https://mmr.khu.ac.ir/ Mathematical Research en daily 1 Sun, 26 Jul 2026 00:00:00 +0330 Sun, 26 Jul 2026 00:00:00 +0330 https://mmr.khu.ac.ir/article_11620.html Abstract: In this paper, we define and discuss the properties of various classes of analytic multivalent functions by using Gegenbauer polynomials. We make use of Gegenbauer polynomials to introduce the new differential operator. This operator is based on the convolution Hadamard product. Also, we define a new subclass of p-valent starlike and convex functions of order alpha by using q-derivative operator. In addition, we derive families of analytic univalent functions associated with Gegenbauer polynomials and q-derivative operator. Also, we obtain coefficient bounds for the functions in such new subclasses of analytic functions. Moreover, we obtain several corollaries and results for p-valent starlike and convex functions of order alpha. We establish certain growth and distortion theorems in such new subclasses of analytic functions. Moreover, using the concept of the (q, delta)-neighborhood, we provide several inclusion symmetric relations for certain (q, delta)-neighborhoods of analytic univalent functions with negative coefficients. Various q-inequities are also discussed in more details https://mmr.khu.ac.ir/article_11621.html This study investigates the role of fear and anxiety induced by the spread of the Chikungunya virus in the community from a mathematical perspective. Fear can have dual effects: increasing fear levels enhances public awareness, promotes adherence to preventive measures, and encourages faster medical consultation by symptomatic individuals; however, excessive fear may lead to delays in hospitalization, increased chronic complications, and wider disease spread. To examine these effects, a‏‎n ‎‎$‎‎11$ ‎‎$11$-compartmental mathematical model for virus transmission was developed, consisting of $8$ human subpopulations and $3$ vector (mosquito) subpopulations. The initial conditions were determined based on real data from Colombia in $2015$ and biological assumptions. The main model parameters were calibrated using weekly data on symptomatic cases. The results indicate that the model successfully reproduces the epidemic trend and the dynamics of infected and chronic populations. Moreover, behavioral parameters such as $gamma_alpha$ and $q_s$ play a crucial role in regulating the burden on the healthcare system and determining the final disease load.‎‎‎‎‎‎‎‎‎‎‎‎ https://mmr.khu.ac.ir/article_11622.html The entropy is an important concept in most of sciences. The aim of this study is introducing mathematical models of the notions of Rényi entropy and exponential Rényi entropy on effect algebra with the Rieze decomposition property. For this purpose, at first the concepts of partition, refinement of partition, join refinement of partitions and state function on effect algebra with the Rieze decomposition property are defined. Then, Rényi entropy and exponential Rényi entropy of order q are introduced and have proved that these entropies are positive, decreasing functions respect to q and finer partitions have bigger entropies. In addition, the property of concavity of states on effect algebra with the Rieze decomposition property has proved. In the next step, the Rényi conditional entropy and Rényi exponential conditional entropy of a partition respect to other partition of order q are introduced. The ergodic properties of introduced entropies are investigated and it is proved that Rényi entropies are a generalization of Shannon entropies. https://mmr.khu.ac.ir/article_11623.html Lie groups and homogeneous spaces, due to their simple structure, have always been considered for testing geometric conjectures and exploring new concepts. In this article, we define the concept of metallic vector fields. Subsequently, we investigate the existence of these fields on three-dimensional homogeneous manifolds equipped with Riemannian and Lorentzian metrics. https://mmr.khu.ac.ir/article_11624.html In this study, we discuss the prediction of k-record values from a future sequence. By considering the Rayleigh distribution, we derive Bayesian point predictions as well as Bayesian prediction intervals for k-record values when the data is collected by the Record ranked set sampling scheme method. At first, based on Squared error and Linex loss functions, the mean squared prediction errors are applied to comparing these point predictors. Next, to evaluate the prediction intervals, the average interval length and coverage probability are computed. Finally, a simulation study and an application example are presented to compare and show the applicability of the paper’s results. https://mmr.khu.ac.ir/article_11625.html In this paper, a new numerical method based on the neural network and the discrete Hahn wavelets is presented for solving the Bratu-type equations. First, the discrete Hahn wavelets and some of their important properties are expressed to construct the Hahn wavelets neural network. The presented neural network consists of three layers: input layer, hidden layer, output layer. In this method, the Hahn wavelets and sinh functions are used as the activation functions of the hidden layer and output layer, respectively. Then, an analytical optimization method is employed to adjust the neural network weights so that the approximated solution satisfies the given problem. Using this method, the original problem is converted into a system of algebraic equations, which is solved by Newton’s iterative method. Finally, the accuracy and efficiency of the proposed method are examined through several numerical examples.