Journal of Advanced Mathematical Modeling
https://jamm.scu.ac.ir/
Journal of Advanced Mathematical Modelingendaily1Wed, 22 Jun 2022 00:00:00 +0430Wed, 22 Jun 2022 00:00:00 +0430On Optimal Estimation of Population Mean
https://jamm.scu.ac.ir/article_17481.html
&lrm;In this paper&lrm;, &lrm;estimating the mean problem of the population when the sampling data have measurement errors has been studied via a new efficient estimator&lrm;. &lrm;We also investigate the efficiency of this estimator compared to other available estimators&lrm;. &lrm;And finally&lrm;, &lrm;we use these results for real data&lrm;. &lrm;We show that the proposed estimator is more efficient than other existing estimators&lrm;.A case study of the sensitivity and topology of nodes of reduced Boolean networks
https://jamm.scu.ac.ir/article_17539.html
Boolean networks are one of the models for studying complex dynamic behaviors in biological systems. The analysis of attractors of these networks is very important .But the exponential dependence of the state transition graph of these models with the number of network nodes is a major problem for large-scale systems analysis. Therefore, it is necessary to use network reduction methods. In these methods, the size of the networks is reduced, while the dynamic properties are preserved, but the reduction methods are not minimal. In this paper, while the two biological networks "abscisic acid" and "breast cancer" have been reduced, also the sensitivity analysis of the nodes of the reduced networks has been performed. The results show that reduced network nodes are important components in the main network dynamics because most of them have zero opposite sensitivity. Also, zero sensitivity nodes in reduced networks can be removed under certain conditions, using From the reduction method and the concept of sensitivity, our proposed method is able to modify the Saadatpour reduction method. Using the proposed method, we obtained reduced networks with fewer nodes that maintain the main network dynamics and have a smaller state space. These nodes are also important in both structural and dynamic aspects of biological networks.The Noncommuting Graph of Bounded Linear Operators on a Hilbert Space
https://jamm.scu.ac.ir/article_17543.html
Let $EuScript{H}$ be a Complex Hilbert space and $EuScript{B(H)}$ be the algebra of allbounded linear operators on $EuScript{H}$. The non-commuting graph of $EuScript{B(H)}$, denoted by $mathnormal{Gamma}(EuScript{B(H)})$ is a graph whose vertices are non-scalar bounded operators and two distinct vertices $A$ and $B$ are adjacent if and only if $AB neq BA$. In this paper, we prove the connectivity of $mathnormal{Gamma}(EuScript{B(H)})$ for separable and non-separable complex Hilbert spaces. Also we show that the noncommuting graphs of the set of all finite rank operators on $EuScript{H}$, the set of all compact operators on $EuScript{H}$, the set of all non-invertible operators on $EuScript{H}$ and the set of all Fredholm operators on $EuScript{H}$ are connected graphs.Maximal Subrings of Prufer Domains
https://jamm.scu.ac.ir/article_17544.html
A proper unital subring of a ring R is called a maximal subring, if it is maximal with inclusion between proper subrings of R. In this paper we present conditions under which a Pr"{u}ferr domain has a maximal subring. We study the Pr"{u}fer and B'{e}zout properties which are shared between an integral domain and its maximal subrings too.Optimal control of linear delay systems involving piecewise constant delay function using hybrid Chebyshev-block pulse method
https://jamm.scu.ac.ir/article_17588.html
In this paper, the optimal control of delay systems with piecewise constant delay function is investigated. Using Chebyshev hybrid functions, an approximate method is proposed to obtain the optimal solution to the control problem of linear delay systems. In order to present an approximate method, integral, product of multiplication and delay operational matrices of the hybrid functions have been introduced and used to solve the problem. The optimal control problem is transformed into an optimization problem with the help of the operational matrices and then solving it, an approximate solution to the original problem is obtained. Efficiency and accuracy of the proposed method are illustrated with two examples of the optimal control problem. &lrm;&lrm;Baire category theorem for the symmetric topology of sublinear quasi-metrics in locally convex cones
https://jamm.scu.ac.ir/article_17589.html
In this paper, we investigate the completeness of cones in the symmetric topology &lrm;induced &lrm;the &lrm;sublinear &lrm;quasi-metrics&lrm; and prove that in the symmetric complete cone the symmetric neighborhoods are of the second category. Then we present an extension of the Baire category theorem for the symmetric topology of locally convex quasi-metric cones.Numerical investigation of a new difference scheme on a graded mesh for solving the time-space fractional sub-diffusion equations with nonsmooth solutions
https://jamm.scu.ac.ir/article_17651.html
&lrm;In this paper&lrm;, &lrm;we provide a new difference scheme on a graded mesh for solving the time-space fractional diffusion problem&lrm;. &lrm;In &lrm;this &lrm;equation &lrm;the &lrm;time &lrm;derivative &lrm;is &lrm;the &lrm;Caputo &lrm;of &lrm;order &lrm;&lrm;$&lrm;&lrm;gammain(0,1)$ &lrm;and &lrm;the &lrm;space &lrm;derivative &lrm;is &lrm;the &lrm;Riesz &lrm;of &lrm;order &lrm;&lrm;$&lrm;&lrm;alphain(1,2]$.&lrm; &lrm;The stability and convergence of the difference scheme are discussed which provides the theoretical basis of the proposed&lrm; &lrm;schemes&lrm;. W&lrm;e prove that the new difference scheme is unconditionally stable&lrm;. Also, &lrm;we find that the difference scheme is convergent with order $min{2-gamma,rgamma}$ in time for all $gammain (0,1)$ and $alpha in (1,2]$&lrm;. &lrm;A test example is given to verify the efficiency and accuracy of the difference scheme&lrm;.A novel matrix technique to solve a new singular nonlinear functional Lane-Emden model
https://jamm.scu.ac.ir/article_17699.html
The present study is devoted to finding the approximate solutions of a new design of a second-order nonlinear functional system of Lane-Emden differential equation with boundary conditions. Our proposed matrix technique is based on the Chelyshkov functions together with collocation points to transform the nonlinear system into an algebraic fundamental matrix equation. The convergence of the spectral Chelyshkov approach is also proved. To show the efficiency and the accuracy of the presented technique, three test examples are solved numerically. Also, comparisons with the exact solutions and with an available method in the literature are performed.An non-polynomial spline approximation for fractional Bagley-Torvik equation
https://jamm.scu.ac.ir/article_17700.html
In this paper, we approximate the solution of fractionalBagley&ndash;Torvik equation by using the non-polynomial spline function andthe shifted Gr"{u}nwald difference operator. The proposed methodsreduce to the system of algebraic equations. The convergenceanalysis of the methods has been discussed. The numerical examplesare presented to illustrate the applications of the methods and tocompare the computed results with the other methods.Design of sliding mode control based on Razumikhin approach and linear matrix inequality for nonlinear fractional time-varying delay systems
https://jamm.scu.ac.ir/article_17701.html
In this paper, a sliding mode control for systems that are nonlinear, having fractional order, andinvolve delay is used. The aim of this paper is to design a sliding mode controller, such that the closed&shy;looped nonlinear system becomes asymptotically stable and its trajectory can be driven onto the slidingsurface in finite time. By using the fractional Razumikhin theorem for the stability of fractional&shy; ordersystems including delay and a linear matrix inequality, necessary conditions on asymptotic stabilizationare obtained. Some numerical examples are given to illustrate the effectiveness of the proposed results.Convergence Analysis of Numerical solution of Secon-order reaction-diffusion equation with boundary conditions
https://jamm.scu.ac.ir/article_17706.html
&lrm;The aim of this work is to provide a specific process for solving a reaction-diffusion partial differential equation with boundary conditions &lrm;(&lrm;RPDEs)&lrm;&lrm;. &lrm;We first convert this &lrm;R&lrm;PDE problem to Volterra-Fredholm integral equation (VFIE)&lrm;, &lrm;because of the good numerical stability properties of integral operators in compare to differential operator&lrm;, &lrm;then apply the numerical Tau method to solve the obtained integral equation&lrm;. &lrm;&lrm;&lrm;&lrm;We present the convergence analysis and error estimation of the Tau method based on the proposed process&lrm;. &lrm;Applying the Tau method yields a system of the ordinary differential equation such that this system is solved by piecewise polynomial collocation methods&lrm;. &lrm;Intended to show advantages of converting &lrm;RPD&lrm;E to an integral equation&lrm;, &lrm;we consider two cases to solve the proposed examples&lrm;. &lrm;In the first case&lrm;, &lrm;we apply the Tau method to solve the &lrm;converted &lrm;&lrm;R&lrm;PDE problem &lrm;(&lrm;integral &lrm;form&lrm;&lrm;&lrm;) and in the second case&lrm;, &lrm;we solve &lrm;the &lrm;R&lrm;PDE &lrm;problem&lrm; &lrm;directly &lrm;(direct &lrm;form&lrm;&lrm;)&lrm; by Tau method&lrm;. &lrm;Comparing the numerical results&lrm;, &lrm;we observe that the results obtained from the &lrm;integral &lrm;form&lrm; &lrm; are higher than which obtained from the &lrm;direct &lrm;form&lrm;&lrm;&lrm;&lrm;.Algorithm for computing all order ideals of ideals of points and its application in biological models
https://jamm.scu.ac.ir/article_17709.html
Ideals of points are considered as a significant and efficient tools in modeling and computingscience, which is why algorithms computing these types of ideals are of crucial importance. This paperproposes an algorithm to compute order ideals for ideals of points. Then those order ideals are used formodeling gene regulatory networks.Modules 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 common
approach 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 performance
of 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 versions
of the distributions. Some statistical features of the new distribution and different kinds of dispersion of
the 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 model
with the innovation of the proposed discrete distribution and evaluate different methods for estimating the
model parameters. Using the counts of death of the COVID-19 data in Cuba, Malawi and Uzbekistan, we
appraise 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 classical
and 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.