Pub Date : 2021-08-17DOI: 10.12962/j24775401.v7i2.6859
H. Debela, G. Duressa, Masho Jima Kebeto
—In this paper, accelerated finite difference method for solving singularly perturbed delay reaction-diffusion equations is presented. First, the solution domain is discretized. Then, the derivatives in the given boundary value problem are replaced by finite difference approximations and the numerical scheme that provides algebraic systems of equations is obtained, which can easily be solved by Thomas algorithm. The consistency, stability and convergence of the method have been established. To increase the accuracy of our established scheme we used Richard- son’s extrapolation techniques. To validate the applicability of the proposed method, four model examples have been considered and solved for different values of perturbation parameters and mesh sizes. The numerical results have been presented in tables and graphs to illustrate; the present method approximates the exact solution very well. Moreover, the present method gives better accuracy than the existing numerical methods mentioned in the literature.
{"title":"Accelerated Numerical Method for Singularly Perturbed Differential Difference Equations","authors":"H. Debela, G. Duressa, Masho Jima Kebeto","doi":"10.12962/j24775401.v7i2.6859","DOIUrl":"https://doi.org/10.12962/j24775401.v7i2.6859","url":null,"abstract":"—In this paper, accelerated finite difference method for solving singularly perturbed delay reaction-diffusion equations is presented. First, the solution domain is discretized. Then, the derivatives in the given boundary value problem are replaced by finite difference approximations and the numerical scheme that provides algebraic systems of equations is obtained, which can easily be solved by Thomas algorithm. The consistency, stability and convergence of the method have been established. To increase the accuracy of our established scheme we used Richard- son’s extrapolation techniques. To validate the applicability of the proposed method, four model examples have been considered and solved for different values of perturbation parameters and mesh sizes. The numerical results have been presented in tables and graphs to illustrate; the present method approximates the exact solution very well. Moreover, the present method gives better accuracy than the existing numerical methods mentioned in the literature.","PeriodicalId":357596,"journal":{"name":"International Journal of Computing Science and Applied Mathematics","volume":"30 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125807422","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}
Pub Date : 2021-08-17DOI: 10.12962/j24775401.v7i2.9776
A. Hakam, Islachiyatul Ummah, Frida Akbar Rani, Nur Asiyah, E. R. Putri
An option is a financial contract between buyers and sellers. The Black-Scholes equation is the most popular mathematical equation used to analyze the option pricing. The exact solution of the Black-Scholes equation can be approached by several approximation methods, one of the method is a Homotopy Perturbation Method (HPM). The simplest type of option, digital options were analyzed using the HPM. The digital option pricing approach using the HPM is in a power series form, which in this paper is presented the solution in the fourth power. This solution is compared with the exact solution of the Black-Scholes equation for digital options. The results show that the approach using HPM is very accurate.
{"title":"Digital Option Pricing Approach Using A Homotopy Perturbation Method","authors":"A. Hakam, Islachiyatul Ummah, Frida Akbar Rani, Nur Asiyah, E. R. Putri","doi":"10.12962/j24775401.v7i2.9776","DOIUrl":"https://doi.org/10.12962/j24775401.v7i2.9776","url":null,"abstract":"An option is a financial contract between buyers and sellers. The Black-Scholes equation is the most popular mathematical equation used to analyze the option pricing. The exact solution of the Black-Scholes equation can be approached by several approximation methods, one of the method is a Homotopy Perturbation Method (HPM). The simplest type of option, digital options were analyzed using the HPM. The digital option pricing approach using the HPM is in a power series form, which in this paper is presented the solution in the fourth power. This solution is compared with the exact solution of the Black-Scholes equation for digital options. The results show that the approach using HPM is very accurate.","PeriodicalId":357596,"journal":{"name":"International Journal of Computing Science and Applied Mathematics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121585490","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}
Pub Date : 2021-08-17DOI: 10.12962/j24775401.v7i2.8663
Giovano Alberto, Alfian Tan
—This research applies the cuckoo search meta- heuristics model to find solutions to the Orienteering Problem (OP). The OP formulation is useful to model a situation in which someone wants to determine an optimal city route that is subject to a specified time constraint. OP can be categorized into NP- Hard Problem which takes a very long time to analytically find the optimal solution as the number of entities involved increases. Therefore, metaheuristics often become an option to deal with this situation. A cuckoo search model based algorithm is developed in this research. An adjustment for discrete combinatorial problem is performed by adopting an idea of binary cuckoo search method. In addition, three types of local search methods are considered to improve the searching performance. This algorithm can eventually find better solutions for some of the 18 cases than two other benchmarked algorithms. Furthermore, experiment on model parameters shows that the worse nest fraction ( Pα ) affects the quality of solutions obtained.
本研究应用布谷鸟搜索元启发式模型寻找定向运动问题(OP)的解。OP公式对于某人想要确定受特定时间约束的最优城市路线的情况进行建模是有用的。OP可以归类为NP- Hard Problem，即随着涉及实体数量的增加，需要很长时间才能解析出最优解。因此，元启发式通常成为处理这种情况的一种选择。本研究提出了一种基于布谷鸟搜索模型的算法。采用二元布谷鸟搜索的思想，对离散组合问题进行了调整。此外，为了提高搜索性能，还考虑了三种局部搜索方法。该算法最终可以在18种情况中找到比其他两种基准算法更好的解决方案。此外，对模型参数的实验表明，较差的巢状分数(Pα)会影响得到的解的质量。
{"title":"An Application of Binary Cuckoo Search Algorithm to Orienteering Problem","authors":"Giovano Alberto, Alfian Tan","doi":"10.12962/j24775401.v7i2.8663","DOIUrl":"https://doi.org/10.12962/j24775401.v7i2.8663","url":null,"abstract":"—This research applies the cuckoo search meta- heuristics model to find solutions to the Orienteering Problem (OP). The OP formulation is useful to model a situation in which someone wants to determine an optimal city route that is subject to a specified time constraint. OP can be categorized into NP- Hard Problem which takes a very long time to analytically find the optimal solution as the number of entities involved increases. Therefore, metaheuristics often become an option to deal with this situation. A cuckoo search model based algorithm is developed in this research. An adjustment for discrete combinatorial problem is performed by adopting an idea of binary cuckoo search method. In addition, three types of local search methods are considered to improve the searching performance. This algorithm can eventually find better solutions for some of the 18 cases than two other benchmarked algorithms. Furthermore, experiment on model parameters shows that the worse nest fraction ( Pα ) affects the quality of solutions obtained.","PeriodicalId":357596,"journal":{"name":"International Journal of Computing Science and Applied Mathematics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127776646","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}
Pub Date : 2021-08-17DOI: 10.12962/j24775401.v7i2.8718
Adin Lazuardy Firdiansyah
—In the present paper, we study the effect of an- tipredator behavior due to fear of predation on a modified Leslie- Gower predator-prey model incorporating prey refuge which predation rate of predators follows Beddington-DeAngelis functional response. The biological justification of the model is demonstrated through non-negativity, boundedness, and permanence. Next, we perform the analysis of equilibrium and local stability. We obtain four equilibrium points where two points are locally asymptotically stable and other points are unstable. Besides, we show the effect of the fear in the model and obtain a conclusion that the increased rate of fear can decrease the density of both populations, and prey populations become extinct. Meanwhile, for the case with a constant rate of fear, the prey refuge helpful to the existence of both populations. However, for the case with the fear effect is large, prey refuge cannot cause the extinction of predators. Several numerical simulations are performed to support our analytical results.
{"title":"Effect of Fear in Leslie-Gower Predator-Prey Model with Beddington-DeAngelis Functional Response Incorporating Prey Refuge","authors":"Adin Lazuardy Firdiansyah","doi":"10.12962/j24775401.v7i2.8718","DOIUrl":"https://doi.org/10.12962/j24775401.v7i2.8718","url":null,"abstract":"—In the present paper, we study the effect of an- tipredator behavior due to fear of predation on a modified Leslie- Gower predator-prey model incorporating prey refuge which predation rate of predators follows Beddington-DeAngelis functional response. The biological justification of the model is demonstrated through non-negativity, boundedness, and permanence. Next, we perform the analysis of equilibrium and local stability. We obtain four equilibrium points where two points are locally asymptotically stable and other points are unstable. Besides, we show the effect of the fear in the model and obtain a conclusion that the increased rate of fear can decrease the density of both populations, and prey populations become extinct. Meanwhile, for the case with a constant rate of fear, the prey refuge helpful to the existence of both populations. However, for the case with the fear effect is large, prey refuge cannot cause the extinction of predators. Several numerical simulations are performed to support our analytical results.","PeriodicalId":357596,"journal":{"name":"International Journal of Computing Science and Applied Mathematics","volume":"135 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115838518","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}
Pub Date : 2021-02-21DOI: 10.12962/j24775401.v7i1.6943
A. Nazra
A real Bott manifold (RBM) is obtained as the orbit space of the n-torus T^n by a free action of an elementary abelian 2-group ZZ_2^n. This paper deals with the classification of some particular types of RBMs of dimension n, so that we know the number of diffeomorphism classes in such RBMs.
{"title":"The Classification of Diffeomorphism Classes of Real Bott Manifolds","authors":"A. Nazra","doi":"10.12962/j24775401.v7i1.6943","DOIUrl":"https://doi.org/10.12962/j24775401.v7i1.6943","url":null,"abstract":"A real Bott manifold (RBM) is obtained as the orbit space of the n-torus T^n by a free action of an elementary abelian 2-group ZZ_2^n. This paper deals with the classification of some particular types of RBMs of dimension n, so that we know the number of diffeomorphism classes in such RBMs.","PeriodicalId":357596,"journal":{"name":"International Journal of Computing Science and Applied Mathematics","volume":"198200 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115186031","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}
Pub Date : 2021-02-21DOI: 10.12962/j24775401.v7i1.7691
Asmudik Asmudik, D. Adzkiya, M. Mardlijah, H. Hariyanto
Human Immunodeficiency Virus (HIV) is an AIDS (Acquired Immuno Deficiency Syndrome) virus that attacks the immune system for which there is no cure. When the immune system has decreased, it is prone to diseases such as Hepatitis B disease. To reduce the error value of the number of subpopulations, we use an interval approximation. One of the simulation calculations that the number of variables initially intervals is Taylor model. Taylor's model can be used to verify that the number of people infected with HIV and Hepatitis B will not exceed the specified number of unsafe sets. To calculate the set of states that are reached by the system over a certain period of time, given the initial conditions and parameters. The initial condition is divided into three scenarios, an affordable set of states, safety verification can be done. As a result of the safety verification of the three scenarios provided there is no set of states that are not safe, so the results of all three scenarios are safe.
{"title":"Safety Verification of SEITR Epidemic Model on Recombination HIV and Hepatitis B Virus using Taylor Model","authors":"Asmudik Asmudik, D. Adzkiya, M. Mardlijah, H. Hariyanto","doi":"10.12962/j24775401.v7i1.7691","DOIUrl":"https://doi.org/10.12962/j24775401.v7i1.7691","url":null,"abstract":"Human Immunodeficiency Virus (HIV) is an AIDS (Acquired Immuno Deficiency Syndrome) virus that attacks the immune system for which there is no cure. When the immune system has decreased, it is prone to diseases such as Hepatitis B disease. To reduce the error value of the number of subpopulations, we use an interval approximation. One of the simulation calculations that the number of variables initially intervals is Taylor model. Taylor's model can be used to verify that the number of people infected with HIV and Hepatitis B will not exceed the specified number of unsafe sets. To calculate the set of states that are reached by the system over a certain period of time, given the initial conditions and parameters. The initial condition is divided into three scenarios, an affordable set of states, safety verification can be done. As a result of the safety verification of the three scenarios provided there is no set of states that are not safe, so the results of all three scenarios are safe.","PeriodicalId":357596,"journal":{"name":"International Journal of Computing Science and Applied Mathematics","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130582580","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}
Pub Date : 2021-02-21DOI: 10.12962/j24775401.v7i1.6975
Sulasri Suddin, Elinora Naikteas Bano
Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. Tuberculosis that fails treatment will develop into multidrug-resistant tuberculosis. Research on the TB epidemic continues, particularly in the field of applied mathematics with modeling. In this study, we analyzed a suitable strategy in controlling the development of susceptible individuals to active tuberculosis and even multidrug-resistant tuberculosis. In this work, local stability analysis was carried out around the equilibrium point. Also, to see the most influential parameters in the epidemic, a sensitivity analysis was performed on basic reproductive factors. Besides, the final work was to do numerical simulations with some cases, so that the model could describe the disease's phenomena and characteristics.
{"title":"Mathematical Modeling and Simulation to Control the Spread of Multidrug-Resistant Tuberculosis","authors":"Sulasri Suddin, Elinora Naikteas Bano","doi":"10.12962/j24775401.v7i1.6975","DOIUrl":"https://doi.org/10.12962/j24775401.v7i1.6975","url":null,"abstract":"Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. Tuberculosis that fails treatment will develop into multidrug-resistant tuberculosis. Research on the TB epidemic continues, particularly in the field of applied mathematics with modeling. In this study, we analyzed a suitable strategy in controlling the development of susceptible individuals to active tuberculosis and even multidrug-resistant tuberculosis. In this work, local stability analysis was carried out around the equilibrium point. Also, to see the most influential parameters in the epidemic, a sensitivity analysis was performed on basic reproductive factors. Besides, the final work was to do numerical simulations with some cases, so that the model could describe the disease's phenomena and characteristics.","PeriodicalId":357596,"journal":{"name":"International Journal of Computing Science and Applied Mathematics","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131702196","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}
Pub Date : 2021-02-21DOI: 10.12962/j24775401.v7i1.8210
T. Prasetyo
The number of companies in the industry, as well as the current economic conditions, have created intense competition between companies. One of the important activities of a company is distributing goods from a warehouse to several agents so that the distribution of goods can be done easily and quickly. National Pure Milk Company is based in Salatiga. There are various flavors of pure milk stored in the form of a cup and a pack that will be distributed to each destination. Each cup and pack has data in the form of mass, volume, destination (distance between the destination location and the warehouse location), and the time when it must be dropped. All items of pure milk will be delivered by 4 truck vehicles with different types. Each vehicle has a mass capacity, volume capacity, mileage capacity, trip duration capacity, and trip number capacity. All the data of the pure milk that distributed must not run over the capacity of the vehicle. In this research, Particle Swarm Optimization (PSO) Algorithm can be modified into the discrete PSO Algorithm to determine the shortest distance of the route and Genetic Algorithms can be modified to determine the exact composition of goods on each vehicle. The optimization problem is limited by the condition that each item is delivered at the same time interval.
{"title":"Particle Swarm Optimization and Genetic Algorithm for Big Vehicle Problem: Case Study in National Pure Milk Company","authors":"T. Prasetyo","doi":"10.12962/j24775401.v7i1.8210","DOIUrl":"https://doi.org/10.12962/j24775401.v7i1.8210","url":null,"abstract":"The number of companies in the industry, as well as the current economic conditions, have created intense competition between companies. One of the important activities of a company is distributing goods from a warehouse to several agents so that the distribution of goods can be done easily and quickly. National Pure Milk Company is based in Salatiga. There are various flavors of pure milk stored in the form of a cup and a pack that will be distributed to each destination. Each cup and pack has data in the form of mass, volume, destination (distance between the destination location and the warehouse location), and the time when it must be dropped. All items of pure milk will be delivered by 4 truck vehicles with different types. Each vehicle has a mass capacity, volume capacity, mileage capacity, trip duration capacity, and trip number capacity. All the data of the pure milk that distributed must not run over the capacity of the vehicle. In this research, Particle Swarm Optimization (PSO) Algorithm can be modified into the discrete PSO Algorithm to determine the shortest distance of the route and Genetic Algorithms can be modified to determine the exact composition of goods on each vehicle. The optimization problem is limited by the condition that each item is delivered at the same time interval.","PeriodicalId":357596,"journal":{"name":"International Journal of Computing Science and Applied Mathematics","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131897262","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}
Pub Date : 2021-02-21DOI: 10.12962/j24775401.v7i1.7023
Zani Anjani Rafsanjani, D. Nurtiyasari, Angga Syahputra
In this paper, we work on the analysis of dynamical change on stock price during Covid-19 pandemic using nonlinear deterministic motion equation. The model is given by the second-order differential equation with constant coefficient over time with some consideration under stock market structure. This coefficient shows the rate of change of stock price throughout Covid-19. Thus, the Least Square estimator is derived to determine the constant factor. Further, we conduct the Multi layered Neural Network algorithm to predict the future stock price. To provide accurate forecasting results, the algorithm used in this paper has to be able to recognize stock price data pattern which has dynamic characteristics. Multi-layered Neural Network solve the data with dynamic characteristics by using more than one hidden layer. The input layers of this network are not directly connected to the output layers of the network. Therefore, this algorithm is expected to provide accurate forecasting results. We use the Jakarta Composite Stock Price Index (IHSG) and Waskita Karya Company stock price's data for the subject of observation.
{"title":"The Dynamics of Stock Price Change Motion Effected by Covid-19 Pandemic and the Stock Price Prediction Using Multi-layered Neural Network","authors":"Zani Anjani Rafsanjani, D. Nurtiyasari, Angga Syahputra","doi":"10.12962/j24775401.v7i1.7023","DOIUrl":"https://doi.org/10.12962/j24775401.v7i1.7023","url":null,"abstract":"In this paper, we work on the analysis of dynamical change on stock price during Covid-19 pandemic using nonlinear deterministic motion equation. The model is given by the second-order differential equation with constant coefficient over time with some consideration under stock market structure. This coefficient shows the rate of change of stock price throughout Covid-19. Thus, the Least Square estimator is derived to determine the constant factor. Further, we conduct the Multi layered Neural Network algorithm to predict the future stock price. To provide accurate forecasting results, the algorithm used in this paper has to be able to recognize stock price data pattern which has dynamic characteristics. Multi-layered Neural Network solve the data with dynamic characteristics by using more than one hidden layer. The input layers of this network are not directly connected to the output layers of the network. Therefore, this algorithm is expected to provide accurate forecasting results. We use the Jakarta Composite Stock Price Index (IHSG) and Waskita Karya Company stock price's data for the subject of observation.","PeriodicalId":357596,"journal":{"name":"International Journal of Computing Science and Applied Mathematics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125392751","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}
Pub Date : 2021-02-21DOI: 10.12962/j24775401.v7i1.7778
P. R. Kishore, Dawit Cherinet Kifetew
A partially ordered group (po-group) is said to be a generalised lattice ordered group (gl-group) if the underlying poset is a generalised lattice. This paper is a study of some properties of finite subsets of a generalised lattice ordered group (gl-group). Finally obtained a lattice ordered group (l-group) from the given interally closed gl-group and concluded that every integrally closed gl-group is distributive.
{"title":"Properties of Generalised Lattice Ordered Groups","authors":"P. R. Kishore, Dawit Cherinet Kifetew","doi":"10.12962/j24775401.v7i1.7778","DOIUrl":"https://doi.org/10.12962/j24775401.v7i1.7778","url":null,"abstract":"A partially ordered group (po-group) is said to be a generalised lattice ordered group (gl-group) if the underlying poset is a generalised lattice. This paper is a study of some properties of finite subsets of a generalised lattice ordered group (gl-group). Finally obtained a lattice ordered group (l-group) from the given interally closed gl-group and concluded that every integrally closed gl-group is distributive.","PeriodicalId":357596,"journal":{"name":"International Journal of Computing Science and Applied Mathematics","volume":"360 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124535575","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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