Journal of Mahani Mathematical Research
Volume:12 Issue: 1, Winter and Spring 2023

‎In this paper‎, ‎a new generalized likelihood ratio (GLR) control chart based on sequentially probability ratio test (SPRT) is introduced to monitor the directional mean of von Mises distribution‎. ‎Different window size of past samples are utilized to construct the GLR chart statistic‎, ‎and the performance of this chart in detecting a wide range of parameter shift is evaluated‎. ‎A simulation study is carried out to investigate the performance of the proposed control chart in comparison with cumulative sum (CUSUM) control chart‎. ‎To guide practitioners‎, ‎a real example is provided‎.

Entropy measures have received considerable attention in quantifying the structural complexity of real-world systems and are also used as measures of information obtained from a realization of the considered experiments. In the present study, new notions of entropy for a dynamical system are introduced. The Rényi entropy of measurable partitions of order and its conditional version are defined, and some important properties of these concepts are studied. It is shown that the Shannon entropy and its conditional version for measurable partitions can be obtained as the limit of their Rényi entropy and conditional Rényi entropy. In addition, using the suggested concept of Rényi entropy for measurable partitions, the Rényi entropy for dynamical systems is introduced. It is also proved that the Rényi entropy for dynamical systems is invariant under isomorphism.

‎For an ordered set $W=\{w_1‎, ‎w_2,\ldots,w_k\}$ of vertices and a‎ vertex $v$ in a connected graph $G$‎, ‎the ordered  $k$-vector‎ ‎$r(v|W)=(d(v,w_1),d(v,w_2),\ldots,d(v,w_k))$ is called the‎ ‎(metric) representation of $v$ with respect to $W$‎, ‎where $d(x,y)$‎ ‎is the distance between the vertices $x$ and $y$‎. ‎The set $W$ is‎ ‎called a resolving set for $G$ if distinct vertices of $G$ have‎ ‎distinct representations with respect to $W$‎. ‎The minimum‎ ‎cardinality of a resolving set for $G$ is its metric dimension‎, ‎and a resolving set of minimum cardinality is a basis of $G$‎. ‎Lower bounds for metric dimension are important‎. ‎In this paper‎, ‎we investigate lower bounds for metric dimension‎. ‎Motivated by a lower bound for the metric dimension $k$ of a graph‎ ‎of order $n$ with diameter $d$ in [S‎. ‎Khuller‎, ‎B‎. ‎Raghavachari‎, ‎and‎ ‎A‎. ‎Rosenfeld‎, ‎Landmarks in graphs‎, ‎Discrete Applied Mathematics‎ ‎$70(3) (1996) 217-229$]‎, ‎which states that $k \geq n-d^k$‎, ‎we characterize‎ all graphs‎ ‎with this lower bound and obtain a new lower bound‎. ‎This new bound is better than the previous one‎, ‎for graphs with diameter more than $3$‎.

In this paper, we generalize the concept of an open locating-dominating set in graphs. We introduce a concept as an open locating-total dominating set in graphs that is equivalent to the open neighborhood locating-dominating set. A vertex set $S \subseteq V(G)$ is an open locating-total dominating if the set $S$ is a total dominating set of $G$ and for any pair of distinct vertices $x$ and $y$ in $V(G)$, $N(x) \cap S\neq N(y) \cap S$. The open locating-total domination number, denoted $\gamma_{t}^{OL}(G)$, of $G$ is the minimum cardinality of an open locating-total dominating set. In this paper, we determine the open locating-total dominating set of some families of graphs. Also, the open locating-total domination number is calculated for two families of trees. The present paper is an extended version of our paper, presented at the 52nd Annual Iranian Mathematics Conference, Shahid Bahonar University of Kerman, Iran, 2021.

‎In this paper we consider the estimation, ‎order and model selection of autoregressive time series model which may be driven by non-normal innovations. ‎The paper makes two contributions. ‎First, ‎we consider the method of moments for a univariate and also a bivariate time series model; the importance of using the method of moments is that it can provide us with consistent estimates easily for any model order and for any kind of distribution that we can assume for the non-normal innovations‎. ‎Second, ‎we provide methods for order and model selection, ‎i.e‎. ‎for selecting the order of the autoregression and the model for the innovation's distribution. ‎Our analysis provides analytic results on the asymptotic distribution of the method of moments estimators and also computational results via simulations‎. ‎Our results show that although the performance of modified maximum likelihood estimators is better than method of moments estimators when the sample size is small but both methods have approximately same performance as the sample size increase and in misspecification case. ‎Also It is shown that focussed information criterion is an appropriate criterion for model selection for autoregressive models with non-normal innovations based on the method of moments estimators.

In this paper, a one-dimensional homogeneous fuzzy wave equation is solved with an analytical procedure using the fuzzy D’Alembert method by considering the generalized differentiability. Then, some definitions related to fuzzy numbers, theorems, and used lemmas are given. Additionally, the physical interpretation and dependency domain of fuzzy wave solutions are investigated by providing examples, where the fuzzy wave solutions are in the form of fuzzy standing, traveling, and recursive waves.

Denote by $\widehat{p_n}$, the largest prime among the primitive prime divisors of $ 2^{2n+1}-1 $ and $ 2^{2(4n+2)}-1 $, where $n\in {\Bbb N}$. In this paper, we prove that if $ q=2^{2n+1}\geq8 $ and $\alpha \leq \widehat{p_n}$, then the direct product of $ \alpha $ copies of $ {\rm Sz}(q)$ is uniquely determined by its complex group algebra.

Let M be a Lorentzian para-Sasakian manifold with a Lorentzian para-Sasakian structure (φ,η,ξ,g). In this paper, we introduce some metallic structures on tangent bundle of the manifold M using vertical, horizontal and complete lifts of the Lorentzian para-Sasakian structure (φ,η,ξ,g) and investigate their parallelity. We also consider fundamental 2-forms and try to find conditions under which these 2-forms are closed.

In this paper, we consider $S$-manifolds endowed with a quarter-symmetric metric connection. We obtain the condition for a curve to be magnetic with respect to this connection. We show that quarter-symmetric magnetic curves are $\theta _{\alpha }-$slant curves of osculating order $r\leq 3$ with constant quarter-symmetric curvature functions. Finally, we give the classification theorem.

A completely distributive complete lattice is called a molecular lattice. It is well known that the category TML of all topological molecular lattices with generalized order homomorphisms in the sense of Wang, is both complete and cocomplete. In this note, we give an example which shows that the structure of equalizers introduced by Zhao need not be true, in general. In particular, we present the structures of equalizers, coequalizers, monomorphisms and epimorphisms in this category.

Forecasting is an essential analytical tool used to make future predictions based on preliminary data. However, the use of small sample sizes during analysis provides inaccurate results, known as asymptotic forecasting. Therefore, this study aims to analyze the unemployment rate of educated people in Indonesia using the bias-corrected forecasting bootstrap technique. Data were collected from a total of 30 time series of educated unemployed from 2015 to 2019 using the bias-corrected bootstrap technique and determined using the interval prediction method. The bootstrap replication used is at intervals of 100, 250, 500, and 1000. The results obtained using the R program showed that the bootstrap technique provides consistent forecasting results, better accuracy, and unbiased estimation. Moreover, the results also show that for the next 10 periods, the number of educated unemployed people in Indonesia is projected to decline. The bootstrap coefficient also tends to decrease with an increase in the number of replications, at an average of 0.958. The interval prediction is also known to be smooth, along with a large number of bootstrap replications.

In this paper, we study the effect of delayed feedback on the dynamics of a three-dimensional chaotic dynamical system and stabilize its chaotic behavior and control the respective unstable steady state. We derive an explicit formula in which a Hopf bifurcation occurs under some analytical conditions. Then the existence and stability of the Hopf bifurcation are analyzed by considering the time delay $ \tau $ as a bifurcation parameter. Furthermore, by numerical calculation and appropriate ascertaining of both the feedback strength $ K $ and time delay $ \tau $, we find certain threshold values of time delay at which an unstable equilibrium of the considered system is successfully controlled. Finally, we use numerical simulations to examine the derived analytical results and reveal more dynamical behaviors of the system.

The main objective of this article is to establish a new model and find some vortex axisymmetric solutions of finite core size for this model. We introduce the hydrodynamical equations governing the atmospheric circulation over the tropics, the Boussinesq equation with constant radial gravitational acceleration. Solutions are expanded into series of Hermite eigenfunctions. We find the coefficients of the series and show the convergence of them. These equations are critically important in mathematics. They are similar to the 3D Navier-Stokes and the Euler equations. The 2D Boussinesq  equations preserve some important aspects of the 3D Euler and Navier-Stokes equations such as the vortex stretching mechanism. The inviscid 2D Boussinesq equations are known as the Euler equations for the 3D axisymmetric swirling flows.This model is the most frequently used for buoyancy-driven fluids, such as many largescale geophysical flows, atmospheric fronts, ocean circulation, clued dynamics. In addition, they play an important role in the Rayleigh-Benard convection.

Being mainly a process of knowledge transmission, mathematics education evolves during time in accordance with the strong assumptions and beliefs which are considered as parts of the mathematics teaching profession. This suggests that explaining the problem-solving process, transmitting the clear and flawless information, and showing the problem-solving procedures, were parts of the role the mathematics teachers have. The main purpose of this study was to compare the mathematical teaching experiences based on the problem-solving approach among the Iranian and Iraq mathematics educators. Through survey method, views of secondary teachers of mathematics are studied. It is used of questionnaire that is proposed by Matlala's (2015). The validity and reliability has been proved by researcher using Cronbach's alpha method with a value more 0/89 This questionnaire was designed with the purpose of identifying challenges and opportunities that every individual encounter with in the way of using a problem-solving approach to facilitate mathematics learning. The statistical population of the study included all the secondary school math teachers in Iran and Iraq. Using the simple random sampling method, 16 secondary school math teachers from the Republic of Iraq (from its capital:Kurdistan) and 14 secondary school math teachers from the Islamic Republic of Iran (from its capital: Tehran) were selected. The use of an electronic questionnaire, was sent to in-service teachers during the school year 2018-2019. findings indicated that Iranian and Iraq teachers' view regard to the implementation of problem solving procedure were positive and they have applied problem solving procedure in their math classes.

Data Envelopment Analysis (DEA) is a theoretical framework for performance analysis and efficiency measurement. Traditional DEA models, which measure the efficiency of simple decision-making with multiple inputs and outputs, have several weaknesses, one of which is the inability to consider intermediate variables. Therefore, Network Data Envelopment Analysis (NDEA) has been developed to address this issue, which is especially important for the analysis of two-stage processes. Also, since real-world data often are non-deterministic and imprecise, fuzzy sets theory and intuitionistic fuzzy sets theory, which are well-equipped to handle such information, can be used to improve the performance of two-stage DEA models. In this study, firstly NDEA models are discussed and then multiplicative method of NDEA is stated to obtain the individual efficiencies and the overall efficiency of the two stages. Also, it is explained how these models can be modified with intuitionistic fuzzy coefficients, and finally is described how arithmetic operators for intuitionistic fuzzy numbers can be used for a conversion into crisp two-stage structures. This paper presents a new two-stage DEA model to study the indirect impact of information technology investment on firm performance operating based on fuzzy intuitionistic numbers. Using this model, the efficiency of the first and second stages of a two-stage decision-making and ultimately its overall efficiency can be estimated with due to intermediate variables. The proposed method is used to solve a numerical example containing 12 DMUs with intuitionistic fuzzy triangular number coefficients.

One of the principal challenges in the cloud is the task scheduling problem. Appropriate task scheduling algorithms are needed to achieve goals such as load balancing, minimum cost, minimum energy consumption, etc. Using meta-heuristic algorithms is a good way to solve scheduling problems in the cloud because scheduling is an NP-hard problem. In recent years, various meta-heuristic algorithms have been introduced, one of the most popular meta-heuristic algorithms to deal with optimization problems is the Grey Wolf Optimizer (GWO) algorithm. This paper introduces a novel GWO-based task scheduling (GWOTS) algorithm to map tasks over the available resources. The principal goal of this paper is to decrease execution cost, energy consumption, and makespan. The efficiency of the GWOTS algorithm is compared with the well-known meta-heuristic algorithms, namely Genetic Algorithm (GA), Dragonfly Algorithm (DA), Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Ant Colony Optimization (ACO), Gravitational Search Algorithm (GSA), Sooty Tern Optimization Algorithm (STOA), Artificial Hummingbird Algorithm (AHA), Multi-Verse Optimizer (MVO), and Sine Cosine Algorithm (SCA). In addition, the performance of GWOTS is compared with three recently scheduling algorithms, namely SOATS, IWC, and CETSA. Experimental results show that the GWOTS algorithm improves performance in terms of makespan, cost, energy consumption, total execution time, resource utilization, throughput, and degree of resource load balance compared to other algorithms.

The fundamental concept of statistical convergence first was put forward by Steinhaus and at the same time but also  by Fast \cite{Fast} independently both for complex and real sequences. In fact, the convergence in terms of statistical     manner can be seen as a generalized form of the common convergence notion that is in the parallel of the theory of usual convergence. Measuring how large a subset of the set of natural number can be possible by means of asymptotic    density. It is intuitively known that positive integers are in fact far beyond the fact that they are perfect squares. This is due to the fact that each perfect square is positive and besides at the same time there are many other positive integers. But it is also known that the set consisting of integers which are positive is not larger than that of those which are perfect squares: both of those sets are countable and infinite and therefore can be considered in terms of $1$-to-$1$ correspondence. However, when the natural numbers are scanned for increasing order, then the squares are seen     increasingly scarcity. It is at this point that the concept of natural density comes into out help and this intuition becomes more precise. In this study, the above mentioned statistical convergence and asymptotic density concepts are     examined in a new space and an attempt is made to fill a gap in the literature as follows. Stancu type extension of the widely known Chlodowsky type \linebreak$\left( \lambda,q\right)  $-operators is going to be introduced. Moreover, the    description of the novel rough statistical convergence having Pascal Fibonacci binomial matrix is going to be presented and several general characteristics of rough statistical convergence are taken into consideration. In the second place, the approximation theory is investigated as the rate of the rough statistical convergence of Chlodowsky type $\left(\lambda,q\right)$-operators.

Let $L$ be a lattice with $1$ and $0$. The small intersection graph of filters of $L$, denoted by $\Gamma(L)$, is defined to be a graph whose vertices are in one to one correspondence with all non-trivial filters of $L$ and two distinct vertices are adjacent if and only if the intersection of corresponding filters of $L$ is a small filter of $L$. In this paper, the basic  properties and possible structures of the graph $\Gamma(L)$ are investigated. Moreover, the complemented property, the domination number and the planar property of $\Gamma(L)$ are considered.

‎In this paper‎, ‎we introduce a class of higher homomorphisms on an algebra $ \mathcal{A} $ and we characterize the structure of them as a linear combination of some ‎sequences‎ of homomorphisms‎.‎ ‎Also ‎‎we prove that for any approximate higher ring homomorphism on a Banach algebra $ \mathcal{A} $ under some sequences of control funtions‎, there exists a unique higher ring homomorphism near it. Using special sequences of control functions, we show that the approximate higher ring homomorphism is an exact higher ring homomorphism.

The year 2020 arrives with COVID-19. The pandemic poses a formidable threat to human existence at onset but is fought with various measures of which quarantine and hospitalization play a key role. In this article, a COVID-19 transmission mathematical model is developed to assess how quarantine and hospitalization aid improvement in the recovery of both asymptomatic and symptomatic infectious individuals during the toughest period of the pandemic in the year 2020. The basic properties of the model in terms of positivity and boundedness of solutions are discussed based on some ample mathematics theorems. The control reproductive ratio is derived using the next generation matrix approach and the local and global stabilities are investigated via stability theory of differential equations, which depend on the size of the derived control reproductive ratio. Numerical simulation is performed to confirm the analytical results. Findings from the simulation show that quarantine and hospitalization are helpful in averting imminent destruction posed by the pandemic in the years 2020 and early 2021 by reducing both  COVID-19 transmission and mortality.