Journal of Advanced Mathematical Modeling
https://jamm.scu.ac.ir/
Journal of Advanced Mathematical Modelingendaily1Fri, 23 Sep 2022 00:00:00 +0330Fri, 23 Sep 2022 00:00:00 +0330Modules satisfying double chain condition on non-small submodules
https://jamm.scu.ac.ir/article_17739.html
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.On order and quasi order Γ-semihypergroups
https://jamm.scu.ac.ir/article_17740.html
The &Gamma;&ndash;hyperstructres algebraic are generalization of hypestructures algebraic and classical structures. One of them is &Gamma; &ndash;semihypergroup that is a generalization of semihypergroups and semigroup. In this paper, we introduce the concept of quasi order &Gamma;-semihypergroup and order &Gamma;-semihypergroup as a generalization of quasi order semihypergroup and order semihypergroup, respectively. Also, we characterize quasi order &Gamma;-semihypergroup by quasi order relation and introduce complete pats and fundamental relation in quasi order &Gamma;-semihypergroup. Finally, we construct quasi order semihypergroup and order semihypergroup by quasi order &Gamma;-semihypergroup and order &Gamma;-semihypergroup.A computational method for a rearrangement minimization related to the Poisson problem on the unit disk in the plane
https://jamm.scu.ac.ir/article_17748.html
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 .Estimating Receiver Operating Characteristic Curve (ROC) Using Birnbaum-Saunders Kernel
https://jamm.scu.ac.ir/article_17755.html
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.Linear quantile autoregressive model estimation using Stochastic EM algorithm
https://jamm.scu.ac.ir/article_17756.html
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.On the properties of the Boolean algebras induced by a unital lattice ordered group
https://jamm.scu.ac.ir/article_17793.html
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.The Balanced Discrete Weibull Distribution and Its Corresponding Integer-value Autoregressive Model: Properties, Estimation and Analysis of Counting Death of COVID-19 Data
https://jamm.scu.ac.ir/article_17794.html
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 approachesInvestigating the effect of volume fraction, Reynolds number and dilation rate of permeable wall of vessel on the heat transfer flow of gold/copper nanofluid of blood using the Adomian decomposition method
https://jamm.scu.ac.ir/article_17805.html
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.Explicit Modeling of Correlation Structure For Bayesian Analysis of Spatial Survival Data: Estimating the Relative Risk of Prostate Cancer Patients
https://jamm.scu.ac.ir/article_17870.html
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.Terwilliger algebras of complete multipartite graphs
https://jamm.scu.ac.ir/article_17872.html
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.On $\alpha$-parallel short modules
https://jamm.scu.ac.ir/article_17876.html
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 $\alpha\leq\ndim\, M\leq\alpha+1$.Investigation of a new method for the numerical solution of a system of hypersingular integral equations
https://jamm.scu.ac.ir/article_17891.html
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.Examining the conflicts between Iran and neighboring countries
using differential games
https://jamm.scu.ac.ir/article_17927.html
In this article, we intend to use differential games to model Iran&#039;s relations with neighboring countries. According to the discussion of time continuity in the real world, the differential game model has been used to model the ongoing issues continuously over a period of time and provide more realistic results. In this article, we first introduce the differential game, then the game model and the Hamilton-Jacobi-Bellman equation are described. In the first method, the famous Cobb-Douglas function was used instead of the utility function, and in the second method, we used this function by making changes to the Berman function. In the first method, in general, the amount of military expenditure and the amount of military equipment are balanced in the situation of the Markovian strategy. But in the second method, by considering the sub-sets of each of the military cost and military equipment sets, we have obtained the values of military costs and the amount of balance equipment for each sub-set in more detailPRICING PERPETUAL AMERICAN OPTIONS UNDER
REGIME SWITCHING JUMP DIFFUSION MODELS
https://jamm.scu.ac.ir/article_17937.html
In this article, we examine the issue of pricing perpetual American option with a differential equation approach with free boundary properties. To describe the underlying asset dynamics in these options, we use the feature of jump-diffusion models under regime switching. In pricing these perpetual options, due to the possibility of early application, we need to solve the ordinary integro-differential equation with a free boundary. For this purpose, we write the equation created from this model first as a linear complementarity problems and then discretize by using the finite difference method. We use linear interpolation to approximate the
integral term. The discrete maximum principle is applied to the linear complementarity
problems to obtain the error estimates. We also illustrate some numerical results in order
to demonstrate and compare the accuracy of the method for our problem.New weighting strategies for spatially correlated Poisson sampling
https://jamm.scu.ac.ir/article_17939.html
In Poisson sampling, each unit is selected independently of the other units with a certain inclusion probability, and the sample size n(s) is a random variable with large variation. Also, if there exists a trend between units of the population, it causes bias in the estimated population parameter. So Poisson-correlated sampling (CPS) and Poisson-correlated spatial sampling (SCPS) were introduced as alternative methods to Poisson sampling that reduces changes in the sample size and bias in the estimated population parameter by weighting strategies. In this paper, new strategies for choosing weights are introduced and it is shown by simulation that the new weighting strategies increase the efficiency of the estimated parameter compared to the earlier weighting strategies.The Banach algebra $U(X)$ on a zero-dimensional space
https://jamm.scu.ac.ir/article_17990.html
In this research, for a zero-dimensional space $X$, a Banach subalgebra $U(X)$ of $C^{*}(X,\mathbb{C})$ is introduced. It is shown that $U(X)$ is the uniform closure of the subalgebras $C^{F}(X,\mathbb{C})$ and $C^{*}_{c}(X,\mathbb{C})$ of the Banach algebra $C^{*}(X,\mathbb{C})$. Moreover a necessary and sufficient condition for the coincidence of $U(X)$ and $C^{*}(X,\mathbb{C})$ is given. It is shown that $U(X)$ consists exactly of all $f\in C^{*}(X,\mathbb{C})$ each of which has an extension to
$\beta_{\circ}X$. Using this fact, an isometric isomorphism from $U(X)$ onto $C(\beta_{\circ}X,\mathbb{C})$ is defined. Finally, a description of the elements of $U(X)$ in terms of the inverse image of the closed subsets of $\mathbb{C}$ is given.HERMITE-HADAMARD INTEGRAL INEQUALITY FOR
$(\alpha,m)$-CONVEX FUNCTIONS
https://jamm.scu.ac.ir/article_17993.html
In this paper, after introducing the $m$-convexity by Toader, as an intermediate among the general convexity and star shaped property, we bring Hermite-Hadamard integral inequality on $(\alpha,m)$-convex function in the new form. Previous results about the Hermite-Hadamard inequality for $m$-convex functions are part of the results of our theorems. Illustrated examples of $(\alpha,m)$-convex and $m$-convex functions are also included in the article.Generalized row substochastic matrices and majorization
https://jamm.scu.ac.ir/article_17999.html
&lrm;The square and real matricx $A$ is called a generalized row substochastic matrix&lrm;, &lrm;if the sum of the absolute values of the entries in each row is less than or equal to one&lrm;.
&lrm;Let $x,y\in \mathbb{R}^n$&lrm;. &lrm;We say that $x$ is right $B$-majorized (resp&lrm;. &lrm;left $B$-majorized) by $y$&lrm;, &lrm;denoted by $x \prec _{rB} y$ ($x \prec _{lB} y$)&lrm;, &lrm;if there exists a substochastic matrix $D$&lrm;, &lrm;such that $x=yD$ (resp&lrm;. &lrm;$x=Dy$)&lrm;. &lrm;In this article&lrm;, &lrm;we have found all the vectors such as $x$ that $x$ is right $B$-majorized (resp&lrm;. &lrm;left $B$-majorized) by $y$&lrm;, &lrm;for all row vector $y$ (resp&lrm;. &lrm;column vector)&lrm;. &lrm;Also&lrm;, &lrm;we show $x \sim _{lB} y$ if and only if $\Vert x\Vert_\infty =\Vert y\Vert_\infty$ and prove $x \sim _{rB} y$ if and only if $\Vert x\Vert_1 =\Vert y\Vert_1$&lrm;.
&lrm;We have also created conditions in which the left $B$-majorization is equivalent to the left majorization&lrm;, &lrm;and created conditions in which the right $B$-majorization is equivalent to the right majorization&lrm;.A Control Model for the Growth of Cancer Stem and Non-Stem
Cells for the Administration of Doxorubicin
https://jamm.scu.ac.ir/article_18000.html
Cells in all tissues of the body are constantly growing and dividing
into new cells. Abnormal proliferation of tissues outside the body leads to
cancer. In all tissues of the body, a type of cell, called a stem cell, is found
that has the ability to become specialized cells in the same tissue to be able to
compensate for damage in tissue disorders. In this paper, based on the existing
mathematical model, the optimal control model is very effective for inhibiting
this growth in exchange for prescribing a specific drug (doxorubicin) is presented.
In order to minimize the number of cancer cells over time, the cancer control
strategy has been modeled as a problem from the theory of optimal control
during the effect of a specific drug on non-cancerous stem cells in this model.
To solve this problem and prescribe the optimal dose of the drug, first with the
help of the maximum principle of Pontriagin and then the analytical solution of
the first-order differential equations, the optimal solution has been determined.
In order to provide the optimal dose of the drug to the patient, the proposed
solution is simulated numerically. This numerical implementation shows how by
applying this amount of drug with a specific dose, how the number of cancer
cells decreases over time, they will be.Construct a matrix with prescribed Ritz values of the order less than or equal to three
https://jamm.scu.ac.ir/article_18002.html
The Ritz values of a matrix are the set of all the eigenvalues of the leading principal submatrices. In this paper, assuming that the set of Ritz values is given from the dimension of maximum three, we find a matrix such that the given set is its Ritz values. The conditions for the existing solution are also studied.On small endomorphic‎, small homomorphic ‎and ‎essential homomorphic modules
https://jamm.scu.ac.ir/article_18003.html
&lrm;In &lrm;this &lrm;paper &lrm;we&lrm; introduce and study the three concepts of small endomorphic, small homomorphic and essential homomorphic modules using the tools of endomorphism and homomorphism which are known in module theory as important means of transmitting some algebraic properties. We have also examined some of the relationships between these three concepts as well as their relationship to different categories of modules.Study of the growth ratio of genetic communities using a new meshless method
https://jamm.scu.ac.ir/article_18026.html
&lrm;In recent decades researchers introduced many numerical methods for solving partial differential equations. Some of these methods have limitations in solving problems with complex domains because of the need to construct meshes. Therefore, scientists developed a new set of numerical methods called meshless methods. In this paper, we introduce the direct meshless local Petrov-Galerkin method to the numerical study of the nonlinear two-dimensional Fisher equation. This method is based on the local weak form of the equation and uses the generalized moving least square method to approximate the unknown function. To show the efficiency and capability of the method, we report the numerical results in regular and irregular domains with a uniform and scattered distribution of nodes. Comparison of the obtained results with other methods indicates the accuracy and efficiency of this method.A computational approach for approximate optimal
control of nonlinear Volterra integral equations
https://jamm.scu.ac.ir/article_18029.html
In this paper, a new method for solving optimal control problems governed
by nonlinear Volterra integral equations is presented. First by converting to
a discretized form, the problem is considered as a quasi assignment problem and then an iterative method is applied to find approximate solution
for discretized form of the integral equation. Next step using evolutionary
algorithms, approximate solution of optimal control problems is obtained.
An analysis for convergence of the proposed iterative method and its implementation for numerical examples are also given.