Communications in Mathematics and Applications

On $*$-$r$-Clean Rings

2025-03-31T09:25:07+0530

A ring with an involution $*$ is called $*$-$r$-clean if every element is a sum of a projection and a regular element (in the sense of von Neumann). In this article, several connections between $*$-$r$-clean rings and $*$-clean rings are given. Different characterizations of $*$-$r$-clean rings are presented. The passage of this property to some extensions of rings is studied.

Pythagorean Fuzzy $(l,u)$-Level Cuts and Their Applications to Fuzzy Normed Subrings

2025-09-11T08:01:51+0530

When attempting to quantify an ill-quantity, the Pythagorean Fuzzy Set (PFS) notion is essential. This study provides a $(l,u)$-level cut of Pythagorean Fuzzy Sets (PFSs). We define $(l,u)$-level cuts of a PFS $(P)$ as crisp sets consisting of elements $(x)$ for which the membership value is greater than $(l)$ and non-membership value is less than $(u)$. The concept of Pythagorean fuzzy normed subring is introduced and its properties are investigated. Additionally, the relationship between PFNSRs and Pythagorean fuzzy $(l,u)$-level sets is analyzed.

Dynamic Erlangian Queueing Model for Telemedicine: A Hybrid Approach to Healthcare Services Efficiency

2025-03-20T03:57:04+0530

In the realm of telemedicine, dynamic and priority-based service requirements are not sufficiently addressed by conventional queueing models. There is a need for more advanced and flexible queueing systems to increase the effectiveness and adaptability of telemedicine platforms. In this study, we present a Time-Dependent Erlangian Hybrid Queuing Model (TEHQM) to effectively schedule patient appointments and reduce waiting times. This approach strengthens our ability to design a telemedicine platform effectively, enhance resource allocation and staffing, facilitate the operation of a call center or help desk, oversee electronic health records (EHRs), optimize patient flow and capacity, evaluate and improve performance, and more. This strategy integrates a flexible queueing system with advanced technology such as artificial intelligence to strengthen real-time management. Furthermore, we present a case study demonstrating how TEHQM applied to flexible resource allocation significantly shortened wait times and queue lengths. We also discuss scalability, limitations, and future opportunities for enhancing telemedicine services using advanced queueing techniques. The findings of this study suggest that TEHQM can provide a robust and comprehensive framework to significantly enhance telemedicine services in real time.

Independent Perfect Secure Domination in Certain Cartesian Product Graphs

2025-09-29T17:03:27+0530

In a graph $G=(V(G),E(G))$, a set $S\subseteq V(G)$ is a dominating set of $G$ when every vertex in $V(G)\setminus S$ is adjacent to at least one vertex in $S$. A dominating set $S$ is called an independent perfect secure dominating set of $G$ if $S$ is an independent set and if for each vertex $w\in V(G)\setminus S$, there exists a unique vertex $v\in S$ such that $v$ is adjacent to $w$ and $(S\setminus\{v\})\cup\{w\}$ is a dominating set of $G$. The minimum cardinality of an independent perfect secure dominating set of $G$ is called the independent perfect secure domination number of $G$. In this paper, we determine the exact value of the independent perfect secure domination number of $G\square H$, where $G$ is a complete graph and $H$ belongs to specific graph classes such as complete graphs, complete bipartite graphs, paths, and cycles. Upper bounds for the independent perfect secure domination number of certain other Cartesian product graphs are also dealt with in this paper.

Polynomial Extensions of Fuzzy Baer and Fuzzy Quasi-Baer Subrings

2025-09-26T10:02:39+0530

This paper introduces and investigates the notion of fuzzy quasi-Baer subrings, establishing fundamental properties relative to classical fuzzy algebraic structures. We demonstrate a hierarchical relationship between fuzzy Baer and fuzzy quasi-Baer subrings, proving that while every fuzzy Baer subring is quasi-Baer, the converse fails in general. The study focuses on polynomial extensions of these structures, demonstrating that the quasi-Baer property is preserved under polynomial extensions, unlike the Baer property. A key result establishes that when a polynomial extension of a fuzzy subring is quasi-Baer, the original fuzzy subring must necessarily be Baer. These findings reveal important structural constraints in fuzzy ring theory and provide new insights into the behavior of annihilator conditions in fuzzy algebraic systems. The work extends classical Baer and quasi-Baer ring theory to the fuzzy setting, while highlighting crucial distinctions between these concepts in polynomial extensions. Our results contribute to the growing body of knowledge in fuzzy algebra and open new directions for research in fuzzy homological algebra and categorical generalizations of noncommutative ring-theoretic properties.

Computational Study for Band Structure Calculation of InPd Intermetallic

2025-02-10T12:00:12+0530

This paper reported the electronic and structural calculations of InPd at computational level. For studying these properties we have used Quantum Espresso code. The CsCl (B2-type) structure is where the current intermetallic crystallises. Calculations are made for the ground state parameters, including the lattice constant $(a_0)$, bulk modulus $(B)$, and its pressure derivative $(B')$. These findings are in good agreement with those that are currently available. In order to determine thermodynamical quantities, we have also examined Murnaghan’s equation of state. Their ductility is confirmed by the current intermetallics.

Early Detection of Melanoma: Deep Learning and $m$-Health for Optimized Patient Outcomes

2024-12-25T13:03:45+0530

Melanoma, an aggressive skin cancer, claims 57,000 lives annually worldwide. Early detection improves survival rates, reduces mortality, enhances treatment outcomes, increases awareness and provides economic benefits. However, detection faces challenges, including limited dermatologist availability, geographical constraints and inaccurate self-assessment. This study proposes an intelligent $m$-Health system using Squirrel Search Stochastic Gradient Descent (SSSGD) with Deep Quantum Neural Network (DQNN). The SSSGD is the integration of Squirrel Search Algorithm (SSA) and Stochastic gradient descent (SGD). Here, Type-2 Fuzzy and Cuckoo Search-Based Filter (T2FCS) is used for pre-processing Enhance image quality, resize, and normalize. Spine Generative Adversarial Network (Spine GAN) lesion segmentation, geometric transformations data augmentation, Grey Level Co-occurrence Matrices feature extraction, and DQNN detection trained by SSSGD, providing clinicians with a reliable Decision Support System (DSS) for early diagnosis and effective treatment, enhancing accuracy, computational efficiency, and patient outcomes. Performance evaluation metrics include loss curves, confusion matrix, sensitivity (98.61%), specificity (98.13%) and accuracy (98.42%). Results demonstrate enhanced performance, providing clinicians with a reliable DSS for early diagnosis and effective treatment.

Common Fixed Point Results for Self-Mappings in Generalized Fuzzy Cone Metric Spaces

2025-06-23T03:17:22+0530

A number of generalized contraction results already existed in Cone Metric Space (CMS), Fuzzy Metric Space (FMS) and generalized Fuzzy Cone Metric (FCM) spaces. In the present manuscript, we established some Common Fixed Point (CFP) results in generalized FCM spaces for compatible and weakly compatible self-maps using continuity and without continuity. We establish a new class of Fuzzy Cone Contraction (FCC) theorems extending existing results in the literature including some related examples to these outcomes.

A Study of Multiple Mappings in Multiplicative Metric Space

2025-06-01T02:01:59+0530

A fixed point result for two pairs of maps has been established in multiplicative metric space. The continuous sub-compatible mappings satisfy the generalized contraction condition. This theorem improves the results, which are accessible in current literature. An example has been discussed in support of the present paper.

Novel Parametric and Non-Parametric Cross-Entropy Models and their Applications in Portfolio Analysis

2025-09-10T11:14:21+0530

For real-world applications in the mathematical sciences, it is important to create adaptable models in probability spaces. Models that are too rigid or too limited typically don't show how unpredictable and complicated these systems really are. To solve this problem, we need families of random models that can make the analytical framework more flexible and strong. This work presents a collection of novel parametric and non-parametric discrete cross-entropy models aimed at improving flexibility while maintaining mathematical precision. The fundamental purpose of these models is to create a framework for creative optimization techniques that may be used across varied situations. The suggested cross-entropy models build on standard probability-based methods by adding new distance metrics that make it easier to judge uncertainty and unpredictability. These models are important in theory and also have evident real-world uses. We specifically concentrate on their use in portfolio analysis, emphasizing risk assessment and the best allocation of assets. By using the created models, we illustrate how investors and decision-makers may more correctly reflect fluctuations in risk and return, leading to better-informed strategies for investing under uncertainty. The research shows that you may use either parametric or non-parametric versions of the models, depending on what data you have and what assumptions you make about the situation. When distributional assumptions are true, parametric forms provide you structured and efficient estimates. When these assumptions are weak or don't exist, non-parametric forms give you more freedom. Together, they provide a complete toolset for addressing uncertainty in complex systems. This paper advances the development of cross-entropy-based models inside probability spaces and demonstrates their efficacy in financial decision-making, especially regarding portfolio risk assessment and optimization

On Some Extended Results in Functional $q(t)$-Calculus: Theoretical and Numerical Applications

2025-07-07T10:41:55+0530

This paper provides further applications of a functional approach to quantum calculus, towards functional $q(t)$-integral, functional $q(t)$-Taylor’s formula difference equations with variable coefficients together with functional quantum congruence theory.

Certain Applications via $(\alpha, \beta)$-$\mathcal{Z}$-Contraction Type Fixed Points in Bipolar Parametric Metric Space

2025-01-31T10:11:49+0530

This work defines $(\alpha, \beta)$-$\mathcal{Z}$ contraction mappings to establish fixed point results in a bipolar parametric metric space. Our findings generalize and enhance several well-known results from the fixed point (FP) theory literature. A good example is also provided to confirm the veracity of the acquired results. In addition, we provide applications for homotopy and integral equations, as well as an explanation of the significance of the obtained results.

On Some Bounds of Fuzzy Secure Domination Number

2025-06-02T06:36:25+0530

In a fuzzy graph $G_f(\rho, \eta)$ with vertex set $V$, a subset $D \subseteq V$ is called a dominating set if each vertex in the graph is either a member of $D$ or has at least one strong neighbor in $D$. A secure dominating set $S$ is a dominating set with the additional property that every vertex outside $S$ has a strong neighbor in $S$, that can swap places with it and still maintain domination. The minimum fuzzy cardinality of such secure dominating sets is called the secure domination number, denoted $\gamma_{sc}(G_f)$. This paper explores bounds for the fuzzy secure domination number and examines its relationship with the domination number, independence number, and matching number.

On the Pendant Regular Domination Number of a Graph

2025-07-02T05:49:42+0530

This paper introduces and explores a novel domination parameter in graph theory, termed the pendant regular domination number. We initiate a foundational study by determining the exact values of this parameter for several standard and well-known graph families, including paths, cycles, stars, and complete graphs. In addition, few fundamental bounds are deduced and the behavior of the pendant regular domination number is examined under various graph operations such as the corona, join, and Cartesian product.

Minimization Makespan Problem With an Aging Effect Based on Improved Arithmetic Optimization Algorithms on Job Shop Machines

2025-03-14T11:56:55+0530

The research delves into optimizing the Job Shop Scheduling Problem (JSSP) by considering aging effects and release time. This paper introduces an Advanced Arithmetic Optimization Algorithm (IAOA) designed specifically to minimize the makespan. IAOA operates by translating the continuous solution space into the discrete realm of JSSP through ROV transformation rules. It encodes and decodes the job shop problem using an insertion greedy decoding algorithm. To refine the conventional Arithmetic Optimization Algorithm (AOA), this study introduces a nonlinear Mathematical Acceleration Function (MOA) along with six neighborhood search strategies. Evaluating its performance involved a comparison of IAOA against AOA, Grey Wolf Optimizer (GWO), and Arithmetic Trigonometric Optimization Algorithm (ATOA) across 33 benchmark problems. The experimental results underscore IAOA’s superior optimization efficacy and its ability to converge efficiently when dealing with JSSP. Notably, IAOA successfully mitigates AOA’s limitations, particularly in achieving higher solution accuracy and faster convergence speed.

A NOVEL FOUR-STEP ITERATION SCHEME WITH NUMERICALS

2025-06-02T06:46:23+0530

This study presents a four-step iteration method for approximating the fixed points of a contractive-like
mapping. We also consider the strong convergence, order of convergence and stability of the proposed method.
Moreover, we present some numerical illustrations to validate our method and these numerical illustrations have
been compared with some similar schemes available in the literature.

Strong zero-divisor graph of p.q.-Baer $*$-rings

2025-08-23T12:50:20+0530

In this paper, we study the strong zero-divisor graph of a p.q.-Baer $*$-ring and establish conditions, based on the smallest central projection in the lattice of central projections, under which the graph contains a cut vertex. We prove that the set of cut vertices forms a complete subgraph. Furthermore, we show that the complement of this graph is connected if and only if the $*$-ring contains at least six central projections. The diameter and girth of the complement are determined, and we characterize p.q.-Baer $*$-rings whose strong zero-divisor graph is complemented.

Applications of Generalized Mersenne Polynomials to a General Subclass of Bi-Bazilevic-Type Functions

2025-08-11T08:38:37+0530

This paper introduces a new subclass of generalized bi-Bazilevic-type functions associated with the generating function of generalized Mersenne polynomials, which encompasses several eminent and widely studied subclasses, such as bi-starlike and bi-convex functions. The use of generalized Mersenne polynomials highlights the applicability of special polynomials in geometric function theory. By applying the generating function of the generalized Mersenne polynomials, we derive coefficient bounds for the initial Taylor–Maclaurin coefficients and provide estimates for the Fekete–Szego inequality. Furthermore, we discuss several corollaries by specifying particular choices of the parameters.

Some New Results on the Generalized Double Laplace Transform and Its Properties

2025-09-10T15:07:21+0530

Integral transformations play a fundamental role in various scientific and engineering domains, providing powerful tools for solving differential, integral, and functional equations. Among these, the Laplace transform is one of the most widely used, and many other emerging integral transforms are direct generalizations or modifications of it. This paper focuses on an extension of the classical Laplace transform to a new generalized double Laplace transform framework. The proposed transform is defined with respect to arbitrary, strictly increasing kernel functions, enabling greater flexibility in handling problems with non-uniform scaling in multiple variables. Fundamental properties of the transform, including linearity, shifting, change of scale, and convolution theorems, are established. Moreover, the study establishes that the classical double Laplace transform arises as a particular case within the framework of the generalized version.The derived framework brings together multiple existing transforms while extending their applicability to a broader range of partial differential equations in mathematics and physics.

Newly Defined Conformable Double Laplace Transform and Partial Differential Equations with Conformable Derivative

2025-06-20T08:57:56+0530

In the present study, newly defined conformable double Laplace transform and conformable derivatives are expressed. Some new properties of conformable double Laplace transform are investigated.The efficiency and reliability of this method is illustrated by finding exact solution of initial and boundary value problems of some known fractional partial differential equations with conformable derivative.

Fractional-Order Williamson Fluid Flow with Slip and Cross-Diffusion Over a Variable-Thickness Sheet

2025-07-22T07:05:29+0530

This study investigates heat and mass transfer in non-Newtonian Williamson fluid flow over a variable-thickness stretching sheet, incorporating Caputo fractional derivatives, velocity slip conditions, and Soret and Dufour effects. A fractional-order model captures memory effects, enhancing the representation of shear-thinning behavior and cross-diffusion phenomena. Governing equations are solved numerically using a hybrid Crank-Nicolson and spectral method, with stability and convergence rigorously analyzed . Results reveal that increasing the fractional order (α) from 0.1 to 0.9 yields a 300% increase in heat transfer rate (from 250 W/m² to 1000 W/m²) and a 53% reduction in thermal boundary layer thickness (from 0.015 m to 0.007 m). Slip conditions further reduce boundary layer thickness by 16%, while magnetic field and cross-diffusion effects amplify transfer rates by 43%. The model offers 20-30% improved accuracy over traditional approaches, with applications in polymer extrusion and biomedical microfluidics. Future work will explore variable material properties and multi-phase flows.

Study of Hybrid Nano Particles Flow in an Inclined Circular Artery

2025-08-27T08:52:52+0530

In the present article steady fluid flow through an inclined tube of non uniform cross section with stenosis and diltation has been investigated under the influence of hybrid nanofluid particles. Homotropy pertubation method is applied to solve the flow equations assuming mild stenosis, to determine the axial velocity, wall shear stress, pressure gradient and stream lines.Studies have examined how parameters effects on pressure gradient, impedance resistance and wall shear stress.

A study on bipolar soft b metric spaces

2025-03-18T08:15:15+0530

In this work, we give a bipolar soft b metric space, which is constructed from b metric space and several soft point sets. Next, using this framework, we illustrate several fixed point theorems using bipolar soft contractive mappings and offer significant clarifications on this idea through medical applications.

Lucas Wavelet Analysis of the Squeeze Film Characteristics between a Sphere and a Flat Plate of Couple Stress Fluid Model

2025-07-04T10:35:51+0530

This study presents a numerical examination of the influence of couple stresses on the squeeze film behavior between a sphere and a flat plate, grounded in microcontinuum theory. The revised Reynolds equation that regulates the squeezing film pressure is formulated by employing the Stokes constitutive equations to incorporate the couple stress effects resulting from the lubricant mixed with distinct additives. Lucas wavelet based numerical scheme is developed for the numerical solution of the governing modified Reynolds equation. The numerical solution indicates that the presence of couple stresses results in an increase in the film pressure. Overall, the effects of couple stress, as defined by the couple stress parameter, lead to an enhancement in the load-carrying capacity when compared to the traditional Newtonian-lubricant scenario. The characteristics of the squeeze film in the system are enhanced.

Cordial Labeling of the Line Graph of Bistar

2025-08-14T06:33:01+0530

A binary vertex labeling f of a graph G is called a cordial labeling if |vf (0) − vf (1)| ≤ 1 and |ef (0) − ef (1)| ≤ 1. A graph which admits cordial labeling is called a cordial graph.
In this paper, the necessary and sufficient conditions for the line graph of Bistar Bn,p to be cordial when p = n + 4m and p = n+4m+2 where m ∈ N ∪ {0} are discussed.

Existence of a solution of an infinite system of weighted Atangana-Baleanu fractional integral equation via measure of non-compactness on a tempered sequence space.

2025-04-04T07:41:45+0530

The goal of this study is to investigate the existence of a solution of an infinite system of weighted Atangana-Baleanu fractional integral equation via a newly constructed generalised form of the Darbo's fixed-point theorem on a tempered sequence space. Furthermore, an example has been illustrated to portray the effectiveness of the obtained result.

Mathematical Modelling on Functioning of Blood Flow in Arteries and Rheology

2025-08-05T14:51:36+0530

Navier-Stokes equations present a comprehensive numerical simulation of arterial flow by integrating fluid dynamics, non-Newtonian blood rheology, and arterial wall mechanics in a coupled framework. Using cylindrical coordinates with axisymmetric assumptions, the flow of blood is presented by the Navier-Stokes equations, while the viscosity is wall dynamics are Carreau-Yasuda non-Newtonian law to reflect the decrease in blood viscosity with increased blood flow. The arterial wall dynamics are represented by a linear elastic model, incorporating radial displacement as a function of internal pressure and wall elasticity. A coupling condition links pressure to wall deformation allowing for accurate simulation of fluid structure interaction. The simulation reveals critical insights into the propagation of pressure and mechanical response of arterial length, the role of shear-dependent viscosity in shaping flow profiles and the transmission and wall compliance effects, validating the physiological relevance of the improved model. The outcomes of this research hold significant potential for applications in cardiovascular diagnostics, treatment strategy, and the design of vascular prosthetics or drug delivery systems.