In this work, traveling wave solutions (TWS) of a diffusive SIS epidemic model incorporating infection age structure and a general nonlinear incidence function are investigated. Through analysis of the associated differential system, the basic reproduction number R-0 is identified as the fundamental threshold parameter: when R-0 <= 1, disease invasion is prevented and no nontrivial wave emerges, whereas for R-0 > 1, the dynamics are characterized by a strictly positive minimal wave speed c & lowast; > 0. By employing spectral methods together with rigorously constructed upper and lower solutions, it is demonstrated that monotone waves connecting the disease free and endemic equilibria exist if and only if the propagation speed satisfies c >= c(& lowast;). Moreover, such waves are shown not to occur for 0 < c < c(& lowast;). Numerical simulations, formulated through phase plane trajectories and traveling wave profiles, are presented to validate the theoretical prediction of a sharp threshold at c = c(& lowast;).
This study identifies all Fibonacci numbers that can be expressed as the sum of two Jacobsthal numbers and all Jacobsthal numbers that can be expressed as the sum of two Fibonacci numbers. More precisely, we identify every non-negative integer solution (a, b, c) of the Diophantine equations Fa + Fb = Jcand Ja + Jb = Fc, where {Fc}c >= 0 and {Jc}c >= 0 are the sequences of Fibonacci and Jacobsthal numbers, respectively. An adaptation of Baker's theorem for linear forms in logarithms and Dujella and Peth & odblac;'s reduction method confirms our main results.
This study investigates the behavior of blood flow in the Left Coronary Artery (LCA) experiencing symmetrical narrowing, focusing on three stenosis geometries: triangular, trapezoidal, and overlapping (W-shape). It aims to develop a mathematical model of post-stenotic flow, assess the effectiveness of the Finite Volume Method (FVM), and analyze how stenosis shape and severity affect velocity and pressure. The governing equations of fluid motion are solved using FVM for spatial discretization and the SIMPLE algorithm to compute flow variables. Results show that FVM accurately simulates blood dynamics in narrowed arterial regions. Notably, when stenosis exceeds 50%, flow velocity increases significantly, reaching a peak at 75% narrowing. This condition also corresponds to a sharp pressure drop, especially in the trapezoidal model, indicating a higher potential for vascular damage and plaque accumulation. These changes in hemodynamic behavior highlight the critical role of stenosis geometry in altering blood flow. Therefore, understanding the influence of narrowing shape and severity is essential for clinical assessment and early diagnosis of coronary artery disease.
The present study numerically investigates the influence of thermal radiation and chemical reaction on thermosolutal mixed convection in a vertical pipe embedded in a porous medium, focusing on air water systems, which are directly applicable in technologies such as humidification-dehumidification desalination units and industrial cooling towers. The flow dynamics are modeled using the non Darcy Brinkman Forchheimer (NDBF) extended framework. The flow is driven by a combination of buoyancy forces arising from temperature and solute concentration gradients, along with an external pressure gradient. The governing coupled differential equations are solved using the Chebyshev spectral collocation method for high accuracy and spectral convergence. The results demonstrate that both the thermal radiation parameter (R) and chemical reaction parameter (gamma) significantly affect the velocity, temperature, and concentration profile of an air-water system. According to our findings, 'R' has a substantial effect on the instability of the fluid flow mechanism. In a Darcy porous media, where the Darcy number ranges from 10-5 to 10-2, the Prandtl number is taken as Pr = 0.71 for air and is Pr = 7 for water, it has been observed that the point of inflection arises faster in radiative flow than in non radiative flow with change of radiation parameter from 1 to 3 and subsequently to 5. The radiation parameter (R) leads to a decrease in temperature profile due to enhanced radiative heat loss, while it causes an increase in concentration profile. Additionally, as the chemical reaction parameter increases, the concentration profile diminishes due to species consumption. A similar suppressive effect on concentration is observed with higher Schmidt number (Sc), which indicates reduced mass diffusivity.
In this paper we consider the Cauchy problem for the second-order polyharmonic equation in an unbounded domain D, where boundary data are given on a part of boundary. The goal is to reconstruct a function v(eta) in D based on the given values of v, its Laplacian, and their normal derivatives. This is the ill-posed inverse problem, hence we use Carleman-type integral representations and stability estimates to ensure well-posed approximations. We construct the Carleman function and prove key inequalities governing its behavior. Additionally, Lavrent'ev regularization is applied to construct an approximate solution. We establish a regularized solution of the Cauchy problem for the biharmonic equation in an unbounded domain. These results provide a foundation for stable reconstruction methods for polyharmonic functions in certain classes of unbounded domains.
The assignment problem is the core concept of fundamental optimization problem in the field of engineering and management sciences. In some situations, decision maker needs to optimize the assignment cost, assignment time, deterioration rate, profit and so on simultaneously which gives way to multi-objective assignment problem. In practical problems, there are some unpredictable conditions due to time constraints, limitations in data, inaccuracy in measurements and so on. So, the single valued trapezoidal neutrosophic numbers is considered here to handle this fact. The objective of this paper is to determine the optimal compromise solution for the neutrosophic bi-objective assignment problem by considering all the parameters as single valued trapezoidal neutrosophic number. Initially using score function, we convert the neutrosophic problem into its deterministic problem. Transformation techniques can assist the decision makers to present their neutral views and manage uncertainties efficiently in the decision-making situations. So, we have developed the transformation techniques for assignment problem such as linear, hyperbolic, exponential membership function, fuzzy programming approach, neutrosophic compromise programming approach, global criteria method and weighted sum method to transform the deterministic bi-objective assignment problem into its single objective assignment problem under neutrosophic environment. The reduced problem is then solved by LINGO to find the optimal compromise solution and it lets the decision maker to specify the targets. To evaluate the viability and accuracy of our study, numerical illustrations have been conducted and comparisons have been made. Sensitivity analysis have been performed in this study. Finally, conclusions and future explorations are depicted.
A novel composite block backward differentiation formula of order four, known as CBBDF(4), has been developed to effectively solve stiff differential equations. This self-starting method approximates solutions by evaluating two points simultaneously at each integration step, incorporating two intermediate points among the interpolating values. The CBBDF(4) scheme is structured through three sub-steps: in the first and second stages, Euler's method computes the intermediate values, setting up the third stage for applying the CBBDF(4) method. The derived method has been established to be convergent and A-stable, making it well-suited for solving stiff problems. To validate the method's accuracy and efficiency, several stiff initial value problems are solved using various step sizes. The numerical results are compared with the existing method in terms of maximum error, average error and computational time. Comparative analysis indicates that the new composite block method is not only practical but also successful in delivering reliable results.
In this study, we develop and analyze efficient numerical schemes for solving the ill-posed complex Helmholtz equation in both two and three spatial dimensions under Dirichlet boundary conditions. The spatial discretization is carried out using the classical finite difference method and the nonstandard finite difference method, with the latter offering enhanced stability. The resulting linear systems are large, sparse, and highly sensitive to perturbations, reflecting the ill-posed nature of the problem. To address these challenges, two advanced iterative solvers are employed: the multigrid method, with the generalized minimal residual used as a smoother, and the bi-conjugate gradient stabilized method. Numerical experiments compare the computed solutions with solutions to verify accuracy, and condition numbers are evaluated to assess illposedness and stability. The results demonstrate that multigrid achieves robust and stable convergence, particularly in cases where the bi-conjugate gradient stabilized method fails, while the nonstandard finite difference method consistently improves numerical stability compared with the classical finite difference method.
This study presents a mathematical model for unsteady magnetohydrodynamics (MHD) fluid flow past a sphere, incorporating mixed convective heat transfer and suspended dust particles. The existence of dust particles significantly alters flow properties, influencing velocity, temperature distribution, and boundary layer behavior. The governing equations for fluid and dust phases are solved numerically using the Keller-box method implemented in MATLAB. The results demonstrate that increasing the magnetic field and dust particle density enhances fluid velocity while reducing temperature, leading to thinner momentum and thermal boundary layers. These effects are attributed to the Lorentz force, which accelerates fluid motion while reducing heat transfer efficiency. The findings provide valuable insights into MHD fluid flow applications, including pollutant dispersion and haze control on blunt surfaces. Additionally, this study is relevant to real-world applications such as cooling spherical electronic components, managing heat in nuclear fuel elements, and controlling thermal processes in plasma and metallurgical industries where dusty flows interact with magnetic fields. The novelty of this work lies in the simultaneous consideration of unsteady MHD effects, mixed convection, and dusty fluid interaction past a sphere, which has not been extensively addressed in previous studies. This integrated approach offers a more realistic framework for predicting heat transfer and flow behavior in complex engineering systems.
The rapid advancement of Pawlak's rough set (PRS) theory has motivated researchers to develop enhanced methodologies for decision-making, including applications in medical diagnosis particularly in identifying disease risk factors. The primary objective of this study is to introduce new mathematical techniques based on basic rough sets (as defined by Abu-Gdairi et al., 2021), employing nearly open concepts to enhance precision. Specifically, we propose the framework of nearly basic rough sets, incorporating pre-, semi-, and gamma-approximations, and present three distinct approximation methods. Their fundamental properties and interrelationships are systematically examined. The proposed approaches demonstrate superior accuracy compared with existing methods, as confirmed through both theoretical analysis and illustrative case studies. In particular, the application to COVID-19 diagnosis yielded an accuracy of 100% in the tested case. Moreover, we introduce a mathematical algorithm suitable for implementation in programming languages, thereby facilitating broader applications in medical research, economic modeling, and related theoretical domains.
Fractional calculus serves as a fundamental framework in mathematics, applied sciences, and the study of integral inequalities, offering versatile tools for modeling complex phenomena. This study focuses on establishing new Milne-type inequalities for various classes of functions within the framework of Atangana-Baleanu fractional integrals. The main contributions include fractional Milne-type inequalities for bounded functions, derived as special cases of the presented theorems and supported by illustrative examples. Furthermore, the work presents applications to the q-digamma function and provides refined error estimates associated with the generalized Milne-type quadrature formula.
For a graph Omega with vertex set V(Omega) and edge set E(Omega), its harmonic index is defined as H(Omega) = Sigma(uv is an element of E(Omega)) 2/du + dv, where d(u) and d(v) denote the degrees of vertices u and v, respectively. The harmonic index captures various structural characteristics of a graph, such as connectivity and the uniformity of its vertex degree distribution, and finds application in many fields, including molecular structure analysis, network layout optimization, and information dissemination analysis. In this paper, we first determine the extremal values of the harmonic index for chemical graphs, and chemical trees. Moreover, using some relevant operations, we fully characterize the trees with branch vertices that achieve the extremal values of the harmonic index.
The abstraction of bounded m-linear operators in normed spaces is extended in a new direction. Three statements on continuity of the operators are proved to be identical, and the space of operators (B (W m, V ), . ) is shown to be Banach if (V, . ) is Banach. Moreover, the definition of bounded m-linear operators in normed spaces is generalized to 2-normed spaces and accordingly, we extend related propositions and theorems.
In this study, using extended convex functions, we present and rigorously derive several new estimates of Hermite-Hadamard type inequalities in the context of quantum integrals. We apply power mean inequality and H & ouml;lder's inequality to extend these bounds further. As consequence of these results, we attain q-midpoint-like, Simpson's like, averaged midpoint-like, and trapezoid type results. In order to verify our presented results, we express those with the help of graphs by certain choices of parameters involved. In the end, to focus on utilization of the results, we offer two novel applications namely averaged midpoint-trapezoid-like and q-trapezoid like results of the produced results.
Mathematics and culture are interrelated things in human life. Culture is a way of life that develops and is shared within a community. Meanwhile, mathematics is the knowledge humans use to solve everyday problems. The use of technology in community life aligns with the development of cultural skills or environmental activities, symbolizing the advancement of mathematical skills within that society. The traditional handcraft is a heritage time immemorial, especially among the Dusun ethnic group in Kiulu, Tamparuli Sabah, as they used it in their daily activities, especially during the harvest seasons. This paper presents the appropriate geometric and symmetry concepts applied in the traditional handicraft products of the Dusun Kiulu community. This study employed a qualitative ethnographic approach using interviews, participatory observation, video recording, and documentation from the fieldwork to explore geometric and symmetry concepts in Dusun traditional handicrafts. The results showed that geometric concepts such as lines and angles, circles, transformations, and curved side geometry applied to the traditional handicrafts products, such as "Barait", "Sirung" and "Nurod" basket of the Dusun Kiulu community.
This work describes a HCV model infection with four state variables, such as uninfected and infected hepatocytes, antibodies, virions. Here, the model contains dual transmission rate such that the disease can be transmitted by infected cell also. The model incorporates two control inputs: ribavirin, which suppresses virion generation, and pegylated interferon(peg-IFN alpha), which targets infected hepatocytes. Four novel non-linear control schemes are introduced, which as the integer and fractional-order terminal, integral, double integral sliding mode controller. These controllers attempt to maximize the uninfected hepatocytes, antibodies and minimize the virions, infected hepatocytes to zero. We studied the comparison results of these controllers. Numerical simulations validate the theoretical conclusions.
Non-parametric and semi-parametric models allow us to predict the gender of individuals based on their survival time in lung-survival data. Primary, we used the North Central Cancer Treatment Group for patients with advanced lung survival dataset to apply the combination of survival models, along with the relevant confidence intervals. Based on the findings of this research, gender is statistically significant based on p-value, determinants in predicting coefficient of -0.5509, and hazard ratio of 0.5765 using cox proportional hazard with Breslow model. The results of these methods' analysis, chi 2 test, were utilized to ascertain whether a gender difference exists. The Kaplan-Meier curve for the entire dataset estimates a mean survival time of 327.5 days and a median survival time of 310 days; for males, the estimated median overall survival is 270 days, and for females, the median survival time is estimated to be 426 days. A study of the dataset indicates that sex significantly influences survival results. Gender is a determinant that impacts the duration of survival, with females often exhibiting a higher median survival time of 426 days. These findings emphasize the importance of considering age and gender when predicting survival outcomes and creating targeted interventions for certain subgroups.
Hamiltonicity plays a crucial role in the design of efficient interconnection networks, as it facilitates optimal routing of information between processors. The study of Hamiltonicity has inspired the development of several related concepts such as Hamiltonian laceability and Hamiltonian connectedness, fault tolerance and path covers etc., have lot of significance in computer networks as the presence of Hamiltonian path in network graphs is vital for addressing data communication challenges. A connected graph G is described as Hamiltonian-todd(teven)-laceable if for every pair of vertices x and y, there exists a Hamiltonian path such that the distance ds(x, y) = t where t is any odd (even) value satisfying 1 <= t <= Dm(G), with Dm(G) representing the graph's diameter. Furthermore, G is Hamiltonian-t-connected when it satisfies Hamiltonian-t-laceable condition for every t in the range 1 <= t <= Dm(G). This article examines the Hamiltonian todd-laceability and Hamiltonian teven-laceability properties of a chained cubic tree interconnection network, denoted as CCT(h, n) specifically for h = 1, n >= 2. The study's findings emphasize the distance specific Hamiltonian-t-connectedness of CCT (h, n) characterized by ds(x, y) = t, for 1 <= t <= Dm(G).
This paper discusses various methods for estimating the parameters of the Kumaraswamy (Kw) distribution and the acceleration factor in constant stress partially accelerated life test (CSPALTs) using Type-I generalized hybrid censored data. The constant stress partially accelerated life test CSPALTs using censored data that is Type-I generalized hybrid is explained in detail. In classical inference, maximum likelihood (ML) estimates are derived for both the model parameters of the Kumaraswamy (Kw) and the acceleration factor. The Fisher Information Matrix (FIM) is utilized to derive the approximate confidence intervals (ACIs) for all model parameters and the acceleration factor. The model parameters and the acceleration factor are estimated using bootstrap approach. Markov chain Monte Carlo (MCMC) method is suggested for Bayesian inference in order to optimize the related credible intervals (CRIs) and the Bayes estimators. In addition to, symmetric loss functions as well as asymmetric ones are considered. A collection of simulated data is analyzed to demonstrate the viability and appropriateness of the proposed methods. Furthermore, a Monte Carlo simulation is conducted to assess the effectiveness of the proposed methods.
Graph theory is extensively used in chemistry for modeling molecular structures, resulting in the formation of molecular graphs. These molecular graphs serve as a crucial link between mathematics and the natural sciences. By associating chemical networks with molecular characteristics, they facilitate the design of biologically active substances through quantitative structure-activity relationship studies. One of the fundamental tools for investigating such relationships is the use of topological indices. These indices can be derived through mathematical operations involving polynomials. Among the existing techniques for structural characterization of molecular graphs, the approach based on neighborhood M-polynomials proves to be particularly effective. The neighborhood M-polynomials offer significant advantages in identifying structural patterns, analyzing molecular configurations, encoding structural information, evaluating structural variance under graph isomorphisms and acting as mathematical descriptors in quantitative structure-activity relationship investigations. They are essential in predicting biological activities and, more importantly, in designing new molecules with specific desired properties. Transition metals such as zinc (II), manganese (II), cobalt (II) and copper (II) are wellknown for their extraordinary properties, which have attracted significant attention in medicine, food industries and production industries. This article aims to mathematically depict the above-mentioned transition metals through the use of neighborhood M-polynomials.
