- AUT Journal of Mathematics and Computing is a peer-reviewed journal published by the Amirkabir University of Technolo... moreAUT Journal of Mathematics and Computing is a peer-reviewed journal published by the Amirkabir University of Technology. The journal is published under our open access policy, published articles are archived online on our website and can be accessed for free. The journal welcomes original research articles, review papers, case studies, and communications from scholars around the world.edit
- Prof. Abdolrasoul Pourabbasedit
This paper considered the cost constrained vehicle scheduling problem under the constraint that the total number of vehicles is known in advance. Each depot has a different time processing cost. The goal of this problem is to find a... more
This paper considered the cost constrained vehicle scheduling problem under the constraint that the total number of vehicles is known in advance. Each depot has a different time processing cost. The goal of this problem is to find a feasible minimum cost schedule for vehicles. A mathematical formulation of the problem is developed and the complexity of the problem when there are more than two depots is investigated. It is proved that in this case, the problem is NP-complete. Also, it is showed that there is not any constant ratio approximation algorithm for the problem, i.e., it is in the complexity class APX.
One of the functions of mathematical logic is studying mathematical objects and notions by logical means. There are several important representation theorems in analysis. Amongst them, there is a well-known classical one which concerns... more
One of the functions of mathematical logic is studying mathematical objects and notions by logical means. There are several important representation theorems in analysis. Amongst them, there is a well-known classical one which concerns probability algebras. There are quite a few proofs of this result in the literature. This paper pursues two main goals. One is to consider some aspects of measure and probability logics and expose a novel proof for the mentioned representation theorem using ideas from logic and by application of an important result from model theory.
The second and even more important goal is to present more connections between two fields of analysis and logic and reveal more the strength of logical methods and tools in analysis. The paper is mostly written for general mathematicians, in particular the people who are active in analysis or logic as the main audience. It is self-contained and includes all prerequisites from logic and analysis.
The second and even more important goal is to present more connections between two fields of analysis and logic and reveal more the strength of logical methods and tools in analysis. The paper is mostly written for general mathematicians, in particular the people who are active in analysis or logic as the main audience. It is self-contained and includes all prerequisites from logic and analysis.
Software architecture is known to be an effective tool with regards to improving software quality attributes. Many quality attributes such as maintainability are architecture dependent, and as such, using an appropriate architecture is... more
Software architecture is known to be an effective tool with regards to improving software quality attributes.
Many quality attributes such as maintainability are architecture dependent, and as such, using an appropriate architecture is essential in providing a sound foundation for the development of highly maintainable software systems.
An effective way to produce a well-built architecture is to utilize standard architectural patterns.
Although the use of a particular architectural pattern cannot have a preserving effect on software maintainability, the mere conformance of a system to any architecture cannot guarantee the system's high maintainability.
The use of an inappropriate architecture can seriously undermine software maintainability at lower levels.
In this article, the effect of standard architectural patterns on software maintainability quality attributes is investigated.
We develop a quality model for maintainability quality attributes, which is later used to compare various standard architectural patterns.
We finish by investigating two real-world experiences regarding the application of a particular pattern to two different existing architectures, exploring the effect of the change in architecture on maintainability quality attributes.
Many quality attributes such as maintainability are architecture dependent, and as such, using an appropriate architecture is essential in providing a sound foundation for the development of highly maintainable software systems.
An effective way to produce a well-built architecture is to utilize standard architectural patterns.
Although the use of a particular architectural pattern cannot have a preserving effect on software maintainability, the mere conformance of a system to any architecture cannot guarantee the system's high maintainability.
The use of an inappropriate architecture can seriously undermine software maintainability at lower levels.
In this article, the effect of standard architectural patterns on software maintainability quality attributes is investigated.
We develop a quality model for maintainability quality attributes, which is later used to compare various standard architectural patterns.
We finish by investigating two real-world experiences regarding the application of a particular pattern to two different existing architectures, exploring the effect of the change in architecture on maintainability quality attributes.
One of the functions of mathematical logic is studying mathematical objects and notions by logical means. There are several important representation theorems in analysis. Amongst them, there is a well-known classical one which concerns... more
One of the functions of mathematical logic is studying mathematical objects and notions by logical means. There are several important representation theorems in analysis. Amongst them, there is a well-known classical one which concerns probability algebras. There are quite a few proofs of this result in the literature. This paper pursues two main goals. One is to consider some aspects of measure and probability logics and expose a novel proof for the mentioned representation theorem using ideas from logic and by application of an important result from model theory.
The second and even more important goal is to present more connections between two fields of analysis and logic and reveal more the strength of logical methods and tools in analysis. The paper is mostly written for general mathematicians, in particular the people who are active in analysis or logic as the main audience. It is self-contained and includes all prerequisites from logic and analysis.
The second and even more important goal is to present more connections between two fields of analysis and logic and reveal more the strength of logical methods and tools in analysis. The paper is mostly written for general mathematicians, in particular the people who are active in analysis or logic as the main audience. It is self-contained and includes all prerequisites from logic and analysis.
Abstract. The target of this paper is to study N(k)-contact metric manifolds with some types of conformal vector fields like φ-holomorphic planar conformal vector fields and Ricci biconformal vector fields. We also characterize N(k)-... more
Abstract. The target of this paper is to study N(k)-contact metric manifolds
with some types of conformal vector fields like φ-holomorphic planar conformal
vector fields and Ricci biconformal vector fields. We also characterize N(k)-
contact metric manifolds allowing conformal Ricci almost soliton. Obtained results are supported by examples.
with some types of conformal vector fields like φ-holomorphic planar conformal
vector fields and Ricci biconformal vector fields. We also characterize N(k)-
contact metric manifolds allowing conformal Ricci almost soliton. Obtained results are supported by examples.
Ranked set sampling is a statistical technique for data collection that generally leads to more efficient estimators than competitors based on simple random sampling. In this paper, we consider estimation of scale parameter of Levy... more
Ranked set sampling is a statistical technique for data collection that generally
leads to more efficient estimators than competitors based on simple random sampling.
In this paper, we consider estimation of scale parameter of Levy distribution
using a ranked set sample. We derive the best linear unbiased estimator
and its variance, based on a ranked set sample. Also we compare numerically, variance of this estimator with mean square error of the maximum likelihood, a median based estimator and an estimator based on Laplace transform. It turns out that the best linear unbiased estimator based on ranked set sampling is more efficient than other mentioned estimators.
leads to more efficient estimators than competitors based on simple random sampling.
In this paper, we consider estimation of scale parameter of Levy distribution
using a ranked set sample. We derive the best linear unbiased estimator
and its variance, based on a ranked set sample. Also we compare numerically, variance of this estimator with mean square error of the maximum likelihood, a median based estimator and an estimator based on Laplace transform. It turns out that the best linear unbiased estimator based on ranked set sampling is more efficient than other mentioned estimators.
A new family of distributions on the circle is introduced which is a generalization of the Cardioid distributions. The elementary properties such as mean, variance, and the characteristic function are computed. The distribution is... more
A new family of distributions on the circle is introduced which is a generalization of the Cardioid distributions. The elementary properties such as mean, variance, and the characteristic function are computed. The distribution is shown to be either unimodal or bimodal. The modes are computed. The symmetry of the distribution is characterized. The parameters are shown to be canonic (i.e. uniquely determined by the distribution). This implies that the estimation problem is well-defined. We also show that this new family is a subset of distributions whose Fourier series has degree at most 2 and study the implications of this property. Finally, we study the maximum likelihood estimation for this family.
In this paper, using the Lie group analysis method, we study the group invariant of the Foam Drainage equation. It shows that this equation can be reduced to ODE. Also we apply the Lie-group classical, and the nonclassical... more
In this paper, using the Lie group analysis method, we study the group invariant of the Foam Drainage equation. It shows that this equation can be reduced to ODE. Also we apply the Lie-group classical, and the nonclassical method due to Bluman and Cole to deduce symmetries of the Foam Drainage equation. and we prove that the nonclassical method applied to the equation leads to new reductions, which cannot be obtained by Lie classical symmetries. Also this paper shows how to construct directly the local conservation laws for this equation
Let $G$ be a Lie group equipped with a left-invariant Randers metric $F$. Suppose that $F^v$ and $F^c$ denote the vertical and complete lift of $F$ on $TG$, respectively. We give the necessary and sufficient conditions under which $F^v$... more
Let $G$ be a Lie group equipped with a left-invariant Randers metric $F$. Suppose that $F^v$ and $F^c$ denote the vertical and complete lift of $F$ on $TG$, respectively. We give the necessary and sufficient conditions under which $F^v$ and $F^c$ are generalized Douglas-Weyl metrics. Then, we characterize all 2-step nilpotent Lie groups $G$ such that their tangent Lie groups $(TG, F^c)$ are generalized Douglas-Weyl Randers metrics.
Let $mathbb {D}$ be the open unit disk in the complex plane $mathbb{C}$ and $H(mathbb{D})$ be the set of all analytic functions on $mathbb{D}$. Let $u, vin H(mathbb{D})$ and $varphi$ be an analytic self-map of $mathbb{D}$. A class... more
Let $mathbb {D}$ be the open unit disk in the complex plane $mathbb{C}$ and $H(mathbb{D})$ be the set of all analytic functions on $mathbb{D}$. Let $u, vin H(mathbb{D})$ and $varphi$ be an analytic self-map of $mathbb{D}$. A class of operator-related weighted composition operators
is defined as follow
begin{align*}
T_{u, v, varphi}f(z) = u(z) f{(varphi(z))}+ v(z) f'(varphi(z)) ,quad fin H(mathbb{D} ), quad zin mathbb{D}.
end{align*}
In this work, we obtain some new characterizations for boundedness and essential norm of
operator $T_{u, v, varphi}$ between Zygmund space.
is defined as follow
begin{align*}
T_{u, v, varphi}f(z) = u(z) f{(varphi(z))}+ v(z) f'(varphi(z)) ,quad fin H(mathbb{D} ), quad zin mathbb{D}.
end{align*}
In this work, we obtain some new characterizations for boundedness and essential norm of
operator $T_{u, v, varphi}$ between Zygmund space.
In this paper, by the order of a group and triviality of $O_p(G)$ for some prime $p$, we give a new characterization for some characteristically simple groups. In fact, we prove that if pϵ{5, 17, 23, 37, 47, 73} and n≤p, where $n$ is a... more
In this paper, by the order of a group and triviality of $O_p(G)$ for some prime $p$, we give a new characterization for some characteristically simple groups. In fact, we prove that if pϵ{5, 17, 23, 37, 47, 73} and n≤p, where $n$ is a natural number, then $Gcong{{rm PSL}(2,p)}^{n}$ if and only if $ |G|=|{{rm PSL}(2,p)}|^{n}$ and $ O_p(G)=1$.}
Recently in [Qin, Yan, Shum and Chen, Comm. Algebra, 2019], the degree prime-power graph of a finite group
have been introduced and it is proved that the Mathieu groups are uniquely determined by their degree prime-power graphs and orders. As a consequence of our results, we show that ${rm PSL}(2,p)^n$, where pϵ{5,17,23,37,47,73} and n≤p are uniquely determined by their degree prime-power graphs and orders.
Recently in [Qin, Yan, Shum and Chen, Comm. Algebra, 2019], the degree prime-power graph of a finite group
have been introduced and it is proved that the Mathieu groups are uniquely determined by their degree prime-power graphs and orders. As a consequence of our results, we show that ${rm PSL}(2,p)^n$, where pϵ{5,17,23,37,47,73} and n≤p are uniquely determined by their degree prime-power graphs and orders.
Let G be a directed graph with m vertices and n edges, I(B) the binomial ideal associated to the incidence matrix B of the graph G, and I_L the lattice ideal associated to the columns of the matrix B. Also let B_i be a submatrix of B... more
Let G be a directed graph with m vertices and n edges, I(B) the
binomial ideal associated to the incidence matrix B of the graph G, and I_L the lattice
ideal associated to the columns of the matrix B. Also let B_i be a submatrix of
B after removing the ith column. In this paper it is determined that which prime
minimal ideals of I(B_i) are Andean or toral. Then we study the rank of the space
of solutions of binomial D-module associated to I(B_i) as A-graded ideal, where A is
a matrix that, AB_i = 0. Afterwards, we define a maximal cellular cycle and prove
that for computing this rank it is enough to consider these components of G. We
introduce some bounds for the number of the vertices of the convex hull generated
by the columns of the matrix A. Finally an algorthim is introduced by which we can
compute the volume of the convex hull corresponded to a cycles with k diagonals, so
by Theorem 2.1 the rank of (D / H_A(I(B_i); beta)) can be computed.
binomial ideal associated to the incidence matrix B of the graph G, and I_L the lattice
ideal associated to the columns of the matrix B. Also let B_i be a submatrix of
B after removing the ith column. In this paper it is determined that which prime
minimal ideals of I(B_i) are Andean or toral. Then we study the rank of the space
of solutions of binomial D-module associated to I(B_i) as A-graded ideal, where A is
a matrix that, AB_i = 0. Afterwards, we define a maximal cellular cycle and prove
that for computing this rank it is enough to consider these components of G. We
introduce some bounds for the number of the vertices of the convex hull generated
by the columns of the matrix A. Finally an algorthim is introduced by which we can
compute the volume of the convex hull corresponded to a cycles with k diagonals, so
by Theorem 2.1 the rank of (D / H_A(I(B_i); beta)) can be computed.
This paper addresses a variant of bus timetabling problem assuming that travel times changes dynamically over the planning horizon. In addition to minimizing the transfer waiting time, another objective, namely minimizing the fruitless... more
This paper addresses a variant of bus timetabling problem assuming that travel times changes dynamically over the planning horizon. In addition to minimizing the transfer waiting time, another objective, namely minimizing the fruitless waiting time, is introduced in this paper as a new realistic objective. First, the problem is formulated as a mixed integer linear programming model. Then, since commercial solvers become inefficient to solve moderate and large sized instances of the problem (due to the NP-hardness), a GRASP heuristic algorithm is developed. Computational experiments over a variety of random instances verify the performance of the proposed method.
Monitoring of the driver decreases accidents by reducing the risky behaviors and causes decreases the fuel consumption by preventing aggressive behavior. But this monitoring is costly due to built-in equipment. In this study, we propose a... more
Monitoring of the driver decreases accidents by reducing the risky behaviors and causes decreases the fuel consumption by preventing aggressive behavior. But this monitoring is costly due to built-in equipment. In this study, we propose a new model to recognize driving behavior by smartphone data without any extra equipment in the vehicles which is an important added value for smartphones. This recognition process is done in this paper based on the continuous wavelet transformation on accelerometer data. Then these patterns are fed to multilayer perceptron neural network to extend the information extracted from the corresponding features. Also the magnetometer sensor is used to detect the maneuvers through the driving period. Results show the accuracy of the proposed system is near 80% for pattern recognition. Driver scale based on a standard questionnaires regarding to driver angry scale (DAS), is also estimated by the proposed multilayer perceptron neural network with 3.7% errors in the average.
The important approaches to statistical and fuzzy clustering are reviewed and compared, and their applications to an agricultural problem based on a real-world data are investigated. The methods employed in this study includes some... more
The important approaches to statistical and fuzzy clustering are reviewed and compared, and their applications to an agricultural problem based on a real-world data are investigated. The methods employed in this study includes some hierarchical clustering and non-hierarchical clustering methods and fuzzy c-means method. As a case study, these methods are then applied to cluster 15 provinces of Iraq based on some agricultural crops. Finally, a comparative and evaluation study of different statistical and fuzzy clustering methods is performed. The obtained results showed that, based on the Silhouette criterion and Xie-Beni index, fuzzy c-means method is the best one among all reviewed methods.
Under dynamic conditions on bridges, we need a real-time management. To this end, this paper presents a rule-based decision support system in which the necessary rules are extracted from simulation results made by Aimsun traffic... more
Under dynamic conditions on bridges, we need a real-time management. To this end, this paper presents a rule-based decision support system in which the necessary rules are extracted from simulation results made by Aimsun traffic micro-simulation software. Then, these rules are generalized by the aid of fuzzy rule generation algorithms. Then, they are trained by a set of supervised and the unsupervised learning algorithms to get an ability to make decision in real cases. As a pilot case study, Nasr Bridge in Tehran is simulated in Aimsun and WEKA data mining software is used to execute the learning algorithms. Based on this experiment, the accuracy of the supervised algorithms to generalize the rules is greater than 80%. In addition, CART decision tree and sequential minimal optimization (SMO) provides 100% accuracy for normal data and these algorithms are so reliable for crisis management on bridge. This means that, it is possible to use such machine learning methods to manage bridges in the real-time conditions.
Let $pi_e(G)$ be the set of elements orders of $ G$. Also let $ s_n$ be the number of elements of order $n$ in $G $ and ${rm nse}(G)= lbrace s_nmid nin pi_e(G) rbrace $. In this paper we prove that if $ G$ is a group such that ${rm... more
Let $pi_e(G)$ be the set of elements orders of $ G$. Also let $ s_n$ be the number of elements of order $n$ in $G $ and ${rm nse}(G)= lbrace s_nmid nin pi_e(G) rbrace $.
In this paper we prove that if $ G$ is a group such that ${rm nse}(G)= {rm nse}(rm PSL(4,7)) $, $19bigvert|G|$ and $19^2nmid|G|$, then $ Gcong rm PSL(4,7)$. As a consequence of this result it follows that Thompson's problem is satisfied for the simple group $rm PSL(4,7)$.
In this paper we prove that if $ G$ is a group such that ${rm nse}(G)= {rm nse}(rm PSL(4,7)) $, $19bigvert|G|$ and $19^2nmid|G|$, then $ Gcong rm PSL(4,7)$. As a consequence of this result it follows that Thompson's problem is satisfied for the simple group $rm PSL(4,7)$.
Statistical inference for extremes has been a subject of intensive research during the last years. In this paper, we generalize the Marshall-Olkin bivariate Pareto distribution. In this case, a new bivariate distribution is introduced by... more
Statistical inference for extremes has been a subject of intensive research during the last years. In this paper, we generalize the Marshall-Olkin bivariate Pareto distribution. In this case, a new bivariate distribution is introduced by compounding the Pareto Type II and geometric distributions. This new bivariate distribution has natural interpretations and can be applied in fatal shock models or in competing risks models. We call the new proposed model Marshall-Olkin bivariate Pareto-geometric (MOBPG) distribution, and then investigate various properties of the new distribution. This model has five unknown parameters and the maximum likelihood estimators cannot be afforded in explicit structure. We suggest to use the EM algorithm to calculate the maximum likelihood estimators of the unknown parameters, and this structure is quite flexible.
Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze a real data set to investigate our purposes.
Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze a real data set to investigate our purposes.
In this paper, a new four-parameters model called the complementary odd Weibull power series (COWPS) distribution is defined and its properties are explored. This new distribution exhibits several new and well-known hazard rate shapes... more
In this paper, a new four-parameters model called the complementary odd Weibull power
series (COWPS) distribution is defined and its properties are explored. This new distribution exhibits several new and well-known hazard rate shapes such as increasing, decreasing,
bathtub-shaped and J-shape hazard rate. Some of its mathematical properties are obtained
including moments, quantiles reliability, and moment generating functions. Maximum likelihood estimation method is used to estimate the vector of parameters. A simulation study
is presented to investigate the performance of the estimators. Finally, The usefulness of the
model has been demonstrated by applying it to a real-life dataset.
series (COWPS) distribution is defined and its properties are explored. This new distribution exhibits several new and well-known hazard rate shapes such as increasing, decreasing,
bathtub-shaped and J-shape hazard rate. Some of its mathematical properties are obtained
including moments, quantiles reliability, and moment generating functions. Maximum likelihood estimation method is used to estimate the vector of parameters. A simulation study
is presented to investigate the performance of the estimators. Finally, The usefulness of the
model has been demonstrated by applying it to a real-life dataset.
Given a set P of n points in the plane, the unit disk cover problem, which is known as an NP-hard problem, seeks to find the minimum number of unit disks that can cover all points of P. In this paper, we present a new 4-approximation... more
Given a set P of n points in the plane, the unit disk cover problem, which is known as an NP-hard problem, seeks to find the minimum number of unit disks that can cover all points of P. In this paper, we present a new 4-approximation algorithm with running time O(n log n) for this problem. Our proposed algorithm uses a simple greedy approach and is easy to understand and implement.
Here, a natural extension of Sobolev spaces is defined for a Finsler structure $F$ and it is shown that the set of all real $C^{∞}$ functions with compact support on a forward geodesically complete Finsler manifold $(M, F)$, is dense in... more
Here, a natural extension of Sobolev spaces is defined for a Finsler structure $F$ and it is shown that the set of all real $C^{∞}$ functions with compact support on a forward geodesically complete Finsler manifold $(M, F)$, is dense in the extended Sobolev space $H_1^p (M)$.
As a consequence, the weak solutions $u$ of the Dirichlet equation $Δu=f$ can be approximated by $C^∞$ functions with compact support on $M$.
Moreover, let $W subset M$ be a regular domain with the $C^r$ boundary $partial W$, then the set of all real functions in $C^r (W) cap C^0 (overline W)$ is dense in $H_k^p (W)$, where $k≤r$. Finally, several examples are illustrated and sharpness of the inequality $k≤r$ is shown.
As a consequence, the weak solutions $u$ of the Dirichlet equation $Δu=f$ can be approximated by $C^∞$ functions with compact support on $M$.
Moreover, let $W subset M$ be a regular domain with the $C^r$ boundary $partial W$, then the set of all real functions in $C^r (W) cap C^0 (overline W)$ is dense in $H_k^p (W)$, where $k≤r$. Finally, several examples are illustrated and sharpness of the inequality $k≤r$ is shown.
The class of (α,β)-metrics is a rich and important class of Finsler metrics, which is extensively studied. Here, we study (α,β)-metrics with Killing of constant length 1-form β and find a simplified formula for their Ricci curvatures.... more
The class of (α,β)-metrics is a rich and important class of Finsler metrics, which is extensively studied. Here, we study (α,β)-metrics with Killing of constant length 1-form β and find a simplified formula for their Ricci curvatures. Then, we
show that if F=α+β+b\frac{β^2}{α} is an Einstein Finsler metric, then α is an Einstein Riemann metric.
show that if F=α+β+b\frac{β^2}{α} is an Einstein Finsler metric, then α is an Einstein Riemann metric.
In this article, first a density by the name "The bimodal standard normal density" is introduced and denoted by bΦ(z). Then, a de ntion for the kurtosis of bimodal densities relative to bΦ(z) is presented. Finally, to illustrate the... more
In this article, first a density by the name "The bimodal standard normal density" is introduced and denoted by bΦ(z). Then, a de ntion for the kurtosis of bimodal densities relative to bΦ(z) is presented. Finally, to illustrate the introduced kurtosis, a few examples
are provided and a real data set is studied,too.
are provided and a real data set is studied,too.
In the current research work, we present an improvement of meshless boundary element method (MBEM) based on the shape functions of radial basis functions-QR (RBF-QR) for solving the two-dimensional elasticity problems. The MBEM has... more
In the current research work, we present an improvement of meshless
boundary element method (MBEM) based on the shape functions of radial
basis functions-QR (RBF-QR) for solving the two-dimensional
elasticity problems. The MBEM has benefits of the boundary integral
equations (BIEs) to reduce the dimension of problem and the
meshless attributes of moving least squares (MLS) approximations.
Since the MLS shape functions don't have the delta
function property, applying boundary conditions is not simple. Here, we
propose the MBEM using RBF-QR to increase the accuracy and
efficiency of MBEM. To show the performance of the new technique,
the two-dimensional elasticity problems have been selected. We solve
the mentioned model on several irregular domains and report simulation results.
boundary element method (MBEM) based on the shape functions of radial
basis functions-QR (RBF-QR) for solving the two-dimensional
elasticity problems. The MBEM has benefits of the boundary integral
equations (BIEs) to reduce the dimension of problem and the
meshless attributes of moving least squares (MLS) approximations.
Since the MLS shape functions don't have the delta
function property, applying boundary conditions is not simple. Here, we
propose the MBEM using RBF-QR to increase the accuracy and
efficiency of MBEM. To show the performance of the new technique,
the two-dimensional elasticity problems have been selected. We solve
the mentioned model on several irregular domains and report simulation results.
Let G = (V, E) be a simple graph without isolated vertices. A set D ⊂ V is a total [1, 2]-dominating set if for every vertex v ∈ V , 1 ≤ |N (v) ∩ D| ≤ 2. The total [1, 2]-domination problem is to determine the total [1, 2]-domination... more
Let G = (V, E) be a simple graph without isolated vertices. A set D ⊂ V is a total [1, 2]-dominating set if for every vertex v ∈ V , 1 ≤ |N (v) ∩ D| ≤ 2. The total [1, 2]-domination problem is to determine the total [1, 2]-domination number γ t[1,2] (G), which is the minimum cardinality of a total [1, 2]-dominating set for a graph G. In this paper, we present a linear-time algorithm to compute γ t[1,2] (G) for a block graph G.
Research Interests:
In the current study, by a general fuzzy automaton we aim at showing a set of propositions related to a given automaton showing that the truth-values are depended on thestates, inputs and membership values of active states at time t. This... more
In the current study, by a general fuzzy automaton we aim at showing a set of propositions related to a given automaton showing that the truth-values are depended on thestates, inputs and membership values of active states at time t. This new approach enables us to consider automata from a different point of view which is more close to logical treatment and helps us make estimations about the behavior of automaton particularly in a nondeterministic mode. The logic consists of propositions on the given GFA and its dynamic nature is stated by means of the so-called transition functor. This logic enables us to derive a certain relation on the set of states labeled by inputs. In fact, it is shown that if our set of propositions is large enough, this recovering of the transition relation is possible. Through a synthesis in the theory of systems, this study contributes to construct a general fuzzy automaton which realizes a dynamic process at least partially known to the user, which has been fully achieved in Theorem 3.6. Also, we study the theory of general fuzzy automata by using the concepts of operators. Such operators help us in the algebraic study of general fuzzy automata theory and provide a platform to use fuzzy topological therein. Further, a Galois connection is obtained between the state-transition relation on states and thetransition operators on propositions. To illustrate the proposed approach, the subject matter is more elaborated in detail through examples.
Research Interests:
The main aim of the current article is to find the solution for Newell-Whitehead-Segel equations with constant coefficients containing Caputo-Prabhakar fractional derivative using the homotopy perturbation transform method. The... more
The main aim of the current article is to find the solution for Newell-Whitehead-Segel equations with constant coefficients containing Caputo-Prabhakar fractional derivative using the homotopy perturbation transform method. The convergence analysis of the obtained solution for the proposed fractional order model is presented. Four examples are presented to illustrate the efficiency and applicability and accurateness of the proposed numerical technique.
Research Interests:
Here, it is proved that the potential functions of Finsler Yamabe solitons have at most quadratic growth in distance function. Also it is obtained a finite topological type property on complete gradient Finsler Yamabe solitons under... more
Here, it is proved that the potential functions of Finsler Yamabe solitons have at most quadratic growth in distance function. Also it is obtained a finite topological type property on complete gradient Finsler Yamabe solitons under suitable scalar curvature assumptions.
Research Interests:
In this paper, the classical Lie symmetry analysis and the generalized form of Lie symmetry method are performed for a general short pulse equation. The point, contact and local symmetries for this equation are given. In this paper, we... more
In this paper, the classical Lie symmetry analysis and the generalized form of Lie symmetry method are performed for a general short pulse equation. The point, contact and local symmetries for this equation are given. In this paper, we generalize the results of H. Liu and J. Li [2], and add some further facts, such as an optimal system of Lie symmetry subalgebras and two local symmetries.
Research Interests:
In this paper, we study the Castelnuovo-Mumford regularity and the graded Betti numbers of the binomial edge ideals of some classes of graphs. Our special attention is devoted to a conjecture which asserts that the number of maximal... more
In this paper, we study the Castelnuovo-Mumford regularity and the graded Betti numbers of the binomial edge ideals of some classes of graphs. Our special attention is devoted to a conjecture which asserts that the number of maximal cliques of a graph provides an upper bound for the regularity of its binomial edge ideal.
Research Interests:
Software Architecture (SA) generally has a considerable influence on software quality attributes. Coordination of software architecture to the requirements of the stakeholders and avoiding common mistakes and faults in designing SA... more
Software Architecture (SA) generally has a considerable influence on software quality attributes. Coordination of software architecture to the requirements of the stakeholders and avoiding common mistakes and faults in designing SA increases the chance of success of the project and satisfaction of the stakeholders. Making the wrong decisions at the architectural design phase usually proves very costly later on. Refactoring is a method which helps in detecting and avoiding complications, improving the internal characteristics of software, while keeping the external behavior intact. Various problems can undermine the architecture refactoring process. The existence of different requirements in different domains, the diversity of architecture description languages, and the difficulty of describing refactoring patterns lead to the difficulty of performing automatic and semi-automatic refactoring on the SA. In this study, we use model transformation as a way to overcome the above mentioned difficulties. In this regard, the first step is converting the SA to a pivot-model. Then, based on the refactoring patterns, the refactoring process is performed on the pivot-model. And finally, the pivot-model is converted back to the original (source) model. In this paper, the requirements of the stakeholders are taken into account in the refactoring process by modeling them as refactoring goals. These goals show the importance of the quality attributes in the project and the process of refactoring. The applicability of the framework is demonstrated using a case study.
Research Interests:
Given a pool table enclosing a set of axis-aligned rectangles, with a total of n edges, this paper studies closed billiard paths. A closed billiard path is formed by following the ball shooting from a starting point into some direction,... more
Given a pool table enclosing a set of axis-aligned rectangles, with a total of n edges, this paper studies closed billiard paths. A closed billiard path is formed by following the ball shooting from a starting point into some direction, such that it doesn't touch any corner of a rectangle, doesn't visit any point on the table twice, and stops exactly at the starting position. The signature of a billiard path is the sequence of the labels of edges in the order that are touched by the path, while repeated edge reflections like abab are replaced by ab. We prove that the length of a signature is at most 4.5n−9, and we show that there exists an arrangement of rectangles where the length of the signature is 1.25n + 2. We also prove that the number of distinct signatures for fixed shooting direction (45 •) is at most 1.5n − 6.
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Mapping reads onto genomes is an indispensable step in sequencing data analysis. A widely used method to speed up mapping is to index a genome by a hash table, in which genomic positions of k-mers are stored in the table. The hash table... more
Mapping reads onto genomes is an indispensable step in sequencing data analysis. A widely used method to speed up mapping is to index a genome by a hash table, in which genomic positions of k-mers are stored in the table. The hash table size increases exponentially with the k-mer length and thus the traditional hash function is not appropriate for a k-mer as long as a read. We present a hashing mechanism by two functions named score1 and score2 which can hash sequences with the length of reads. The size of hash table is directly proportional to the genome size, which is absolutely lower than that of hash table built by the conventional hash function. We evaluate our hashing system by developing a read mapper and running the mapper on E. coli genome with some simulated data sets. The results show that the high percentage of simulated reads can be mapped to correct locations on the genome.
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In this paper, we consider the Homicidal Chauffeur (HC) problem as an interesting and practical differential game. At first, we introduce a bilevel optimal control problem (BOCP) and prove that a saddle point solution for this game exists... more
In this paper, we consider the Homicidal Chauffeur (HC) problem as an interesting and practical differential game. At first, we introduce a bilevel optimal control problem (BOCP) and prove that a saddle point solution for this game exists if and only if this BOCP has an optimal solution in which the optimal value of the objective function is equal to 1. Then, BOCP is discretized and converted to a nonlinear bilevel programming problem. Finally, an Artificial Bee Colony (ABC) algorithm is used for solving this problem, in which the lower-level problem will be considered as a constraint and solved by an NLP-solver. Finally, to demonstrate the effectiveness of the presented method, various cases of HC problem are solved and the simulation results are reported.
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In this paper, we study the directed multicut and directed multi-multiway cut problems. The input to the directed multi-multiway cut problem is a weighted directed graph G = (V, E) and k sets S 1 , S 2 , ..., S k of vertices. The goal is... more
In this paper, we study the directed multicut and directed multi-multiway cut problems. The input to the directed multi-multiway cut problem is a weighted directed graph G = (V, E) and k sets S 1 , S 2 , ..., S k of vertices. The goal is to find a subset of edges of minimum total weight whose removal will disconnect all the connections between the vertices in each set S i , for 1 ≤ i ≤ k. A special case of this problem is the directed multicut problem whose input consists of a weighted directed graph G = (V, E) and a set of ordered pairs of vertices (s 1 , t 1), ..., (s k , t k). The goal is to find a subset of edges of minimum total weight whose removal will make for any i, 1 ≤ i ≤ k, there is no directed path from s i to t i. In this paper, we present two approximation algorithms for these problems. The so called region growing paradigm is modified and used for these two cut problems on directed graphs. using this paradigm, we give an approximation algorithm for each problem such that both algorithms have the approximation factor of O(k) the same as the previous works done on these problems. However, the previous works need to solve k linear programming, whereas our algorithms require only one linear programming. Therefore, our algorithms improve the running time of the previous algorithms.
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This paper proposes a smartphone-based warning system to evaluate the risk of a motor vehicle for vulnerable pedestrians (VP). The acoustic sensors are embedded in the roadside to receive vehicle sounds and they are classified into heavy... more
This paper proposes a smartphone-based warning system to evaluate the risk of a motor vehicle for vulnerable pedestrians (VP). The acoustic sensors are embedded in the roadside to receive vehicle sounds and they are classified into heavy vehicles, light vehicles with low speed, light vehicles with high speed, and no vehicle classes. For this aim, we extract new features by Mel-frequency Cepstrum Coefficients (MFCC) and Linear Predictive Coefficients (LPC) algorithms. We use different classification algorithms and show that MLP neural network achieves at least 96.77% accuracy criterion. To install this system, directional microphones are embedded on the roadside and the risk is classified. Then, for every microphone, a danger area is defined and the warning alarms have been sent to every VPs' smartphones covered in this danger area.