Communications in Mathematics and Applications

Path Fuzzy Bitopological Spaces on Fuzzy Directed Graphs

P. S. Gholap, V. E. Nikumbh, P. G. Andhare, S. B. Gaikwad — Sat, 30 Nov 2024 00:00:00 +0000

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.

A mathematical study on SIR epidemic model during COVID-19

Dr. V. ANANTHASWAMY — Thu, 20 Feb 2025 00:00:00 +0000

In this study, a novel epidemic model for mathematics (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 semi-analytical results for the five compartments represented by primary communicators, onlookers, secondary communicators, immunizers as well as quitters are obtained by employing 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.

A Semi-analytical study on non-linear differential equations in typhoid fever disease

J. Chitra, V. Ananthaswamy, M. Shruthi — Thu, 20 Feb 2025 00:00:00 +0000

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, Exposed, Infected and Recovered . 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 , the rate of human recruitment (birth) , the rate of disease interaction , the rate of unprotected symptoms , the rate of infectious recovery , the rate at which humans who have recovered lose temporary immunity ,and the total number of people who die from illness in the compartment of Susceptible , Exposed , Infected and Recovered . The homotopy analysis technique is employed to solve SVEIR(Susceptible-Vaccinated-Exposed-Recovered),SEIR(Susceptible-Exposed Infected-Recovered),SIR(Susceptible-Infected-Recovered),andSVEIHR(Susceptible-Vaccinated-Exposed-Infected-Hospitalized-Recovered).

Coefficient Problems on bi-univalent functions with (p,q) -Gegenbauer polynomials

Govinda Raju R, Ruby Salestina M, N B Gatti — Thu, 20 Feb 2025 00:00:00 +0000

In this paper our main aim is to study the new subclasses of biunivalent functions and to obtain initial coefficient bounds of starlike and convex biunivalent functions involving (p,q) - Gegenbauer polynomials. Also we aim at obtaining sharp bound for Fekete-Szego functional.

Stochastic modelling by combining a random contraction and a random dilation for decision making

Constantinos T. Artikis, Panagiotis T. Artikis — Thu, 20 Feb 2025 00:00:00 +0000

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.

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

Anshu Sharma — Thu, 20 Feb 2025 00:00:00 +0000

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.

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

Ambeswar Phukon, Nabani Narzary — Thu, 20 Feb 2025 00:00:00 +0000

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.

Lacunary statistical convergence of order \alpha for generalized difference sequences in partial metric space.

Ritu — Thu, 20 Feb 2025 00:00:00 +0000

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.

Border singularities as solutions of an ordinary differential equation

Hussein kadhim — Thu, 20 Feb 2025 00:00:00 +0000

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 to Solve Fourth Order Convection Reaction Diffusion Problems with Boundary Layers

Charuka Wickramasinghe — Thu, 20 Feb 2025 00:00:00 +0000

This paper presents an approach to decoupling singularly perturbed boundary value prob- lems for fourth-order ordinary differential equations, which feature a small positive parameter ε multiplying the highest derivative. These equations have various real-world applications in engineering and physics, such as describing the behavior of diffusing chemical species, viscous flows with convection and diffusion effects, and heat transfer in microfluidic channels or electronic chips. We focus on Lidstone boundary conditions and demonstrate how to break down fourth-order differential equations into a system of second-order problems—one without the parameter and one with ε multiplying the highest derivative. Singularly per- turbed problems often involve boundary layers where the solution changes rapidly near the boundaries. Numerical solutions for higher-order problems are significantly more challeng- ing than those for lower-order problems. We propose a linear finite element algorithm and incorporate the Shishkin mesh scheme to capture the solution near the boundary layers. We prove that the solution obtained from the second-order system is equivalent to that of the fourth-order problem. Our solver is both direct and highly accurate, with computation time scaling linearly with the number of grid points.

A SEMI-ANALYTICAL STUDY ON MULTISCALE POROUS BIOCATALYTIC ELECTRODES IN THE ENZYME REACTION PROCESS

Dr. V. ANANTHASWAMY — Thu, 20 Feb 2025 00:00:00 +0000

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 differential equations in non-linear. Approximate analytical findings of the glucose concentrations, current, as well as 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 technique. It also investigates how parameters affect current. Our approximate analytical expressions are validated by the numerical simulation (Matlab).

On Bivariate Distributions with N Deleted Areas: Mathematical Definition

Mohamed El-Hadidy, R. Alraddadi — Thu, 20 Feb 2025 00:00:00 +0000

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.

Rainbow coloring of Magic Fuzzy Random Graphs

ABIRAMI R — Thu, 20 Feb 2025 00:00:00 +0000

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.

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

Feriha GURMAN, Musa Cakir — Thu, 20 Feb 2025 00:00:00 +0000

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.

Painlevé analysis, Lie symmetries and abundant wave solutions for family fifth order KdV equations

Ahmed Gaber, Doaa M Mostafa — Thu, 20 Feb 2025 00:00:00 +0000

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 have different applications in many fields, including: fluid mechanics, oceans science and optics. We utilized Painlevé property for governing equation to prove that the equation possessing Painleve test. Then, 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 that contained kink wave, singular wave, anti-kink wave, periodic wave and solitary wave solution.

PBIB-Designs and 2-Steiner distance eigenvalues of split graphs

Medha Huilgol, Sreepriya Asok — Thu, 20 Feb 2025 00:00:00 +0000

In this paper, we have considered split graph Kn XK1 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 Kn XK1. 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 Kn XK1. Furthermore, we have
given interlacing for adjacency, distance and 2-Steiner distance spectra of split graph Kn XK1. Time
complexity and algorithm for finding rank of a matrix is given. A conjecture concludes the paper.

Second Hankel Determinant for certain Subclass of p-valent Analytic Function

Ashwini s, Ruby Salestina M, Kaliappan Vijaya — Thu, 20 Feb 2025 00:00:00 +0000

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

Custom Filter-based Enhancement of MRI Images for Impulse Noise

Kalpana Patil, Varsha Bendre — Thu, 20 Feb 2025 00:00:00 +0000

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 that of 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.

On the spectrum of generalized zero-divisor graph of the ring $\mathbb Z_{p^\alpha q^\beta}$

Anita Lande, Dr. Anil Khairnar — Thu, 20 Feb 2025 00:00:00 +0000

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 $\Gamma'(\mathbb Z_{p^{\alpha}q^{\beta}})$.

A study of coupled fixed point in Multiplicative S-Metric space

Manjusha Gandhi, Anushree Aserkar, Shiney Chib — Thu, 20 Feb 2025 00:00:00 +0000

This study presents a novel common coupled fixed point result for two mappings in multiplicative S-metric space. The 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.

Characteristics of Soft Semitrees: Enhancing the Soft Semigraph Framework

Bobin George, Rajesh K. Thumbakara, Sijo P. George, Jinta Jose — Thu, 20 Feb 2025 00:00:00 +0000

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 generalized form of graphs introduced by Sampathkumar. The integration of soft set theory into semigraphs led to the creation of soft semigraphs. Due to its adeptness in handling parameterization, 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.

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

Ali Hassan — Thu, 20 Feb 2025 00:00:00 +0000

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, Poincar´e maps, and orbits. The Poincar´e-Andronov-Hopf bifurcation theorem and center manifold theory are used in the local bifurcation analysis to investigate pitchfork and Hopf bifurcation at zero equilibrium point. Numerical simulations have confirmed the mathematical discoveries.

Fixed point theorems for α-ψ- contractive mappings of integral type in C*-algebra valued metric space

Manoj Kumar Antil, Neetu — Thu, 20 Feb 2025 00:00:00 +0000

In this paper, we introduce two classes of generalized α-ψ- contractive type mappings of integral type and analyse 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.

Higher-order numerical technique based on strong stability preserving method for solving nonlinear Fisher equation

VIKASH VIMAL — Thu, 20 Feb 2025 00:00:00 +0000

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 L2 and L∞ errors with the exact solution, resulting in high
accuracy. The scheme is found to be better compared to existing schemes with less
computational effort

Characterisation of KrishSupra-P Distribution and Its Biomedical Application

PRASEEJA C B, PRASANTH C B, Subramanian C, Unnikrishnan T — Thu, 20 Feb 2025 00:00:00 +0000

Here 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.

Travelling wave solutions to fourth-order nonlinear equation

Salisu Ibrahim — Thu, 14 Nov 2024 00:00:00 +0000

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.

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

Dr. Asha Rani, Bharti — Thu, 20 Feb 2025 00:00:00 +0000

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.