فصلنامه مدل سازی پیشرفته ریاضی
سال دوازدهم شماره 3 (پاییز 1401)

In this article, we study modules that satisfy the double infinite chain condition on non-small submodules, denoted by ns-DICC. Using this concept we extend some of the basic results of DICC modules to ns-DICC modules. We show that if an R-module M satisfies the double infinite chain condition on non-small submodules, then M has non-small Krull dimension. Moreover, we observe that an R-module M is ns-DICC if and only if for any non-small summand A of M, either A satisfies the descending chain condition on non-small submodules, or M/A is Noetherian.

The Γ–hyperstructres algebraic are generalization of hypestructures algebraic and classical structures. One of them is Γ –semihypergroup that is a generalization of semihypergroups and semigroup. In this paper, we introduce the concept of quasi order Γ-semihypergroup and order Γ-semihypergroup as a generalization of quasi order semihypergroup and order semihypergroup, respectively. Also, we characterize quasi order Γ-semihypergroup by quasi order relation and introduce complete pats and fundamental relation in quasi order Γ-semihypergroup. Finally, we construct quasi order semihypergroup and order semihypergroup by quasi order Γ-semihypergroup and order Γ-semihypergroup.

In this paper, we consider a rearrangement minimization problem related to the Poisson equation on the unit open disk in the plane. We show that this problem has a unique solution that is radially symmetric. In addition, we prove by computational method that this solution is an increasing function .

Many researchers use the receiver operating characteristic curve (ROC) as a popular way of displaying, evaluating and comparing the discriminatory accuracy of diagnostic tests. The most commonapproach for estimating the ROC curve is using nonparametric kernel estimates in two parts, sensitivity and specificity. Kernel estimators, however, at the beginning and end points of the data domain, known as boundary points, have a slower convergence rate than other points in the domain and are not convergent to the actual value of the probability distribution. This problem is known as the boundary problem. One way to solve the boundary problem in kernel estimators is to use asymmetric kernels. This paper proposes a new kernel estimator for the ROC curve based on the asymmetric Birnbaum-Saunders (B-S) kernel and the asymptotic convergence of the proposed estimator is shown. In addition, the analytical superiority of the proposed estimator over the corresponding symmetric kernel-type estimator is shown. The performanceof the proposed estimator is illustrated via a numerical study. The results show that the proposed estimator outperforms the other commonly-used methods. The application of the proposed method to a set of medical data is also presented.

In this paper, the quantile autoregressive time series model is introduce and then the model parameters are estimated using the Stochastic EM algorithm, which is an iterative method to compute maximum likelihood estimates. The likelihood function for the quantile autoregressive model is constructed based on the asymmetric Laplace distribution and a scale mixture representation of this distribution is used to estimate the model parameters via Stochastic EM algorithm.The efficiency and application of the proposed method are illustrated by some simulation studies and analyzing a real dataset.

In this paper we study the relations between unital lattice-ordered groups and Boolean algebras. At first we prove some main results about the properties of lattice-ordered groups. Then we see that every unital lattice-ordered group induces a Boolean algebra and we investigate some properties of the Boolean algebra. For instance, we prove that the Boolean algebra induced by the lattice-ordered group of all measurable real valued functions on a measure space, consists of all characteristic functions. We also see that in some cases, these Boolean algebras are trivial.

In this paper, we introduce a new discrete Weibull distribution based on the balanced discretization method, which preserves the partial moments between the two discrete and continuous versionsof the distributions. Some statistical features of the new distribution and different kinds of dispersion ofthe proposed distribution are presented based on various selections of parameters. In addition to introducing the new version of balanced discrete Weibull, we provide the integer-valued autoregressive modelwith the innovation of the proposed discrete distribution and evaluate different methods for estimating themodel parameters. Using the counts of death of the COVID-19 data in Cuba, Malawi and Uzbekistan, weappraise the performance of the new process in fitting real data to some classical integer-valued autoregressive models. Finally, the forecasting of the process is checked based on real data using both classicaland sieve bootstrap approaches

In this paper, the effects of volume fraction, Reynolds number and dilation rate on the permeable walls of the vessel in the gold-copper-nanofluid heat transfer model in two-dimensional of blood are investigated. For this purpose, we consider blood as the base fluid in which units of gold or copper nanoparticles are injected. The mathematical model of this phenomenon is in the form of nonlinear ordinary differential equation of the fourth order. In this paper, the Adomian decomposition method is used to numerically solve this nonlinear model with boundary conditions. Comparing the numerical solutions obtained from the Adomian decomposition method with the analytical solutions obtained from the homotopy analysis method (HAM), shows that the numerical and analytical solutions are in good agreement. Also, according to the obtained results, it can be understood that with increasing the number of gold-copper nanoparticles in the base fluid, what will be the thermal properties.

Models with spatial stochastic effects are commonly used to model the relationship between response variables and spatially dependent observations and explanatory variables. In many applications, some models' explanatory variables are dependent. Depending on the type of dependence, the statistical inference of the models with random effects and their applications are complicated; because the explanatory variables, random effects, and model error expression compete with each other in explaining the variability of the response variable.In this paper, a method for modeling and analyzing spatial survival data is proposed to solve this problem. Instead of using spatial stochastic effects in the model, the spatial dependence of observations is explicitly included in density, survival, and hazard functions. Then, in a simulation study, the effects of explanatory variables in the model are calculated and evaluated using the comparative Metropolis-Hastings algorithm. The proposed method is then used to analyze patients' data with prostate cancer, and the Bayesian approach is used to estimate the relative death risk of patients. Finally, a discussion and conclusion will be presented.

Let $\Gamma=K_{p_1,...,p_r}$ be complete multipartite graph and $ x_0 $ be a fix vertex. Let $ T $ be Terwilliger algebra of $ \Gamma $ with base point $ x_0 $. In this paper, we study the modular structure of this algebra and it will be shown that up to isomorphism there are either $ s+2 $ or $ s+3 $ irreducible modules in which $ s $ is the number of distinct numbers in $ {p_1,...,p_r} $. Along with other results, the dimensions of these modules will be computed as complex vector spaces.

An $R$-module $M$ is called $\alpha$-parallel short modules, if for each parallel submodule $N$ to $M$ either $\pndim\, N \leq \alpha$ or $\ndim\, \frac{M}{N}\leq\alpha$ and $\alpha$ is the least ordinalnumber with this property. Using this concept, we extend some of the basic results of $\alpha$-short modulesto $\alpha$-parallel short modules.Also, we have studied the relationship between $\alpha$-parallel short modules and their parallel Noetherian dimension and we show that if $M$ is a $\alpha$-parallel short module, then $M$ has parallel Noetherian dimension and$\alpha\leq\pndim\, M\leq \alpha+1$. Furthermore, we prove that if $M$ is an $\alpha$-parallel shortmodule with finite Goldie dimension, then $M$ has Noetherian dimension and $\alpha\leq\ndim\, M\leq\alpha+1$.

The system of hypersingular integral equations occurs naturally in several branches of scienceand engineering during the formulation of many boundary value problems. The analytical solution for thesystem of dominant equations is known. However, many real-world problems, such as cracking problemsin fracture mechanics, may not be formulated as a set of dominant equations. Therefore, we propose anumerical method to find an approximate solution for such a generalized form. The convergence of theproposed method is proved. This convergence helps to derive the error bound for the error between theexact and the approximate solution. Finally, by providing a numerical example, the efficiency of thismethod will be presented.