia distribution under Type-I censoring, employing both the maximum likelihood approach and the least squares method. The assessment of estimation methods involves a comprehensive simulation study, complemented by the analysis of a real dataset for illustrative purposes. The findings reveal the least square estimation method outperforms maximum likelihood estimation, considering biases and mean square errors.

On Interior Bases of Ordered Semigroups

2023-10-20T13:03:38+08:00

In this paper, the notions of interior bases of ordered semigroups are introduced, and some examples are also presented. We describe a characterization when a non-empty subset of an ordered semigroup is an interior base of an ordered semigroup. Finally, a characterization when an interior base of an ordered semigroup is a subsemigroup of an ordered semigroup will be given.

Solving a Nonlinear Fractional Integral Equation by Fixed Point Approaches Using Auxiliary Functions Under Measure of Noncompactness

2024-01-24T00:40:34+08:00

This manuscript is devoted to ensure the existence of a solution to nonlinear fractional integral equations with three variables under a measure of noncompactness. In order to accomplish our main goal, we develop a new fixed point theorem that generalizes Darbo’s fixed point theorem by utilizing a measure of noncompactness and a new contraction operator. A related tripled FP theorem is also obtained. Finally, we use this generalized Darbo’s fixed point theorem to solve a nonlinear fractional integral equation involving three variables, and an example to demonstrate our results is presented.

Improving the Performance of a Series-Parallel System Based on Gamma Distribution

2023-10-19T18:30:39+08:00

The performance of a series-parallel system is improved by using the reliability equivalence factors technique. The lifetimes of the components are assumed to be gamma distributed. The system reliability is improved by using three different methods: (i) Reduction method, (ii) Hot duplication method, (iii) Cold duplication method. The reliability function and mean time to failure for each method are derived. Finally, the numerical application is introduced.

Qualitative Behavior for a Discretized Conformable Fractional-Order Lotka-Volterra Model With Harvesting Effects

2024-01-21T03:07:12+08:00

The predator-prey model is a widely mathematical structure that explains the dynamics between two interacting populations: predators and prey. The predator-prey interaction represents a fundamental dynamic in nature, influencing the stability and balance of ecosystems worldwide. The purpose of this article is to provide insight into the complex interactions and feedback mechanisms between predators and prey in ecological systems via mathematical tools such as stability and bifurcation. We investigate a fractional-order Lotka-Volterra model with a harvesting effect using stability and bifurcation theory. The equilibrium points and local stability of the purposed model are presented in this article. The bifurcation analysis, which is a potent approach used to analyse the qualitative behavior of the predator-prey system as the parameter values are varied, is also explored. In particular, a Neimark-Sacker bifurcation and a period-doubling bifurcation are theoretically and numerically examined. Furthermore, we illustrate some 2D figures to show the phase portriat and bifurcations of this model at various points.

Dynamical Analysis of Thirtieth-Order Difference Equations

2023-12-29T18:41:20+08:00

The main goal of this paper is to determine exact solutions of a family of thirtieth-order difference equations with variable coefficients. We use similarity variables obtained via symmetries to lower the order of the equations. We then reverse the transformations and obtain closed form solutions. We compare our solutions to those found in the literature for special cases. We investigate the periodic nature of the solutions and present some numerical examples to confirm the results. Finally, we analyze the stability of the equilibrium points. The method employed in this work can be applied to equations of higher order provided that they admit non zero characteristics.

On Cesaro-Hypercyclic Operators

2024-02-07T20:13:22+08:00

In this paper we characterize some properties of the Cesaro-Hypercyclic and mixing operators. At the same time, we also give a Cesaro-Hypercyclicity criterion and offer an example of this criterion.

Estimation of Parameters for the Mathematical Model of the Spread of Hepatitis B in Burkina Faso Using Grey Wolf Optimizer

2024-01-22T15:52:45+08:00

In this paper, we developed a mathematical model of differential susceptibility, taking into account vaccination and treatment, to simulate the transmission of the hepatitis B virus in the population of Burkina Faso. The existence and uniqueness of non-negative solutions are proved. The model has a globally asymptotically stable disease free equilibrium when the basic reproduction number R₀ < 1 and an endemic equilibrium when R₀ > 1. We estimated the parameters of the model based on hepatitis B cases from 1997 to 2020 by using a Grey Wolf Optimizer Algorithm (GWO). The results demonstrated the efficacy of the GWO algorithm in estimating the model parameters. A sensitivity analysis was carried out to determine the determining factors in the spread of hepatitis B in Burkina Faso. The estimated parameters were used to simulate the spread of hepatitis B in Burkina Faso from 1997 to 2020.

Strictly Wider Class of Soft Sets via Supra Soft δ-Closure Operator

2024-01-16T04:16:14+08:00

In this work, we use the supra soft δ-closure operator to present a new notion of generalized closed sets in supra soft topological spaces (or SSTSs), named supra soft δ-generalized closed sets. We show that, this notion is more general than many of previous notions, which presented before in famous papers. We illustrate many of its essential properties in detail. Specifically, we illustrate that the new collection neither forms soft topology nor supra soft topology. Moreover, we study the behavior of the soft image and soft pre-images of supra soft δ-generalized closed sets under new types of soft mappings, named supra soft irresolute and supra soft δ-irresolute closed. In addition, we define the concept of supra soft δ-generalized open sets, as a complement of supra soft δ-generalized closed sets. Finally, the relationships with other forms of generalized open sets in SSTSs are explored, supported by concrete examples and counterexamples. Therefore, I think the development of the notions presented in this paper are sufficiently general relevance to allow for future extensions.

Inertial Algorithms for Bifunction Harmonic Variational Inequalities

2024-01-30T21:43:23+08:00

In this paper, we introduce and study some new classes of bifunction harmonic variational inequalities. Various new and known classes of variational inequalities and complementarity problems can obtained as special classes of bifunction harmonic variational inequalities. The auxiliary principle technique is applied to suggest and analyze some hybrid inertial iterative methods for finding the approximate solutions of the bifunction harmonic variational inequalities. The convergence analysis of these iterative methods is also considered under some suitable conditions. Results proved in this paper can be viewed as a refinement and improvement of the known results. It is an interesting open problem to develop some implementable numerical methods for solving these problems and to explore the applications in mathematical and engineering sciences.

Mathematical Investigation for Two-Bacteria Competition in Presence of a Pathogen With Leachate Recirculation

2024-01-04T05:05:02+08:00

This paper provides a thorough exploration of two-species competition in a continuous bioreactor when adding a pathogen that affects only one species and with leachate recirculation inside the reactor. The dynamics is modelled by a well-constructed system of nonlinear differential equations extending the classical model of the chemostat by adding more realism, enhancing its applicability. The nonnegativity and boundedness of trajectories, the determination of steady states and their local stability strengthens the credibility of the proposed system. The global stability analysis was conducted using uniform persistence theory. The coexistence of both species under somewhat natural assumptions is a key finding, contradicting the well-known competitive exclusion principle. Several numerical examples offer a practical demonstration of the theoretical concepts.

Application of an Ansatz Method on a Delay Model With a Proportional Delay Parameter

2023-12-16T01:13:56+08:00

Delay differential equations are fundamental tools to modeling various real-world problems. A particular type of these models is considered in this paper in the form y’(t) = ay(t) + ae^aty(at), where a is a proportional delay parameter. Solving delay equations is usually a difficult task. This is because there are no standard/well-known methods for solving such kind of equations. This paper proposes a simple procedure to solve the above delay equation. The solution is obtained in closed form which is optimal. The suggested analysis can be invested to analyze more complex models in physics and engineering sciences.

On Null Vertex in Fuzzy Graphs

2023-11-06T02:22:58+08:00

We introduce a new type of vertex in fuzzy graphs, namely null vertex, which is neither a boundary vertex nor an interior vertex. Here, we initiate a study on the null vertex in fuzzy graphs, explore its properties and establish its presence in various types of fuzzy graphs.

A New Four-Step Iterative Approximation Scheme for Reich-Suzuki-Type Nonexpansive Operators in Banach Spaces

2023-12-30T03:59:45+08:00

In this paper, we present a new four-step iterative scheme namely DH-iterative which is faster than many super algorithms in the literature for numerical reckoning fixed points. Under this algorithm, some fixed point convergence results and ω 2 -stability for contractive-like and Reich-Suzuki-type nonexpansive mappings are proposed. Our results extend and improve several related results in the literature. Finally, some numerical examples are given to study the efficiency and effectiveness of our iterative method.

Analysis of the Economic Cost of Coxian-2 Service with Encouraged Arrival and Balking

2023-10-07T17:32:54+08:00

The queuing model is widely used in the production, inventory, and service industries. In order to improve the performance of a queuing model, it is crucial to characterize the practical queuing characteristics. The purpose of this work is to examine an analysis of the economic cost of Coxian-2 service with encouraged arrival and balking in a queuing system. In particular, we discussed Coxian-2 service-encouraged arrival queuing system and an accelerated distribution. According to our presumption, units (customers) enter the system one at a time in an encouraged arrival procedure, and the server offers Coxian-2 service one at a time according to the first in first out (FIFO) rule. As probability-generating functions, the typical customer count, and the typical customer wait time in the system and queue, respectively. We also derive steady-state probabilities and performance measures for the proposed model. Finally, the economic analysis of the model is performed by introducing cost model with an empirical example is given to show the effectiveness of the proposed model. The created formula also fulfills Little’s formula.

Entropy Analysis of Nanofluid flow in a Fluidized Bed Dryer in Presence of Induced Magnetic Field

2023-10-13T16:33:54+08:00

The study investigates generation of entropy in an unsteady, incompressible nanofluid flow occurring within a fluidized bed dryer used in tea processing industries. The study considered the presence of variable magnetic field, influence of viscous dissipation, thermal radiation and chemical reaction. The nonlinear partial differential equations of momentum, energy and concentration were derived. A finite difference numerical scheme was employed to obtain an approximate solution for the nonlinear partial differential equations governing the flow. Entropy generation is then determined from velocity, concentration and temperature profiles obtained from solution of momentum, mass and energy equations. The study illustrated the impact of various flow parameters on entropy generation and Bejan number through graphical presentations while numerical values for skin friction coefficient, heat and mass transfer rates were provided in tabular form. Study of entropy generation allows one identify factors which contribute to energy inefficiencies in a thermal system and allows different stakeholders or designers of bed dryers in tea factories identify ways of improving the dryer or designing more effective dryers. Bejan number is used in thermodynamics to evaluate efficiency of thermal systems such as fluidized bed dryers. It helps one design heat exchangers which maximizes heat transfer while minimizing energy losses. The findings of this study are essential in improving the performance, efficiency and the design of a fluidized bed dryer involving heat and mass transfer as well as fluid flow.

Some Results of Malcev-Neumann Rings

2023-12-24T02:36:58+08:00

Let us consider the function σ, which maps elements from the group G to the group of automorphisms of the ring R. In this paper, we are studying new conditions under which the Malcev-Neumann ring R∗((G)) is a PS, APP, PF, PP, and a Zip rings, respectively. It has been demonstrated that if R is a reduced ring and σ is weakly rigid, then the Malcev-Neumann ring R∗((G)) over a PS-ring is a PS. Furthermore, if σ is weakly rigid and the ring R satisfies the descending chain condition on left annihilators, then the Malcev-Neumann ring R∗((G)) is a right APP-ring if and only if, for any G-indexed generated right ideal A of R, r_R(A) is left s-unital. Additionally, we have proven that if R is a commutative ring and σ is weakly rigid, then the Malcev-Neumann ring R∗((G)) is a PF ring if and only if, for any two G-indexed subsets A and B of R such that B⊆ann_R(A), there exists c∈ann_R(A) such that bc = b for all b ∈ B. These results extend the corresponding findings for polynomial rings and Laurent power series rings.

Single-Valued Neutrosophic Roughness via Ideals

2024-01-17T23:12:47+08:00

In this paper, we connect the idea of single-valued neutrosophic ideal to the concept of single-valued neutrosophic approximation space to define the concept of single-valued neutrosophic ideal approximation spaces. We present the single-valued neutrosophic ideal approximation interior operator int^ψ_Φ and the single-valued neutrosophic ideal approximation closure operator cl^ψ_Φ, and we present the single-valued neutrosophic ideal approximation preinterior operator pint_ψ^Φ and the single-valued neutrosophic ideal approximation pre-closure operator pcl_ψ^Φ about this concerning single-valued neutrosophic ideal defined on the single-valued neutrosophic approximation space (χ˜,ϕ) related with some single-valued neutrosophic set ψ∈ξ^χ˜. Also, we present single-valued neutrosophic separation axioms, single-valued neutrosophic connectedness, and single-valued neutrosophic compactness in single-valued neutrosophic approximation spaces and single-valued neutrosophic ideal approximation spaces as well, and prove the associations in between.

Conformable Granular Fractional Differentiability for Fuzzy Number Valued Functions

2023-09-12T00:48:08+08:00

This paper deals with the utilization of the concept of the granular differentiability to establish a fractional derivative of the conformable type for fuzzy number valued functions. Subsequently, we introduce the notion of a conformable granular integral and provide evidence of its fundamental properties pertaining to differentiability and integrability through illustrative examples. Lastly, we delve into the discussion of the solution approach for the conformable granular initial value problem (CGIVP), as well as the solution of conformable granular differential equations (CGDEqs) associated with growth and decay.

Impact of Dataset Scaling on Hierarchical Clustering: A Comparative Analysis of Distance-Based and Ratio-Based Methods

2023-11-01T18:39:23+08:00

In this study, the distance-based agglomerative hierarchical clustering techniques were compared to a ratio-based approach. Two real datasets, which were also used in a prior study by Roux (2018), were considered. Firstly, it was observed that the type of scaling applied to the datasets was found to affect the results of hierarchical clustering. Thus, various scaling methods were employed prior to implementing hierarchical clustering. Furthermore, two rank-based goodness-of-fit measures were used to evaluate the hierarchical clustering methods. In contrast to Roux (2018) findings, it was observed that the distance-based methods, such as Median linkage, Average linkage, and centroid linkage, performed better than the ratio-based method. The ratio-based methods also showed issues with branch crossing in the hierarchical clustering dendrogram. Consequently, this study illustrates that, with appropriate dataset scaling, the distance-based methods outperform ratio-based methods in terms of goodness-of-fit measures.

Bertrand Offsets of Spacelike Ruled Surfaces With Blaschke Approach

2023-12-17T16:20:06+08:00

Dual parametrizaions of the Bertrand offset- spacelike ruled surfaces are assigned and sundry modern outcomes are acquired in view of their integral invariants. A modern characterization of the Bertrand offsets of spacelike developable surfaces is specified. Further, many connections among the striction curves of Bertrand offsets of spacelike ruled surfaces and their integral invariants are gained.

Optimal Impulse Control for Systems Deriven by Stochastic Delayed Differential Equations

2023-11-07T16:04:08+08:00

In this paper we study the problem of optimal impulse control for stochastic systems with delay in the case when the value function of the impulse problem depends only on the initial data of the given process through its initial value (value at zero) and some weighted averages. A verification theorem for such impulse control problem is given. As an example the optimal stream of dividends with transaction costs is solved.

Characterizations of Almost (τ1, τ2)-Continuous Functions

2023-09-28T18:47:43+08:00

This paper is concerned with the concept of almost (τ₁, τ₂)-continuous functions. Moreover, some characterizations of almost (τ₁, τ₂)-continuous functions are investigated.

Practical Aspects for Applying Picard Iterations to the SIR Model Using Actual Data

2023-12-15T23:00:35+08:00

The updated version of the Picard method for solving systems of differential equations is employed to solve the SIR system. A local performance of the Picard iteration algorithm combined with the Gauss-Seidel approach is applied to the SIR model. The integral form of the SIR model, in addition to the use of Gauss-Seidel philosophy (using the most recent calculated values), achieved more accuracy in the computational work than those obtained using the differential forms. Documented data regarding the spread of corona virus 19 in the Kingdom of Saudi Arabia region from April to the end of December 2020 were used to calculate the corresponding actual values for the parameters and the initial conditions. Due to efficient management and to obtain representable behaviours, we restricted the size of the study to only 1% of the population. The global characteristics of the integral formulation have affected the calculations accurately. The initial conditions and the model’s parameters are established depending on the documented data. The results illustrate the superiority of the updated Picard formulation over the classical Picard within their domain of convergence. The results of this study illuminate and validate the importance of mathematical modeling. These findings can provide valuable insights into mathematical modeling for those involved in environmental health research, especially those responsible for devising strategic plans.

A Kinetic Non-Steady-State Analysis of Immobilized Enzyme Systems Without External Mass Transfer Resistance

2023-11-15T19:30:00+08:00

In this paper, a non-steady-state non-linear reaction diffusion in immobilized enzyme on the nonporous medium is considered for its mathematical analysis. The non-linear terms in this model are related to the Michaelis-Menten kinetics. For the considered model, the approximate analytical expressions of the substrate concentration and the effectiveness factor for the various geometric profiles of immobilized enzyme pellets are obtained using homotopy perturbation method (HPM). The obtained approximate analytical expressions proved to be fit for all values of parameters. Numerical solutions are also provided using the MATLAB software. When comparing the analytical and the numerical solutions, satisfactory results are noted. The effects of Thiele modulus and Michaelis-Menten kinetic constants on the effectiveness factor are also analyzed.

Application of Deep Belief Network in Weather Modeling: PM2.5 Concentration in Thailand

2023-09-13T20:37:55+08:00

In Thailand, the number of particles matter with diameter of less than 2.5 microns or PM_2.5 concentration exceed the standard in many areas, especially in Chiang Mai. This affects the image of the country in terms of economy, health, and environment. The objective of this research is to study the structure of model for PM_2.5 concentration by using a Deep Belief Network (DBN) with the daily data set of PM_2.5 concentration from the air quality monitoring station at Yupparaj Wittayalai School, Chiang Mai. The data was analyzed through an unsupervised path using the Minimizing Contrastive Divergence (MCD) algorithm, followed by a supervised path using Back-Propagation Neural Network (BPNN) algorithm to estimate the parameters of DBN. The result shows that the optimal DBN structure has 5 input nodes and 20 hidden neurons in the first hidden layer. This model has an 88.4 percent accuracy in forecasting PM_2.5 concentration. In addition, this model can be applied for other weather forecasting such as rainfall or water level in a basin.

A Class of Non-Bazilevic Functions Subordinate to Gegenbauer Polynomials

2023-11-29T16:45:52+08:00

In this paper, we introduce and investigate a class non-Bazilevic functions that associated by Gegenbauer Polynomials. The coefficient estimates of functions belonging to this class are derived. Moreover, we obtain the classical Fekete-Szegö inequality of functions belonging to this class.

Convergence of Modified S-Iteration to Common Fixed Points of Asymptotically Nonexpansive Mappings in Hyperbolic Spaces

2023-12-15T15:06:34+08:00

In this paper, we provide some sufficient conditions for the strong convergence of an improved form of modified S-iteration for approximating common fixed points of two asymptotically nonexpansive mappings defined on a closed convex subset of a uniformly convex hyperbolic spaces.

Tripled Fixed Point Approaches and Hyers-Ulam Stability With Applications

2023-11-17T01:24:04+08:00

In this paper, we present tripling fixed point results for extended contractive mappings in the context of a generalized metric space. Many publications in the literature are improved, unified, and generalized by our theoretical results. Furthermore, the Ulam-Hyers stability problem for the tripled fixed point problem in vector-valued metric spaces has been examined as a stability analysis for fixed point approaches. Finally, as a type of application to support our research, the theoretical conclusions are used to explore the existence and uniqueness of solutions to a periodic boundary value problem.

Single-Valued Neutrosophic Ideal Approximation Spaces

2023-12-01T19:51:57+08:00

In this paper, we defined the basic idea of the single-valued neutrosophic upper (α_n)^δ, single-valued neutrosophic lower (α_n)_δ and single-valued neutrosophic boundary sets (α_n)^B of a rough single-valued neutrosophic set αn in a single-valued neutrosophic approximation space (F˜, δ). Based on α_n and δ, we introduced the single-valued neutrosophic ideal approximation interior operator int^δ_αn and the single-valued neutrosophic ideal approximation closure operator Cl^δ_αn. We joined the single-valued neutrosophic ideal notion with the single-valued neutrosophic approximation spaces and then introduced the single-valued neutrosophic ideal approximation closure and interior operators associated with a rough single-valued neutrosophic set α_n. single-valued neutrosophic ideal approximation connectedness and the single-valued neutrosophic ideal approximation continuity between single-valued neutrosophic ideal approximation spaces are introduced. The concepts of single-valued neutrosophic groups and their approximations have also been applied in the development of fuzzy systems, enhancing their ability to model and reason using uncertain and imprecise information.

Optimal Quadrature Formula of Hermite Type in the Space of Differentiable Functions

2023-11-19T14:54:55+08:00

In this research work, a new derived optimal quadrature formula is discussed, which includes the sum of the values of the function and its first and second order derivatives at the points located at the same distance on the interval [0,1] in the L₂^(m)(0,1) space. we first obtain an analytical representation of the error function norm, and a system of equations of the Wiener-Hopf type construct using the method of Lagrange unknown multipliers for finding the conditional extremum of multivariable functions. Optimal coefficients found by solving the system. Using the exact form of the optimal coefficients, the norm of the error functional of the optimal quadrature formula for m=3 and m=4 calculate and the order of approximation was shown to be O(h^m). The obtain theoretical conclusions confirmed by numerical experiments.

Modified Intuitionistic Quantum Fuzzy Operators for Binary Optimization Problems

2023-09-19T22:01:53+08:00

To facilitate the realization of this groundbreaking concept, this paper presents an original approach to represent intuitionistic fuzzy sets and operators through quadratic optimization problems. This approach aims to enable the deployment of fuzzy inference mechnism on a specific category of quantum computers referred to as quantum annealers.

The Exact Norm of Modified Hardy Operator in Power-Weighted Lebesgue Spaces

2023-11-02T08:58:52+08:00

We consider the necessary and sufficient condition for boundedness of modified Hardy operators from a power-weighted Lebesgue space to another. We also compute the exact norm of modified n-dimensional Hardy operators from those spaces.

Generalization of Homotopy Analysis Method for q-Fractional Non-linear Differential Equations

2023-04-01T23:50:37+08:00

This paper presents a generalization of the Homotopy analysis method (HAM) for finding the solutions of nonlinear q-fractional differential equations (q-FDEs). This method shows that the series solution in the case of generalized HAM is more likely to converge than that on HAM. In order that it is applicable to solve immensely non-linear problems and also address a few issues, such as the impact of varying the auxiliary parameter, auxiliary function, and auxiliary linear operator on the order of convergence of the method. The generalized HAM method is more accurate than the HAM.

On the Spectral Theory of Regularized Quasi-Semigroups

2023-12-01T18:35:01+08:00

We have shown a spectral inclusion between a different spectrum of a C₀-quasi-semigroups in [9]. Precisely for Saphar, essentially Saphar, quasi-Fredholm, Kato and essentially Kato spectra. In this paper, we extend these results for a C-quasi-semigroups (regularized quasi-semigroups) where C is a bounded injective operator.

Fixed Point Set and Equivariant Map of a S-Topological Transformation Group

2023-10-12T11:21:31+08:00

The fixed point set and equivariant map of a S-topological transformation group is explored in this work. For any subset K of G, it is established that the fixed point set X^K is clopen in X and for a free S-topological transformation group, it is proved that the fixed point set of K is equal to the fixed point set of closure and interior of the subgroup of G generated by K. Subsequently, it is proved that the map between STC_G(X) and STC_G’(X’) is a homomorphism under a Φ’- equivariant map. Also, it is proved that there is an isomorphism between the quotient topological groups and some basic properties of fixed point set of a S-topological transformation group are studied.

Numerical Study for MHD Flow of an Oldroyd-B Fluid Over a Stretching Sheet in the Presence of Thermal Radiation with Soret and Dufour Effects

2023-11-23T04:47:40+08:00

This paper investigates the impact of Soret and Dufour's MHD flow of an Oldroyd-B fluid over a stretching sheet in the presence of thermal radiation. By a similarity transformation, the controlling partial differential equations are transformed into a system of nonlinear ordinary differential equations. Using the successive linearization method (SLM), the linear system is solved. A determination and discussion of the impacts of specific fluid parameters on the temperature, concentration distribution, and velocity are presented. As the magnetic field increases, we observe that the temperature and concentration profiles rise, while the velocity profile falls. In addition, increases in the Dufour and Soret levels will also result in an improvement in the temperature and concentration distribution. The validity of the acquired results is tested by comparing them to previously published works, with particular attention paid to the accuracy and convergence of the solution.

On the Stability of Quadratic-Quartic (Q2Q4) Functional Equation over Non-Archimedean Normed Space

2023-10-20T13:43:21+08:00

In the present work the stability of Hyers-Ulam mixed type of quadratic-quartic Cauchy functional equation
g(2x+y)+g(2x−y)=4g(x+y)+4g(x−y)+2g(2x)−8g(x)−6g(y)
has been proved over Non-Archimedean normed space.

A Hybrid Laplace Transform-Optimal Homotopy Asymptotic Method (LT-OHAM) for Solving Integro-Differential Equations of the Second Kind

2023-11-21T22:32:34+08:00

The new proposed hybrid method between optimal homotopy asymptotic method and Laplace transform namely LT-OHAM is formulated for the first time in our paper. This hybrid method presents significant features of LT-OHAM and its capability of handling IDEs. This formulation is developed to find the solution of IDEs. By using the new presented hybrid method, some applications of IDEs are solved. This hybrid method seems very efficient and easy to solve these types of equations.

Sufficient Reduction Method for Bivariate Zero-Inflated Poisson Process

2023-10-12T15:22:36+08:00

The sufficient reduction (SR) method was developed for detecting a mean shift in a bivariate zero-inflated Poisson process. The derived sequence of statistics from the reduction was monitored with the EWMA and EWMA-SN charts for monitoring a mean shift in a process. The detection performance was compared against other SR methods developed for a Poisson process and evaluated via the simulations under the different shift sizes and proportions of zero in the process. The results showed that the presence of zeros in the process influenced the performance of SR methods by delaying shift detection and reducing the detection accuracy, especially when shift size was small. The proposed method with the EWMA chart gave the shortest delay for detecting a small to moderate shift and gave the highest true alarm rate and the lowest non-detection rate for detecting a small shift compared to other methods.

Fear and Hunting Cooperation's Impact on the Eco-Epidemiological Model's Dynamics

2023-10-02T18:39:49+08:00

Due to the fact that living organisms do not exist individually, but rather exist in clusters interacting with each other, which helps to spread epidemics among them. Therefore, the study of the prey-predator system in the presence of an infectious disease is an important topic because the disease affects the system's dynamics and its existence. The presence of the hunting cooperation characteristic and the induced fear in the prey community impairs the growth rate of the prey and therefore affects the presence of the predator as well. Therefore, this research is interested in studying an eco-epidemiological system that includes the above factors. Therefore, an eco-epidemiological prey-predator model incorporating predation fear and cooperative hunting is built and examined. It is considered that the disease in the predator is of the SIS kind, which means that the infected predator can recover and become susceptible through medical treatment. All possible equilibrium points have been found. The solution's positivity and boundedness are examined. Local and global stability analyses are performed. The uniform persistence conditions are established. The local bifurcation around the equilibrium points is studied. Finally, numerical simulation is performed to validate the obtained results and comprehend the parameter impact on system dynamics.

Global Stability of a Delayed Model for the Interaction of SARS-CoV-2/ACE2 and Adaptive Immunity

2023-10-25T13:07:05+08:00

The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the culprit behind the coronavirus disease 2019 (COVID-19), which has killed millions of people. SARS-CoV-2 binds its spike (S) protein to the angiotensin-converting enzyme 2 (ACE2) receptor to inter the epithelial cells in the respiratory tracts. ACE2 is a crucial mediator in the SARS-CoV-2 infection pathway. In this paper, we construct a mathematical model to describe the SARS-CoV-2/ACE2 interaction and the adaptive immunological response. The model predicts the effects of latently infected cells as well as immunological responses from cytotoxic T lymphocytes (CTLs) and antibodies. The model is incorporated with three distributed time delays: (i) delay in the formation of latently infected epithelial cells, (ii) delay in the activation of latently infected epithelial cells, (iii) delay in the maturation of new released SARS-CoV-2 virions. We show that the model is well-posed and it admits five equilibria. The stability and existence of the equilibria are precisely controlled by four threshold parameters R_i, i=0,1,2,3. 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 do sensitivity analysis and identify the most sensitive parameters. We look at how the latent phase, ACE2 receptors, antibody and CTL responses, time delays affect the dynamical behavior of SARS-CoV-2. Although the basic reproduction number R₀ is unaffected by the parameters of antibody and CTL responses, it is shown that viral replication can be hampered by immunological activation of antibody and CTL responses. Further, our findings indicate that R₀ is affected by the rates at which the ACE2 receptor grows and degrades. This could provide valuable guidance for the development of receptor-targeted vaccines and medications. Furthermore, it is shown that, increasing time delays can effectively decrease R₀ and then inhibit the SARS-CoV-2 replication. Finally, we show that, excluding the latently infected cells in the model would result in an overestimation of R₀.

Associative Types in a Semi-Brouwerian Almost Distributive Lattice With Respect to the Binary Operation ρ

2023-09-07T15:39:43+08:00

In this paper, we exhibit a detailed analysis of non-associativity and non-commutativity of the binary operation ρ in a semi-Brouwerian almost distributive lattice and characterize the algebraic structure in terms of the different associative types.

Bipolar Fuzzy Almost Quasi-Ideals in Semigroups

2023-11-06T11:14:15+08:00

The aim of paper, we give the concept bipolar fuzzy, almost quasi-ideal in semigroups. We present the properties of bipolar fuzzy, almost quasi-ideals in semigroups. Moreover, we prove the relationship between almost quasi-ideals and bipolar fuzzy quasi-ideals in semigroups.

New Approach to Solving Fuzzy Multiobjective Linear Fractional Optimization Problems

2023-10-16T18:53:35+08:00

In this paper, an iterative approach based on the use of fuzzy parametric functions is proposed to find the best preferred optimal solution to a fuzzy multiobjective linear fractional optimization problem. From this approach, the decision-maker imposes tolerance values or termination conditions for each parametric objective function. Indeed, the fuzzy parametric values are computed iteratively, and each fuzzy fractional objective is transformed into a fuzzy non-fractional parametric function using these values of parameters. The core value of fuzzy numbers is used to transform the fuzzy multiobjective non-fractional problem into a deterministic multiobjective non-fractional problem, and the ε-constraint approach is employed to obtain a linear single objective optimization problem. Finally, by setting the value of parameter ε, the Dangtzig simplex method is used to obtain an optimal solution. Therefore, the number of solutions is equal to the number of used values, and the optimal solution is chosen according to the preference of the decision-maker. We have provided a didactic example to highlight the step of our approach and its numerical performances.

Weakly p(Λ, p)-Open Functions and Weakly p(Λ, p)-Closed Functions

2023-09-28T18:42:29+08:00

Our main purpose is to introduce the concepts of weakly p(Λ, p)-open functions and weakly p(Λ, p)-closed functions. Moreover, several characterizations of weakly p(Λ, p)-open functions and weakly p(Λ, p)-closed functions are investigated.

Cooperative Investment Problem With an Authoritative Risk Determined by Central Bank

2022-09-05T12:14:39+08:00

In this paper, we are interested in providing an analytic solution for cooperative investment risk. We reformulate cooperative investment risk by writing dual representations for each risk preference (Coherent risk measure). Finding an analytic solution for this problem for both cases individual and cooperative investment by using dual representation for each risk preference has a strong effect on the financial market. In addition, we formulate a problem that covers the risk minimization with an expected return maximization problem with risk constraint, for the general case of an arbitrary joint distribution for the asset return under certain conditions and assuming that all coherent risk measure is continuous from below. Thus, the optimal portfolio is written as the optimal Lagrange multiplier associated with an equality-constrained dual problem. Furthermore, a unique equilibrium allocation as a fair optimal allocation solution in terms of equilibrium price density function for each agent is also shown.

Applications of Bipolar Fuzzy Almost Ideals in Semigroups

2023-11-08T10:08:48+08:00

In this paper, we give the concept of bipolar fuzzy almost ideal, minimal almost bipolar fuzzy ideals, and prime (semiprime, strongly prime) bipolar fuzzy almost ideals in semigroups. We investigate the basic properties of bipolar fuzzy almost ideals in semigroups. Finally, we study the relationship between almost ideals and bipolar fuzzy almost ideals in semigroups.

Effects of Rotation and Magnetic Field on Rayliegh Benard Convection

2023-10-25T18:16:54+08:00

In this paper, a numerical method based on the Chebyshev tau method is applied to analyze the effects of rotation and magnetic fields on Rayleigh-Bénard convection. The rotation and magnetic fields are assumed to be parallel to the vertical direction. The perturbation equations and boundary conditions are analyzed using normal mode analysis. The equations are then converted into a non-dimensional form and transformed into a generalized eigenvalue problem of the form AX=RBX, where R represents the eigenvalue corresponding to the Rayleigh number. The MATLAB software package is utilized to determine the relationship between the Rayleigh number and the Taylor number (rate of rotation), as well as the relationship between the Rayleigh number and the magnetic parameter (strength of the magnetic field) for different boundary conditions (free-free, rigid-rigid, or one free and the other rigid). The numerical and graphical results are presented and found to be in full agreement with the results obtained from previous analytical and numerical studies of the problem.

Mathematical Modeling for a CHIKV Transmission Under the Influence of Periodic Environment

2023-11-16T20:38:31+08:00

We studied a simple mathematical model for the chikungunya virus (CHIKV) spread under the influence of a seasonal environment with two routes of infection. We investigated the existence and the uniqueness of a bounded positive solution, and we showed that the system admits a global attractor set. We calculated the basic reproduction number R₀ for the both cases, the fixed and seasonal environment which permits us to characterise both, the extinction and the persistence of the disease with regard to the values of R₀. We proved that the virus-free equilibrium point is globally asymptotically stable if R₀≤1, while the disease will persist if R₀>1. Finally, we gave some numerical examples confirming the theoretical findings.

Weighted Polynomial Approximation Error, Szegö Curve and Growth Parameters of Analytic Functions

2023-10-13T14:05:46+08:00

The Szegö curve is denoted by S_Ro={z∈C: |ze¹^−z|=R_o, |z|≤1} and let H_R be the class of functions analytic in G_R but not in G_R’ if R<R’, G_Ro=int S_Ro’, 0<R_o<R<1. In this paper we have studied growth parameters in terms of weighted polynomial approximation errors on S_Ro for the functions f∈H_R having rapidly increasing maximum modulus so that the order of f(z) is infinite.

Comparison of Test Statistics for Mean Difference Testing Between Two Independent Populations

2023-10-07T11:46:32+08:00

The purpose of the article is to evaluate the efficiency of seven test statistics for mean difference testing between two independent populations. The evaluation was based on the probability of type I error and power of the test at 0.05 significance level under population distributions assumed to be normal, exponential, log-normal, gamma, and Laplace with equal sample sizes, and both equal and unequal variances. The results showed that for equal variance, the test statistics with the highest testing power controlled the probability of type I error were Z-test for normal and exponential distributions, Welch based on rank test (WBR) for log-normal and gamma distributions, and Mann-Whitney U test (MWU) for Laplace distribution. For unequal variance, Z-test was more efficient under normal, exponential, log-normal, and gamma distributions, while WBR was appropriate for Laplace distribution.

Instabilities and Stabilities of Additive Functional Equation in Paranormed Spaces

2023-08-06T13:00:39+08:00

In this paper, we solve the general solution in vector space and prove the Hyers-Ulam stability of the following additive functional equation

in paranormed spaces by using the direct and fixed point methods. Also we present its pertinent counter examples for instabilities.

Bipolar Fuzzy Filters of Gamma-Near Rings

2023-10-25T16:03:04+08:00

The main objective of this paper is to present the notation of bipolar fuzzy filters of Γ-near rings and ordered Γ-near rings. As a consequence, we deal with bipolar fuzzy prime ideals of Γ-near rings and ordered Γ-near rings. Also, we examine the one-to-one correspondence of bipolar fuzzy filters and crisp filters of Γ-near rings. Later, we define and study the homomorphism of ordered Γ-near rings.

On Some Graphs Based on the Ideals of JU-Algebras

2023-10-18T19:12:10+08:00

We will construct few types of simple graphs (with no multiple edges or loops) based on the ideal annihilator, right ideal annihilator, left ideal annihilator for JU-algebras. We will also study some graph invariants, such as connectivity, regularity, and planarity for these graphs.