Communications in Mathematics and Applications

Path Fuzzy Bitopological Spaces on Fuzzy Directed Graphs

2024-08-14T09:13:57+00:00

In this paper, we introduce a new concept of fuzzy topological spaces on fuzzy directed graphs by utilizing path relations between vertices and discuss several key results related to fuzzy topological spaces on various fuzzy digraphs. We define strongly connected, symmetric, and asymmetric fuzzy directed graphs, demonstrating that the associated path topological spaces are indiscrete. Furthermore, by employing path fuzzy topological spaces, we define a path fuzzy bitopological space associated with a fuzzy digraph. Various separation axioms, such as fuzzy pairwise \(T_{0}\), \(T_{1}\), \(T_{2}\) and fuzzy pairwise weakly \(T_{2}\), are studied for path fuzzy bitopological spaces, and the interrelations between path topological spaces and path fuzzy bitopological spaces are examined. This paper also initiates the concept of fuzzy bitopological spaces for fuzzy directed graphs.

Hyponormality of Toeplitz Operators on Symmetric-type Circulant Trigonometric Polynomial Symbols: An Extremal Case

2024-09-23T06:22:24+00:00

In this paper, we give some necessary and sufficient conditions to determine the hyponormality of Toeplitz operators on symmetric-type circulant trigonometric polynomial symbols in Hardy-Hilbert spaces of analytic functions considering an extremal case.

Stochastic Modelling by Combining a Random Contraction and a Random Dilation for Decision Making

2024-06-20T15:30:29+00:00

Random contractions and dilations of positive variables are essential probabilistic tools in the discipline of stochastic modelling. The present paper establishes two stochastic models that are formulated via the combination of the random contraction of a random variable with the random dilation of random variable. The theoretical contribution is based on the computation of the corresponding characteristic function, while the practical contribution is attained through the application of the proposed stochastic models in decision making within the field of financial management and risk management.

Lacunary Statistical Convergence of Order \(\alpha\) for Generalized Difference Sequences in Linear Partial Metric Space

2024-04-25T12:17:05+00:00

In the present study, with the use of generalized difference operator \(\Delta^p\), we have the notion of \(\Delta^p\)-lacunary statistical \(\varphi\)-convergence and \(\Delta^p\)-lacunary strongly \(\varphi\)-Cesàro summability of order \(\alpha\), in partial metric space \((X,\varphi)\), where \(\varphi\) is a partial metric on \(X\). We also analyse these notions with the fusion of modulus function. In addition we also establish some relationship between these concepts.

Higher-Order Numerical Technique Based on Strong Stability Preserving Method for Solving Nonlinear Fisher Equation

2024-07-04T18:27:19+00:00

This paper presents higher-order numerical methods for solving nonlinear Fisher equations. These types of equations arise in various fields of sciences and engineering, the main application of this equation has been found in the biomedical sciences. The solution of this equation helps to determine the size of the brain tumor. In this paper, we have constructed the numerical method based on the method of lines and higher order strong stability preserving schemes of order three and four. These schemes are explicit in nature and easy to implement specially to solve the nonlinear problems. Due to the stability-preserving nature of the scheme, the restriction on time steps is very mild. These schemes are very practical to use and produce very accurate results. Various test problems are considered to validate the scheme along with a comparison of \(L_2\) and \(L_\infty\) errors with the exact solution, resulting in high accuracy. The scheme is found to be better compared to existing schemes with less computational effort.

Coefficient Problems on Bi-Univalent Functions With \((p,q)\)-Gegenbauer Polynomials

2024-05-22T15:43:44+00:00

In this paper, our main aim is to study a new subclass of bi-univalent functions and to obtain initial coefficient bounds of starlike and convex bi-univalent functions involving \((p,q)\)-Gegenbauer polynomials. Also, we aim at obtaining sharp bound for Fekete-Szegö functional.

Fixed Point Theorems for \(\alpha\)-\(\psi\)-Contractive Mappings of Integral Type in \(C^*\)-algebra Valued~Metric Space

2024-05-30T07:33:17+00:00

In this paper, we introduce two classes of generalized \(\alpha\)-\(\psi\)-contractive type mappings of integral type and analyze the existence of fixed point for these mapping in \(C^*\)-algebra valued metric space. Our study extends and generalizes the result of several studies in the literature.

On the Spectrum of Generalized Zero-Divisor Graph of the Ring \(\mathbb{Z}_{p^\alpha q^\beta}\)

2024-05-20T16:09:49+00:00

The generalized zero-divisor graph of a commutative ring \(R\), denoted by \(\Gamma'(R)\), is a simple (undirected) graph with vertex set \(Z^*(R)\), the set of all nonzero zero-divisors of \(R\) and two distinct vertices \(x\) and \(y\) are adjacent if \(x^ny=0\) or \(y^nx=0\), for some positive integer \(n\). In this paper, we determine the adjacency spectrum of \(\Gamma'(\mathbb{Z}_{p^{\alpha}q^{\beta}})\), where \(p,q\) are distinct primes and \(\alpha, \beta\) are positive integers. Also, we obtain the clique number, stability number, diameter, and the girth of \(\Gamma'(\mathbb{Z}_{p^{\alpha}q^{\beta}})\).

Study of Activation Energy ofMagnetohydrodynamic Radiative Casson Nanofluid With Heat Source/sink and Cattaneo Christov Heat Flux Model Over Exponential Stretching Sheet

2024-03-09T10:02:23+00:00

The present work uses numerical analysis to examine the activation energy (A.E.) of a magnetohydrodynamic (MHD), mixed convective, radiative Casson nanofluid with heat source/sink, Cattaneo Christov’s heat flow model, “zero normal flux of the nanoparticles” across an exponentially stretched sheet, together with convective boundary condition. Numerous parameters’ impacts on the temperature profile, velocity, and concentration profile were graphically interpreted after investigation. The findings are very comparable to those found in openly available literature. The velocity profile was observed for Casson fluid parameter (β) buoyancy parameter (N), mixed convection parameter (λ), Magnetic parameter (M) and Suction parameter (S). Observed temperature profile for Magnetic parameter (M), mixed convection parameter (λ), Thermophoresis parameter (Nt), Biot number (Bi), Heat source/sink Parameter (Hg), Thermal relaxation parameter (δT), Prandtl Number (Pr), Eckert number (Ec), Radiation parameter (R). Examined concentration profile for Activation Energy (A.E.), temperature difference (δ), Thermophoresis parameter (Nt), Magnetic parameter (M), chemical reaction rate constant (σ∗), parameter of Brownian motion (Nb), Solute relaxation parameter (δC), and Schmidt Number (Sc). Additionally, for a range of values, the local Sherwood number, skin friction coefficient, and local Nusselt number were obtained.

The Dynamics of Local Bifurcation in a Novel Four-dimensional Hyperchaotic System

2024-05-08T10:29:49+00:00

This paper reports the findings of a novel four-dimensional autonomous quadratic hyperchaotic system characterized by three nonlinear terms. This system is developed by introducing nonlinear state feedback into the second equation of the three-dimensional Yang chaotic system. A comprehensive dynamical study follows the presentation of the mathematical model. The study includes dissipation and symmetry, stability of equilibrium points, and dynamic behaviors such as the Lyapunov exponent spectrum, bifurcation diagram, Poincaré maps, and orbits. The Poincaré-Andronov-Hopf bifurcation theorem and center manifold theory are used in local bifurcation analysis to investigate pitchfork and Hopf bifurcation at zero equilibrium points. Numerical simulations have confirmed the mathematical discoveries.

Characterisation of KrishSupra-P Distribution and Its Biomedical Application

2024-07-28T17:16:42+00:00

In this article, an innovative generalization of Sauleh distribution is considered and named it as KrishSupra-P Distribution (KSPD). Its several statistical properties were discussed and the model parameters are predicted using the Maximum Likelihood Estimation (MLE) approach. The model’s biomedical application using a real data set is discussed and contrasted with some other famous distributions.

A Study of Coupled Fixed Point in Multiplicative \(S\)-Metric Space

2024-06-18T13:27:35+00:00

This study presents a novel common coupled fixed point result for two mappings in multiplicative \(S\)-metric space. Uniqueness of this point is proven through the utilization of a compatibility condition, validated through a provided example. Additionally, an application to integral equations is discussed within this article.

PBIB-Designs and 2-Steiner Distance Eigenvalues of Split Graphs

2024-07-04T10:47:35+00:00

In this paper, we have considered split graph \(K_{n}\circ K_{1}\) with exactly four distinct adjacency eigenvalues. Since these graphs are not regular, it is laborious to construct block designs out of them. In this paper, we have shown the existence (hence construction) and non-existence of block designs arising out of split graphs \(K_{n}\circ K_{1}\). In the second half of this paper, we have partially tried an \(NP\)-hard problem of finding 2-Steiner distance matrix of the split graph \(K_{n}\circ K_{1}\). Furthermore, we have given interlacing for adjacency, distance and 2-Steiner distance spectra of split graph \(K_{n}\circ K_{1}\). Time complexity and algorithm for finding rank of a matrix is given.

A Mathematical Study on SIR Epidemic Model During COVID-19

2024-02-20T06:19:51+00:00

In this study, a novel epidemic model for COVID 19 (information propagation model) which explains the dissemination of information is examined. The model is related to the total number of primary communicators, onlookers, secondary communicators, immunizers, as well as quitters at network nodes. The approximate analytical results for the five compartments represented by primary communicators, onlookers, secondary communicators, immunizers as well as quitters are obtained by employing the Homotopy analysis approach. Our approximate analytical expressions are compared with the numerical simulation (MATLAB) and are shown to be a very good fit with all parameter values. The impacts of several parameters including initial transmission rate, propagation rates, exit rate, network average degree along with quit probability are shown in the graphical representation. With the help of this technique, the epidemic models SIR (Susceptible-Infected-Recovered), SVIR (Susceptible-Vaccinated-Infected-Recovered), SEIR (Susceptible-Exposed-Infected-Recovered), SVEIR (Susceptible-Vaccinated-Exposed-Infected-Recovered) of COVID 19, malaria, tuberculosis, and HIV can be readily solved.

Custom Filter-based Enhancement of MRI Images for Impulse Noise

2024-04-26T06:57:16+00:00

This paper introduces a novel approach for enhancing MRI images corrupted by impulse noise. Impulse noise often degrades image quality, especially in medical imaging applications where accurate representation is critical. The proposed method employs a custom filter to remove impulse noise while maintaining essential image features. The custom filter is designed by altering the average value of its surrounding pixels depending on whether the pixel is entirely black or completely white. The filter’s design is determined by the specifications of MRI images and noise patterns typically encountered in such data. The proposed custom filter exhibits the effective operation of the denoising technique and fully utilizes the benefits of the improved median filter in eliminating impulse noise. The results demonstrate an improvement in image quality based on various quality metrics. There is a 6% improvement in Peak Signal Noise Ratio, 0.5% in Mean Square Error, 1% in Structural Similarity Index Measure, 0.7% in Image Quality and 0.3% in Average Gradient compared to a conventional median filter. Experimental results demonstrate significant improvements in image quality and preservation of diagnostic information compared to existing methods. The proposed approach offers a promising solution for enhancing MRI images affected by impulse noise, thereby aiding in more accurate diagnosis and treatment planning in medical imaging.

Border Singularities as Solutions of an Ordinary Differential Equation

2024-05-20T08:16:37+00:00

The border singularities of a sixth-degree smooth function will be examined in this article by using real analysis and catastrophe theory. Next that, we provide an application of an ordinary differential equation (ODE) together with its boundary conditions. Using the local Lyapunov-Schmidt approach, we demonstrate that this function is identical to the key function that corresponds to the functional of the ODE. The bifurcation analysis of the function has been investigated by border singularities. The parametric equation for the bifurcation set (caustic) and its geometric description together with the critical points’ bifurcation spreading has been found.

A Numerical Scheme for Solving Fourth-Order Convection–Reaction–Diffusion Problems with Boundary Layers

2024-06-17T07:15:55+00:00

This paper presents a numerical approach for decoupling singularly perturbed boundary value problems involving fourth-order ordinary differential equations, characterized by a small positive parameter ϵ multiplying the highest derivative. Such equations arise in various engineering and physics applications, including the modeling of diffusing chemical species, viscous flows with convection and diffusion, and heat transfer in electronic chips or microfluidic channels. We focus on problems with Lidstone boundary conditions and demonstrate how the fourth-order equation can be decomposed into a system of two second-order problems—one independent of \(\varepsilon\), and the other singularly perturbed with ϵ multiplying the highest derivative. These problems often exhibit boundary layers, where the solution undergoes rapid changes near the domain boundaries. Numerical solutions to such higher-order problems are typically more challenging than those for lower-order ones. To address this, we propose a linear finite element method combined with a Shishkin mesh to accurately resolve boundary layers. We prove that the solution obtained from the decoupled second-order system is equivalent to that of the original fourth-order problem. The proposed method is direct and highly accurate, with computational time increasing linearly with the number of grid points.

A Second-Order Numerical Approximation for Volterra-Fredholm Integro-Differential Equations With Boundary Layer and an Integral Boundary Condition

2024-04-30T10:59:29+00:00

This study introduces a novel second-order computational technique to effectively tackle Volterra-Fredholm integro-differential equations, which are characterized by integral conditions and boundary layers. Initially, some analytical properties of the solution are given. Then, the approach involves implementing a finite difference scheme on the piece-wise uniform mesh (Shishkin type mesh). It integrates a composite trapezoidal formula for the integral component and utilizes interpolating quadrature rules and linear exponential basis functions for the differential part. The analysis of the method demonstrates that both the numerical scheme and its convergence rate exhibit second-order accuracy, ensuring uniform convergence with respect to the small parameter in the discrete maximum norm. Finally, two test examples are given.

On Bivariate Distributions with \(N\) Deleted Areas: Mathematical Definition

2024-07-29T08:49:27+00:00

A new definition of deleting \(N\)-intervals from the domain of two random variables which have known bivariate distribution (\(N\)-truncated bivariate distribution) has been provided. This type of distribution is useful in real life applications, where it gives us the opportunity to delete \(N\)-intervals of data. This will increase the accuracy of statistical analysis, which facilitates decision-making. As a result of this multiple truncation, changes occur in the statistical properties of the bivariate distribution from its original version. We have thoroughly processed these properties and applied this definition to the bivariate normal distribution.

Inventory Optimization Model for Deteriorating Items under Inventory Follows Shortage (IFS) and Shortage Follows Inventory (SFI) Policies

2024-07-26T17:42:39+00:00

This study focuses on optimizing inventory control for perishable commodities using preservation technologies, where payment delays and shortages are acceptable. Implementing correct preservation technology can help retailers reduce the negative impact of product deterioration on their earnings. We examine preservation technology as well as the permitted payment delay and aim to minimize the total cost under two different policies: SFI and IFS. The flow of inventory is quantitatively described for both policies using dynamic differential equations and the necessary boundary conditions. The decision variables’ values are determined using the derivative method of calculus. Furthermore, the optimum values of the Total cost function satisfy the Hessian matrix requirement, confirming its convexity. Based on all the results of the study we compare both the models for optimum Total Cost and found out the most and least affecting parameters for this model. The key finding of this study is the comparison of these models under two different policies to identify which policy is better to minimize the total cost for the retailers. We observed that IFS performs well to optimize the total cost. Numerical examples are also provided to show the practical use of the proposed model. Given the presence of preservation technology, we observed that the total cost in IFS policy is 6.81% higher than that of the case when it is absent, whereas in SFI the total cost is 5.29% higher than when it is not there. A table showing the effect of various parameters on the total cost function is provided and subsequent insights that are beneficial for retailers are also drawn and some unanswered queries are the highlights of this problem.

A Semi-Analytical Study on Non-Linear Differential Equations in Typhoid Fever Disease

2024-04-29T15:28:13+00:00

Typhoid infection dynamics is proposed in this work. The homotopy analysis method is used to solve the relevant equations, producing the approximate analytical solutions for the four compartments, such as Susceptible \((S)\), Exposed \((E)\), Infected \((I)\) and Recovered \((R)\). The numerical simulation is utilised using a Matlab programme. In addition, the problem's numerical simulation is provided. A comparison between the numerical simulation and the analytical solution reveals excellent agreement. A number of other parameters are also discussed and graphically represented, such as the rate of innate dying \(\psi\), the rate of human recruitment (birth) \(\varphi\), the rate of disease interaction \(\alpha\), the rate of unprotected symptoms \(\tau\), the rate of infectious recovery \(\theta\), the rate at which humans who have recovered lose temporary immunity \(\sigma\), and the total number of people who die from illness \(\delta\) in the compartment of Susceptible \((S)\), Exposed \((E)\), Infected \((I)\) and Recovered \((R)\). The homotopy analysis technique is employed to solve SVEIR, SEIR, SIR, and SVEIHR.

Rainbow Coloring of Magic Fuzzy Random Graphs

2024-04-05T08:07:38+00:00

This study introduces the concept of rainbow coloring to magic fuzzy random graphs, which combine the properties of fuzzy random graphs and magic graphs. A comprehensive study of rainbow coloring is presented in this study, which explores fundamental properties and computational issues. Also, it explores the role of rainbow coloring in magic fuzzy random graph connectivity and robustness, provides insights into the interaction between graph coloring and structure. Rainbow coloring is inherently theoretical and this finding contributes to our understanding of network design and distributed systems as well.

Painlevé Analysis, Lie Symmetries and Abundant Wave Solutions for Family Fifth Order Kdv Equations

2024-05-29T20:08:34+00:00

In this paper, we study integrability, similarity reduction and obtaining abundant solutions for the family fifth-order KdV equation. This equation expresses five different forms of the KdV equation, each of these equations has different applications in many fields, including fluid mechanics, ocean science and optics. We utilized Painlevé property for the governing equation to prove that the equation possesses Painlevé test. Then, the symmetry method is used to study the similarity reductions for the governing equation. Subsequently, we obtained a novel type of exact solutions for family KdV fifth-order by using \((G'/G)\)-expansion method. The obtained solutions included hyperbolic and trigonometric functions. The solutions are also presented in 3D shapes to show their properties contained kink wave, singular wave, anti-kink wave, periodic wave and solitary wave solution.

A Semi-Analytical Study on Multiscale Porous Biocatalytic Electrodes in the Enzyme Reaction Process

2024-07-14T16:25:50+00:00

A multiscale porous biocatalytic electrode’s oxidation of glucose is explained theoretically. The model that describes diffusion and response within a hydrogel film is composed by two non-linear differential equations. Approximate analytical findings of the glucose concentrations, current, and the oxidised mediator have been obtained via the new homotopy perturbation technique. Furthermore, an analytical calculation is performed to determine the ideal electrode thickness for the film by employing Ananthaswamy-Sivasankari Method (ASM). It also investigates how parameters affect current. Our approximate analytical expressions are validated by the numerical simulation (MATLAB).

Second Hankel Determinant for Certain Subclass of \(p\)-Valent Analytic Function

2024-07-26T04:44:02+00:00

The aim of this paper is to find sharp upper bound for the Second Hankel determinant and Fekete-Szegö functional for certain subclass of \(p\)-valent analytic function.

Travelling Wave Solutions to Fourth-Order Nonlinear Equation

2023-11-20T05:40:37+00:00

In this paper, we study the soliton solutions of the fourth-order nonlinear partial differential equations (NPDE). The Riccati-Bernoulli (RB) sub-ODE method is applied to the fourth-order NPDE to investigate the exact and traveling wave solutions. We secure singular periodic wave solutions, kink-type soliton solution, dark soliton and singular soliton solution, which have unlimited application in mathematical physic, science and engineering. Some figures for the obtained solutions are demonstrated.

Characteristics of Soft Semitrees: Enhancing the Soft Semigraph Framework

2024-07-23T13:29:47+00:00

Molodtsov pioneered the concept of soft sets, offering a method to classify elements of a universe based on a specified set of parameters. This approach serves to model vagueness and uncertainty. Semigraphs are a generalised form of graphs introduced by Sampathkumar et al. (Semigraphs and Their Applications, Academy of Discrete Mathematics and Applications, Mysore, India, 337 pages (2019)). Integrating soft set theory into semigraphs led to the creation of soft semigraphs. Due to its adeptness in handling parameterisation, the field of soft semigraph theory is rapidly evolving. In this study, we introduce the concept of soft semitrees and explore some of their characteristics.

Study of Mappings and Metric Spaces in Fixed Point Theory: A Review

2024-04-12T13:14:45+00:00

Fixed point theory is a rich, fascinating, and intriguing subject of mathematics. Though it is a completely established field of research, but very fresh. It has been a hot topic of research since its inception. In this work, we present an overview of the major branches of fixed-point theory along with the key results. The focus of this article is to investigate different types of mappings and their variants. Furthermore, a survey of several extensions of metric space has also been carried out.