Communications in Mathematics and Applications

Some Common Fixed-Point Theorems in Fuzzy Metric Space in the Context of Single and Set-Valued Mapping via OWC Mapping

2024-12-21T10:56:11+00:00

This study aims to construct some common theorems in FMS for two pairs of single and set-valued OCM mappings that satisfy integral type contractive requirements. Our findings expand upon and generalize a number of related findings from previous research for independent of continuity and completeness.

Developing a Risk Index for Start-Up Businesses in SMEs Using the Fuzzy Delphi Method (FDM)

2024-09-26T02:18:33+00:00

The growth of business start-ups, especially small and medium-sized enterprises, has grown due to their importance in driving economic development and creating jobs. However, many people who establish businesses struggle to sustain them beyond five years and eventually close them down. The challenges entrepreneurs face during their journeys are caused by the different risks and obstacles they face. In this context, effective management of risks is necessary for entrepreneurs to recognize and reduce such risks. This research article aims to construct a risk index for start-up businesses in SMEs by achieving expert consensus on major risk elements during start-up stages using the Fuzzy Delphi Method (FDM). The study employed a questionnaire developed through semi-structured interviews with entrepreneurs. Twenty one entrepreneurs from three industries were selected as a sample for this study. Analysing data using Microsoft Excel FDM showed four major risk factors affecting start-up businesses in small and medium-sized companies: Strategic Risk, Entrepreneurial Traits, Financial Risk, and Operational Risk. Using these factors, it is possible to generate a risk model for start-up firms within SMEs, which will serve as a guideline for entrepreneurs and other stakeholders in Malaysia. In addition, this study also assigned a weightage for every risk factor based on their priority. Lastly, using the weightage and basic formulation of the composite index, a general mathematical formulation of the Enterprise Risk Management Index was developed for start-up businesses in SMEs. Therefore, it will reduce the failure rate of start-up enterprises and increase the possibility of their success.

Sensitivity Analysis of a General Lung Diseases Progression Stochastic Model Considering Two Types of Diagnostic Tests

2025-01-11T08:45:33+00:00

Lung is a vital organ in the human body that is affected by many diseases each with different causes, symptoms and treatments. In the present paper, a general stochastic model for lung diseases has been developed considering various stages of progression of the disease. In the model, two types of diagnostic tests viz. normal and advance diagnostic tests have been taken into account. For the survival analysis purpose, mean sojourn times and mean survival time have been calculated for the model using concepts of Markov process and regenerative point techniques. Sensitivity and relative sensitivity analyses have also been performed to find out how the variation in parameters affect the mean survival time under certain specific conditions.

Mixed Hegselmann-Krause Dynamics III

2024-12-14T18:47:22+00:00

The mixed Hegselmann-Krause (HK) model encompasses both the Deffuant and HK models. Building upon our previous work (Mixed Hegselmann-Krause dynamics II, Discrete and Continuous Dynamical Systems - B 28(5) (2023), 2981 – 2993), we delve into the mixed HK model within a heterogeneous interaction framework. This involves either pair interaction, where all interacting pairs approach each other equally at their rate, or group interaction at each time step. Our research focuses on identifying circumstances conducive to consensus formation within this heterogeneous interaction paradigm. Furthermore, we delve into pair interaction scenarios where interacting pairs can approach each other at distinct rates. This differs from the Deffuant model, where an interacting pair can only approach each other at the same rate under a homogeneous threshold. Our investigation also aims to elucidate the conditions under which consensus can be attained under pair interaction with distinct approaching rates.

New Fixed Point Theorem for Generalized Expansion Mappings Utilizing Banach Algebra in \(\bar{\mathcal{G}}\)-CMSs

2024-10-25T12:20:34+00:00

Beg et al. [3, 4] were the first to propose generalized cone metric spaces as a comprehensive framework. They established the presence of fixed points in cone metrics for mappings and generalized metric spaces that adhere to specific contractive conditions. In our article, we introduce novel findings concerning fixed points within the context of \(\bar{\mathcal{G}}\)-Cone Metric Spaces using Banach Algebras (referred to as \(\bar{\mathcal{G}}\)-CMSBA) by utilizing generalized expansion mappings within the framework of Banach algebras.

On Adjacency Spectrum of Non-Zero Divisor Graph of \(\mathbb{Z}_n\)

2024-11-19T06:50:56+00:00

In this article, utilizing the concept of the \(H\)-generalized join graph, we derive the adjacency spectrum of \(\Phi(\mathbb{Z}_{p^k})\), where \(p\) be a prime and \(k \geq 1\) is a positive integer.

Advancing Fuzzy Algebra: Polynomial Subrings, Zero Divisors, and Related Properties

2025-01-09T06:20:39+00:00

This paper aims to expand classical ring theory into the fuzzy context, thereby strengthening the theoretical framework of fuzzy algebra. It introduces various types of fuzzy subrings, including fuzzy polynomial subrings and fuzzy matrix subrings, and explores their properties using the concept of fuzzy zero divisors. A significant contribution of this work is the development of the McCoy theorem for fuzzy polynomial subrings, leading to the definition of fuzzy McCoy subrings. Further, by building upon the notion of fuzzy zero divisors, the paper defines new classes of fuzzy subrings, such as fuzzy Armendariz subrings and fuzzy reduced subrings, and examines their fundamental properties and interconnections.

Investigating Weakly Connected 2-Domination in the Complementary Prism of Graphs and in Some Unary Graph Operations

2024-07-31T04:12:49+00:00

This paper dealt with the concepts of weakly connected 2-domination in the complementary prisms of graphs and graphs obtained by reducing their edges and vertices. In particular, bounds and exact values of the weakly connected 2-domination number in the complementary prism of graphs, graphs resulting from deleting an edge and vertex and line graphs are presented. In addition, properties of the graphs with weakly connected 2-domination number of complementary prism equal to 2 and 3, are provided.

Application of MBJ-Neutrosophic in BRK-Algebra

2024-10-20T07:04:17+00:00

This paper introduces the concept of MBJ-neutrosophic ideals and subalgrbras in BRK-algebras. We study various properties regarding these concepts. Also, a relationship between MBJ-neutrosophic ideals and MBJ-neutrosophic subalgrbras is presented. Moreover, various characterisations for MBJ-neutrosophic ideals are proved.

Efficacy Analysis of Different Modes of Learning in Undergraduate Courses During and Post COVID-19 Pandemic

2024-11-02T16:10:21+00:00

Prior to COVID-19, taking undergraduate courses Online was an added option. Most of the universities in Telangana offered classes in Physical mode prior to COVID-19, Online mode during COVID-19, and have been currently offering classes in Hybrid mode. The current study aims at analyzing a variety of elements from the perspectives of Online education to assess the quality as well as its effectiveness in undergraduate courses that are widely practiced in most of the colleges of Telangana State, India due to the unprecedented challenges posed by the pandemic. The present study would like to focus on the administrators of e-learning platforms, teachers, and learners. To compare the relative weights of various elements while comparing Hybrid learning, Virtual learning, and Physical learning, the Analytical Hierarchy Process (AHP) approach was utilized. The results of this study can also serve as the foundation for evaluating hybrid, online, and offline learning in undergraduate courses.

Natural Cubic Spline for Hyperbolic Equations With Constant Coefficients

2024-11-24T15:34:00+00:00

In this paper, we have considered second-order hyperbolic equations by implementing Natural Cubic Spline (NCS) method. Wave propagation and dynamic systems represents hyperbolic equations. We have considered the class of hyperbolic partial differential equations (PDEs) with constant coefficients and implemented NCS method both explicitly and implicitly. In our implementation we replaced spatial derivatives by second derivative of Natural cubic spline and time derivatives by central finite difference operator. To show the effectiveness of proposed method we have considered numerical examples having both Dirichlet and Neumann conditions. In order to evaluate the NCS method’s performance in managing various boundary behaviours which are frequently seen in real-world applications like heat conduction issues or wave propagation in bounded domains. The results are represented graphically exhibiting the accuracy of proposed NCS method. To check the efficiency of the NCS method we compared the results with analytical solution. The research not only demonstrates the Natural Cubic Spline’s flexibility in resolving hyperbolic PDEs, but also emphasizes its benefits, including its capacity to smooth spatial discretization, adjust to different boundary conditions, and work with both explicit and implicit time integration schemes. The findings verify that the NCS approach is a reliable tool for numerical simulations in domains where hyperbolic equations are used, including fluid dynamics, acoustics, and other domains.

Mean Iterative Approach for Multiple Polynomial Zeros and Convergence

2024-12-25T19:25:22+00:00

In this study, we propose a mean iterative approach of third order for solving a polynomial equation that has multiple type zeros. We used three prominent third-order algorithms for this build: Chebyshev, Halley and Super-Halley (CHS). For this CHS Combined Mean Method, we developed two forms of local convergence theorems to determine the convergence. We used the gauge function to determine the convergence of our technique. We employed two distinct forms of initial conditions on a field with norm to prove the local convergence theorems for the CHS combined mean technique. Our convergence analysis includes error estimates.

Common Fixed Point Results for Three Pairs of Self-Maps in Generalized \(E\)-Fuzzy \(b\)-Metric Space

2024-05-30T04:38:11+00:00

In this article, we introduce a new notion of generalized \(E\)-fuzzy \(b\)-metric space and proceed to establish common fixed point theorems for three pairs of self-mappings in this space. These theorems extend and improve specific existing fixed point theorems found in the literature.

Optimal Fourth- and Eighth-Order Iterative Solver and Their Basins of Attraction

2024-10-04T11:10:03+00:00

We developed a new, fourth- and eighth-order optimal approach for solving nonlinear equations in this study. With three function evaluations, the new methods’ convergence order is four; with four function evaluations, it is eight. Furthermore, according to the Kung-Traub hypothesis, it is optimal. In comparison to the suggested approaches, numerical results are provided to verify the superior computing efficiency of the current robust methods. We examine a wide range of practical issues, including projectile velocity to verify the suitability and efficacy of our suggested approaches. Lastly, in order to illustrate their dynamic behaviour on the complex plane, the basins of attraction are also provided.

The Wiener Index for Neutrosophic Labeling Graphs and Its Application in River Ecosystem Analysis

2024-11-28T14:54:22+00:00

This paper explores several topological indices in neutrosophic labeling graphs, including Randic’s, Zagreb, connectivity, and harmonic indices. Theorems linked to concepts are proved using appropriate instances. Application of the Wiener index is analyzed in river basin ecosystems across different seasons to understand seasonal changes in the ecosystem’s structure and interactions. This approach gives detailed information about the uncertainties and natural variations in river systems.

Eco-Epidemic Dynamics With Infected Communicable Infection From Prey to Predator: Effect of Recovery Delay for Predator

2024-11-22T18:08:56+00:00

In this paper, the system including communicable infection from prey to predator, represented by the growing rate of the prey as a healing of a predator’s, has been utilized to develop and analyze a four-dimensional, non-linear eco-epidemic model. In the context of the analysis, the exploration of all potential equilibrium points, along with an examination of their local stability conditions, has been conducted both with and without considering time delays. Additionally, the model’s positivity and boundedness have been confirmed. The positive and negative impact of the proposed model on the prey-predator population has been investigated aided by sensitivity analysis where the presence and validence of Bifurcation were elucidated by the numerical studies. The parameters were identified which explained the influence of disease and recovery delay over the model population. A right base for the perception of the behavioural effects of the prey-predator on eco-epidemiology has been prepared through the theoretical result. Based on the analytical result, numerical simulations were done so that the authenticity of the author’s numerical analytical approach using parameter values could be verified.

Upper bound Estimates of Fourth Order Hankel and Toeplitz Determinants for Certain Analytic Functions Connected with Three Leaf Function

2024-10-20T17:04:05+00:00

The purpose of this paper is to compute upper bounds of Hankel and Toeplitz determinants up to fourth order for some normalized univalent functions defined on the open unit disk in the complex plane associated with three leaf function. Suitable examples are provided in support of proven results.

Magneto-Thermoelastic Analysis of Ferromagnetic Plate Exposed to High-Frequency Induction Heater

2024-11-11T18:03:30+00:00

A mathematical model for studying the consequences of a moving high-frequency induction heater on a ferromagnetic plate material was presented in the context of Maxwell’s equation. Conducting currents are generated when the material is exposed to electromagnetic fields operating at high frequency. The losses due to conducting currents and the hysteresis effect are summed and considered as the total heat loss of the problem. The expressions for heat losses, temperature field, elastic field, and magnetic field are obtained across the plate material in the context of Maxwell’s equations and Ohm’s law and are solved using the double finite Fourier sine and Marchi-Fasulo integral transforms. Lastly, the effects of the plate dimensions, frequency, and velocity of the heater and the resistivity are discussed and analyzed graphically. The result of the presented investigation will enable us to ensure the feasibility of the efficient design and construction of electric devices with magnetic circuits characterized by reduced heat losses.

Continues Classical Quaternary Boundary Optimal Control Problem of Quaternary Linear Hyperbolic System

2024-12-03T16:01:43+00:00

This work concerns with the study of the continuous classical quaternary boundary optimal control problem or for brief quaternary boundary optimal control problem (QBOCP) controlling by quaternary linear hyperbolic system (QLHS). The existence theorem for a unique quaternary state vector solution (QSVS) for the QLHS as well as for its quaternary adjoint linear system (QALS) is proved via the method of Galerkin (MG) with given continuous boundary control quaternary vector (CBCQV). The existence theorem of a continuous boundary optimal control quaternary vector (CBOCQV) controlling by the QLHS is demonstrated. The directional derivative (DDV) for the objective functional (OF) is derived. Lastly, the necessity conditions for optimality (NCO) of the problem is studied.

Orthogonal Generalized \((\sigma, \tau)\)-Derivations on Semiprime \(\Gamma\)-Semirings

2024-12-28T07:25:01+00:00

In this study, we regard \(M\) as a semiprime \(\Gamma\)-semiring and introduce the notion of orthogonal \((\sigma,\tau)\)-derivations within such structures. We explore various characterizations of semiprime \(\Gamma\)-semirings and determine the conditions under which two \((\sigma,\tau)\)-derivations are orthogonal.

A Steady State Behavior of M/M/1 Queue with an Optional Differentiated Working Vacation and Arrival Restriction

2024-07-10T00:29:15+00:00

In this paper, we aim to study the steady-state behaviour of an M/M/1 queue with an optionally differentiated working vacations I and II. After finishing a busy period, the server takes either an optional working vacation I or an optional working vacation II. Customer arrivals are restricted when the server is either on an optional working vacation I or an optional working vacation II. The model’s stable solution is derived using the probability generating function. Additionally, specific expressions are used to discuss several performance measurements for the provided model. For cost optimization analysis, the Particle Swarm Optimization (PSO) method is also employed to reduce the total cost. We minimize the total cost of providing the best service by using the PSO optimization method. A few numerical examples are provided to illustrate the effects of different arrival rates, service rates, server vacation times, and customer waiting times.

Some New Oscillation Criteria for Certain Class of Quasilinear Elliptic Equations

2024-10-14T06:33:39+00:00

The main goals of this paper is to investigate a new oscillation for a certain class of quasilinear elliptic equations by using Riccati technique. Our main results are demonstrated with an example.

On Distribution of the Stock Market Risk with a Maximum Drawdown of a Wiener Process

2024-10-26T16:10:03+00:00

In this article, we investigate the Wiener stock market risk’s maximum drawdown distribution. The danger of stochastic volatility in stock prices can be reduced by taking into account the most reliable and accurate decisions using this distribution. We extract various significant dependability aspects of this distribution, including the hazard and inverted hazard rate functions, in addition to presenting the closed-form pricing formula, which demonstrated the precise maximum drawdown distribution of the price path from the perspective of mathematical analysis. Additionally, a Wiener stock market risk’s estimated value is calculated. This predicted value can be used to forecast future risk. Furthermore, we present a multivariate distribution of a maximum drawdown for an m-dimensional Wiener process and its key reliability aspects when this risk depends on the n separate and distinct primary stock market risks.

Impact of Variable Viscosity on Heat Transfer in a Horizontal Channel With Uniform Transverse Magnetic Field and Non-Uniform Wall Temperature

2024-11-24T09:39:18+00:00

This study reconnoiters variable viscosity fluid flow through horizontal channel with parallel walls imperiled to non-uniform temperature and uniform transverse magnetic field. The governing equations have been solved analytically by perturbation process for velocity and temperature fields. The volume flow rate athwart channel, skin friction, Nusselt number at lower and upper plates are calculated and epitomized the impacts of significant parameters through tables. The verdicts show that velocity, temperature are enhanced by increasing viscosity variation parameter.

A Note on Linear Multiplier Fractional \(q\)-Differintegral Operator With Varying Arguments

2024-12-23T12:11:08+00:00

We introduce new subclasses of analytic functions with varying arguments by making use of linear multiplier fractional \(q\)-differintegral operator. For functions belonging to these classes, we obtain coefficient estimates, distortion theorems, extreme points, \(q\)-Bernardi integral operator, and many more properties.

Independent Perfect Secure Domination in Graphs

2025-02-10T14:39:13+00:00

For a graph \(G=(V,E)\), a subset \(Y\subseteq V\) will be a dominating set if each vertex \(y\in V\backslash Y\) possesses a neighbour in \(Y\). A perfect secure dominating set of \(G\) is a dominating set in which every vertex \(y\in V\backslash Y\), has a unique vertex \(x\in Y\) such that \(xy\in E\) and \((Y\backslash \{x\})\cup \{y\}\) is a dominating set. In addition, if \(Y\) is an independent set, then \(Y\) is an independent perfect secure dominating set of \(G\). We have introduced the concept of independent perfect secure domination, presented the fundamental properties of this new parameter and investigated the independent perfect secure domination in certain classes of graphs such as the connected split graphs and the spiders in this paper. The complexity of the parameter is also discussed.

Estimation of Two Parameter Birnbaum-Saunders Distribution Based on Type-II Right Censored Reliability Data Using Genetic Algorithm

2023-03-29T21:58:49+00:00

The Birnbaum-Saunders (BS) distribution is a common reliability distribution used in scientific studies. There have been studies in the literature on parameter estimates for this distribution. Furthermore, in many studies, it is recommended to use Genetic Algorithm (GA) optimization methods for parameter estimation in modeling. This article focuses on estimating the model parameters of a twoparameter Birnbaum-Saunders distribution for Type II right censored reliability data. For parameter estimation of the Birnbaum-Saunders distribution, we propose the Genetic Algorithm (GA) method as an alternative to the Maximum Likelihood (ML) estimation method. Psi31 data is often used as an example to show the limitations of prediction methods when using inaccurate data. In addition, the performances of ML and GA methods were investigated through Monte Carlo simulation with different sample sizes and censorship rates.

Restrained Regular Domination on a Litact Graph

2024-09-28T09:18:11+00:00

We present the first research on restrained regular domination, which is a variant of standard domination. Assume that is a graph. If every vertex in has at least one neighbour in both and , and every vertex in has an identical degree, then a set is a ‘restrained regular dominating set’, abbreviated RRDS. The least cardinality of all G’s RRDS is the ‘RRD number of G’, represented by . We ascertain the optimal bounds that can be applied to , and we identify the most optimal lower bounds for and , both and are connected. We also characterise those graphs satisfying these bounds.

A Multifaceted Novel Approach to Identify Deceptive Reviews Based on Psychology Theories: A New Dataset

2025-08-07T04:39:41+00:00

As deception negatively impacts various areas, deception detection is an important field of study. This paper introduces a framework to detect online review deception. It studied aspects of deceptive reviews, considering the complex nature of deception in textual data and the low chance of direct detection. Furthermore, the paper presents a new corpus for deceptive reviews labeled using deception hints. This dataset was compiled in English and extracted from Google Maps reviews. We focused on the reviews of “restaurants” in New York. The novelty of this dataset is that the truthful and deceptive reviews were not deliberately collected; that is, participants were not requested to write lies, but the texts were collected after the individuals had written them. We used predefined criteria using deception indicators to differentiate deceptive and truthful reviews for this dataset. Each suggested indicator is not a definitive indicator on its own, but we assessed review authenticity using a set of indicators together. This paper aims to discuss lie detection strategies and theories, design a theory-based framework to detect deception in online reviews and implement the framework on a real-world dataset to provide a foundation for future empirical research and practical applications. The experimental results obtained from our labeled benchmark dataset showcase the effectiveness of this approach.