In the proposed article, the existence of a solution is investigated for a pointwise multi-singular fractional differential equation with integral boundary conditions. In the following, the existence of a common solution will be considered for two singular fractional equations. Likewise, some examples are represented to demonstrate our main results.
{"title":"Investigation of a common solution for a multi-singular fractional system by using control functions method","authors":"A. Malekpour, Mehdi Shabibi","doi":"10.30495/JME.V15I0.1927","DOIUrl":"https://doi.org/10.30495/JME.V15I0.1927","url":null,"abstract":"In the proposed article, the existence of a solution is investigated for a pointwise multi-singular fractional differential equation with integral boundary conditions. In the following, the existence of a common solution will be considered for two singular fractional equations. Likewise, some examples are represented to demonstrate our main results.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46925164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, by using control functions, the existence of a solution for a bi-singular fractional differential equation with multi-point initial value conditions is considered. In the following, an example elucidates our main result.
{"title":"Bi-singular type of a fractional-order multi-points boundary value condition problem","authors":"Mehdi Shabibi","doi":"10.30495/JME.V15I0.1963","DOIUrl":"https://doi.org/10.30495/JME.V15I0.1963","url":null,"abstract":"In this article, by using control functions, the existence of a solution for a bi-singular fractional differential equation with multi-point initial value conditions is considered. In the following, an example elucidates our main result.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45960887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, to each two elements y; u of a BCK-algebra X, we assign a subset of X, denoted by Sy(u), and investigate some related properties. We show that Sy(u) is a subalgebra of X for all y; u in X. Using these subalgebras, we characterize the involitive BCK-algebras, and give a necessary and suucient condition for a bounded BCK-algebra to be a commutative BCK-chain. Finally, we show that the set of all subalgebras Sy(u) forms a bounded distributive lattice.
{"title":"On Class of Subalgebras of Bounded BCK-algebras","authors":"H. Harizavi","doi":"10.30495/JME.V0I0.1660","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1660","url":null,"abstract":"In this paper, to each two elements y; u of a BCK-algebra X, we assign a subset of X, denoted by Sy(u), and investigate some related properties. We show that Sy(u) is a subalgebra of X for all y; u in X. Using these subalgebras, we characterize the involitive BCK-algebras, and give a necessary and suucient condition for a bounded BCK-algebra to be a commutative BCK-chain. Finally, we show that the set of all subalgebras Sy(u) forms a bounded distributive lattice.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42725974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we shall apply symmetry analysis to second order functional differential equations with constant coefficients. The determining equations of the admitted Lie group are constructed in a manner different from that of the existing literature for delay differential equations. We define the standard Lie bracket and make a complete classification of the second order linear functional differential equations with constant coefficients, to solvable Lie algebras. We also classify some second order non-linear functional differential equations with constant coefficients, to solvable Lie algebras.
{"title":"Classification of Second Order Functional Differential Equations with Constant Coefficients to Solvable Lie Algebras","authors":"Jervin Zen Lobo, Y. S. Valaulikar","doi":"10.30495/JME.V0I0.1810","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1810","url":null,"abstract":"In this paper, we shall apply symmetry analysis to second order functional differential equations with constant coefficients. The determining equations of the admitted Lie group are constructed in a manner different from that of the existing literature for delay differential equations. We define the standard Lie bracket and make a complete classification of the second order linear functional differential equations with constant coefficients, to solvable Lie algebras. We also classify some second order non-linear functional differential equations with constant coefficients, to solvable Lie algebras.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45634004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
One of the attractive subjects in decision analysis is the investigating of the uncertain data which is inevitable in many real-world applications. A variety of tools can be used by researchers to study the problems in the presence of uncertain data. For example, fuzzy sets theory has been introduced to investigate the uncertain data which formulates the uncertainty by using the membership functions. However, in many real world applications, it is difficult to determine the exact amount of the membership value and so the skepticism can be raised during the decision-making process. The new perspective manages the uncertainty caused by the skepticism and in this case, the most important issues are to collect the hesitant fuzzy information and to select the optimal alternative. This study develops the deviation-oriented hesitant fuzzy envelopment analysis (DHFEA) based on the slack based measure (SBM) in terms of deviation values; and on basis of different production possibility set (PPS) can be formulated. For this purpose, a two-stage method is proposed for ranking the Decision Making Units (DMUs) by using the DHFEA and the Analytic Hierarchy Process (AHP). Given that in many cases the importance of input or output indices plays an important role in decision-making, therefore, the first stage of the proposed method evaluates and compares the DMUs and the second stage constructs the pair-wise comparisons matrix by using the obtained results of DHFEA model and then proposes a complete ranking of DMUs by applying AHP method. The potential application of the proposed method is illustrated with a numerical example with the hesitant fuzzy data and the obtained results are compared with the results of the existing ranking methods.
{"title":"A Hybrid DHFEA/AHP Method for Ranking Units with Hesitant Fuzzy Data","authors":"T. R. Taziani, M. Ahmadi, M. Shahryari","doi":"10.30495/JME.V0I0.1794","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1794","url":null,"abstract":"One of the attractive subjects in decision analysis is the investigating of the uncertain data which is inevitable in many real-world applications. A variety of tools can be used by researchers to study the problems in the presence of uncertain data. For example, fuzzy sets theory has been introduced to investigate the uncertain data which formulates the uncertainty by using the membership functions. However, in many real world applications, it is difficult to determine the exact amount of the membership value and so the skepticism can be raised during the decision-making process. The new perspective manages the uncertainty caused by the skepticism and in this case, the most important issues are to collect the hesitant fuzzy information and to select the optimal alternative. This study develops the deviation-oriented hesitant fuzzy envelopment analysis (DHFEA) based on the slack based measure (SBM) in terms of deviation values; and on basis of different production possibility set (PPS) can be formulated. For this purpose, a two-stage method is proposed for ranking the Decision Making Units (DMUs) by using the DHFEA and the Analytic Hierarchy Process (AHP). Given that in many cases the importance of input or output indices plays an important role in decision-making, therefore, the first stage of the proposed method evaluates and compares the DMUs and the second stage constructs the pair-wise comparisons matrix by using the obtained results of DHFEA model and then proposes a complete ranking of DMUs by applying AHP method. The potential application of the proposed method is illustrated with a numerical example with the hesitant fuzzy data and the obtained results are compared with the results of the existing ranking methods.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42108774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Protecting important nodes in a network against natural disasters, security threats, attacks and so on is one of the main goals of network planners. In this paper, a new model is presented for protecting an important node (NMPN) in a typical network based on defensive location problem where the threatening agent (t-agent) has the ability to reinforce its power at some nodes. The NMPN is a bi-level programming problem. At the upper level, the planner agent (p-agent) try to find the best locations for protecting resources in order to protect the important node. The lower level problem is represented as the shortest path problem in the network in which the edges are weighted with positive values and sometimes negative values. Thus, Bellman-Ford algorithm is applied to solve the lower level problem. The NMPN is an NP-hard problem. In this work, the genetic, ant colony optimization, binary artificial bee colony with differential evolution, artificial bee colony algorithms and a modified tabu search (MTS) algorithm are used to solve the problem. A test problem is randomly generated to investigate the performance of the used metaheuristic algorithms in this paper. Parameters of the metaheuristic algorithms are tuned by the Taguchi method for solving the test problem. Also, the ANOVA and Tukey tests are used to compare the performance of metaheuristic algorithms. The best results are obtained by the MTS algorithm
{"title":"A Bi-Level Programming Model for Protecting an Important Node in a Network","authors":"H. Maleki, Z. Maleki, R. Akbari","doi":"10.30495/JME.V0I0.1732","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1732","url":null,"abstract":"Protecting important nodes in a network against natural disasters, security threats, attacks and so on is one of the main goals of network planners. In this paper, a new model is presented for protecting an important node (NMPN) in a typical network based on defensive location problem where the threatening agent (t-agent) has the ability to reinforce its power at some nodes. The NMPN is a bi-level programming problem. At the upper level, the planner agent (p-agent) try to find the best locations for protecting resources in order to protect the important node. The lower level problem is represented as the shortest path problem in the network in which the edges are weighted with positive values and sometimes negative values. Thus, Bellman-Ford algorithm is applied to solve the lower level problem. The NMPN is an NP-hard problem. In this work, the genetic, ant colony optimization, binary artificial bee colony with differential evolution, artificial bee colony algorithms and a modified tabu search (MTS) algorithm are used to solve the problem. A test problem is randomly generated to investigate the performance of the used metaheuristic algorithms in this paper. Parameters of the metaheuristic algorithms are tuned by the Taguchi method for solving the test problem. Also, the ANOVA and Tukey tests are used to compare the performance of metaheuristic algorithms. The best results are obtained by the MTS algorithm","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":"124 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41260010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this paper is to define a newclass of analytic, normalizedfunctions in the open unit disk $Delta={ z:zin mathbb{C}quad text{and}quad leftvertzrightvert <1}$ subordinating with crescent shaped regions, and to derive certain coefficient estimates $a_2$ , $a_3$ and Fekete-Szeg"{o} inequality for $finmathscr{M}_q(alpha,beta,lambda)$. A similar result have been done for the function $ f^{-1}. $ Further application of our results to certain functions defined by convolution products with a normalizedanalytic function is given, in particular we obtainFekete-Szeg"{o} inequalities for certainsubclasses of functions defined through Poisson distribution series.
{"title":"Fekete-Szeg\"{o} inequality for certain Subclasses of analytic functions related with Crescent-Shaped domain and application of Poison distribution series","authors":"G. Murugusundaramoorthy","doi":"10.30495/JME.V0I0.1697","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1697","url":null,"abstract":"The purpose of this paper is to define a newclass of analytic, normalizedfunctions in the open unit disk $Delta={ z:zin mathbb{C}quad text{and}quad leftvertzrightvert <1}$ subordinating with crescent shaped regions, and to derive certain coefficient estimates $a_2$ , $a_3$ and Fekete-Szeg\"{o} inequality for $finmathscr{M}_q(alpha,beta,lambda)$. A similar result have been done for the function $ f^{-1}. $ Further application of our results to certain functions defined by convolution products with a normalizedanalytic function is given, in particular we obtainFekete-Szeg\"{o} inequalities for certainsubclasses of functions defined through Poisson distribution series.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42115207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce the notion of braiding crossed polymodule and $Gamma$_equivariant braided crossed polymodule of polygroups and we give some of its properties. Further we have concept Fiber hyper product. Our results extend the classical results of crossed squares to crossed polysquares. One of the main tools in the study to polygroups is the fundamental relations. Additionally, we study on crossed polysquare version of homotopy kernels.
{"title":"On crossed polysquare version of homotopy kernels","authors":"M. Dehghani, B. Davvaz, M. Alp","doi":"10.30495/JME.V0I0.1778","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1778","url":null,"abstract":"In this paper, we introduce the notion of braiding crossed polymodule and $Gamma$_equivariant braided crossed polymodule of polygroups and we give some of its properties. Further we have concept Fiber hyper product. Our results extend the classical results of crossed squares to crossed polysquares. One of the main tools in the study to polygroups is the fundamental relations. Additionally, we study on crossed polysquare version of homotopy kernels.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45645791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The agricultural sector ensures food security in every country.Optimal agricultural practices presuppose the optimal allocationof resources, including water, soil, etc., by official authorities in everycountry because excessive use of natural resources would have harmfulconsequences for posterity despite meeting ad hoc needs. Therefore,sustainable agricultural practices in different regions should be basedon environmental, social, and economic criteria in the decision-makingprocess for the future. This study investigated the agricultural practicesin two stages: environmental stage (planting and maintaining)and economic stage (harvesting), which use shared resources. A networkDEA model was proposed for developing sustainable agriculturalpractices based on the proposed process. The development of sustainableagricultural practices in different regions presupposes the optimal allocation of water and human resources, which is realized by the improvementof irrigation methods and the quality of life of farmers. Innetwork DEA models, weight restrictions are used to determine sustainabledevelopment. The proposed model was analyzed with and withoutweight restrictions to determine the sustainable development of agriculturein Sistan and Baluchestan Province, Iran, between 2013 and 2017.On the other hand, given the important role human resources play inthe development of sustainable agricultural practices, some models weresuggested for determining the maximum required human resources foreach stage according to the obtained performance levels.
{"title":"Sustainability and Optimal Allocation of Human Resource of Agricultural Practices in Sistan and Baluchestan Province Based on Network DEA","authors":"Azizalah Kord, A. Payan, S. Saati","doi":"10.30495/JME.V0I0.1562","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1562","url":null,"abstract":"The agricultural sector ensures food security in every country.Optimal agricultural practices presuppose the optimal allocationof resources, including water, soil, etc., by official authorities in everycountry because excessive use of natural resources would have harmfulconsequences for posterity despite meeting ad hoc needs. Therefore,sustainable agricultural practices in different regions should be basedon environmental, social, and economic criteria in the decision-makingprocess for the future. This study investigated the agricultural practicesin two stages: environmental stage (planting and maintaining)and economic stage (harvesting), which use shared resources. A networkDEA model was proposed for developing sustainable agriculturalpractices based on the proposed process. The development of sustainableagricultural practices in different regions presupposes the optimal allocation of water and human resources, which is realized by the improvementof irrigation methods and the quality of life of farmers. Innetwork DEA models, weight restrictions are used to determine sustainabledevelopment. The proposed model was analyzed with and withoutweight restrictions to determine the sustainable development of agriculturein Sistan and Baluchestan Province, Iran, between 2013 and 2017.On the other hand, given the important role human resources play inthe development of sustainable agricultural practices, some models weresuggested for determining the maximum required human resources foreach stage according to the obtained performance levels.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42933599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Data Envelopment Analysis(DEA) is a non-parametric method for evaluating the efficiency of those Decision Making Units (DMUs) that have the same functionality and use multiple inputs to generate multiple outputs. DMUs may sometimes be divided into several groups according to a series of criteria, and it is intended to evaluate a group of similar DMUs. In this paper, each group was considered as a player in a cooperative game and a subset of groups was considered as a coalition. Assuming the Production Possibility Set is made up of the members of the coalition, a characteristic function was defined in terms of the sum of the efficiency of all units to determine the marginal effect of each group in different coalitions. The groups were then evaluated using the Shapley Value as a solution of the cooperative game. Some Examples were provided to describe and apply the method.
{"title":"Evaluating Groups of Decision Making Units in the Data Envelopment Analysis based on Cooperative Games","authors":"S. Rahmati, R. Fallahnejad","doi":"10.30495/JME.V0I0.1736","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1736","url":null,"abstract":"Data Envelopment Analysis(DEA) is a non-parametric method for evaluating the efficiency of those Decision Making Units (DMUs) that have the same functionality and use multiple inputs to generate multiple outputs. DMUs may sometimes be divided into several groups according to a series of criteria, and it is intended to evaluate a group of similar DMUs. In this paper, each group was considered as a player in a cooperative game and a subset of groups was considered as a coalition. Assuming the Production Possibility Set is made up of the members of the coalition, a characteristic function was defined in terms of the sum of the efficiency of all units to determine the marginal effect of each group in different coalitions. The groups were then evaluated using the Shapley Value as a solution of the cooperative game. Some Examples were provided to describe and apply the method.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48026607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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