Pub Date : 2022-03-25DOI: 10.22342/jims.28.1.1011.52-68
Nadir Benkaci-Ali
In this paper, we give existence and uniqueness results of nontrivial positive solution of the singular and non-autonomous kind of Duffing oscillator by using fixed point index theory.
本文利用不动点指标理论，给出了奇异非自治Duffing振子非平凡正解的存在唯一性结果。
{"title":"Existence and Uniqueness Results of Positive Solution of a Class of Singular Duffing Oscillators","authors":"Nadir Benkaci-Ali","doi":"10.22342/jims.28.1.1011.52-68","DOIUrl":"https://doi.org/10.22342/jims.28.1.1011.52-68","url":null,"abstract":"In this paper, we give existence and uniqueness results of nontrivial positive solution of the singular and non-autonomous kind of Duffing oscillator by using fixed point index theory.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46020354","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 : 2022-03-21DOI: 10.22342/jims.28.1.1056.31-43
R. Bandaru, A. Borumand Saeid, Y. Jun
The notion of a belligerent GE-filter in a GE-algebra is introduced, and the relationships between a GE-filter and a belligerent GE-filter will be given. Conditions for a GE-filter to be a belligerent GE-filter are provided. The product and the union of GE-algebras are discussed and its properties are investigated.
{"title":"Belligerent GE-filters in GE-Algebras","authors":"R. Bandaru, A. Borumand Saeid, Y. Jun","doi":"10.22342/jims.28.1.1056.31-43","DOIUrl":"https://doi.org/10.22342/jims.28.1.1056.31-43","url":null,"abstract":"The notion of a belligerent GE-filter in a GE-algebra is introduced, and the relationships between a GE-filter and a belligerent GE-filter will be given. Conditions for a GE-filter to be a belligerent GE-filter are provided. The product and the union of GE-algebras are discussed and its properties are investigated.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44017028","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 : 2022-03-20DOI: 10.22342/jims.28.1.1106.19-30
A. Pourgholam, M. Sabbaghan, F. Taleghani
In this paper, the notion of limit property (-Tayyab kamran, 2004-) and common limit property (-Yicheng Liu & Jun Wu & Zhixiang Li, 2005-) for singlevalued and multi-valued mappings on metric spaces are generalized to S-metric spaces. This idea is used to make some common fixed point theorems for singlevalued and multi-valued mappings by using a generalization of coincidence point in S-metric spaces. We give an example of an S-metric which is not continuous.
{"title":"Common Fixed Points of Single-Valued and Multi-Valued Mappings in S-Metric Spaces","authors":"A. Pourgholam, M. Sabbaghan, F. Taleghani","doi":"10.22342/jims.28.1.1106.19-30","DOIUrl":"https://doi.org/10.22342/jims.28.1.1106.19-30","url":null,"abstract":"In this paper, the notion of limit property (-Tayyab kamran, 2004-) and common limit property (-Yicheng Liu & Jun Wu & Zhixiang Li, 2005-) for singlevalued and multi-valued mappings on metric spaces are generalized to S-metric spaces. This idea is used to make some common fixed point theorems for singlevalued and multi-valued mappings by using a generalization of coincidence point in S-metric spaces. We give an example of an S-metric which is not continuous.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41729941","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 : 2022-03-13DOI: 10.22342/jims.28.1.1036.8-18
S. B. Pimpare, C. S. Sutar
The term thermal stresses are related to mechanics of materials. The thermal stress is formed due to any changes in temperature of a material. The large change in temperature concludes to higher the thermal stresses. Also, there is an effect of thermal expansion coefficient on thermal stresses. The thermal expansion coefficient is different for different materials. In the present paper, the design of a mathematical model concerning the thermal stresses in hollow cylinder subject to the heat conduction with initial and boundary conditions have developed. The basic aim of this work is related to calculations of thermal stresses and thermoelastic displacement in the hollow cylinder by using the reduced differential transform method. The analytical solution is satisfied with the aim of special cases for the copper material properties. The numerical results are illustrated graphically by using mathematical software SCILAB.
{"title":"Hollow Cylinder with Thermoelastic Modelling by Reduced Differential Transform","authors":"S. B. Pimpare, C. S. Sutar","doi":"10.22342/jims.28.1.1036.8-18","DOIUrl":"https://doi.org/10.22342/jims.28.1.1036.8-18","url":null,"abstract":"The term thermal stresses are related to mechanics of materials. The thermal stress is formed due to any changes in temperature of a material. The large change in temperature concludes to higher the thermal stresses. Also, there is an effect of thermal expansion coefficient on thermal stresses. The thermal expansion coefficient is different for different materials. In the present paper, the design of a mathematical model concerning the thermal stresses in hollow cylinder subject to the heat conduction with initial and boundary conditions have developed. The basic aim of this work is related to calculations of thermal stresses and thermoelastic displacement in the hollow cylinder by using the reduced differential transform method. The analytical solution is satisfied with the aim of special cases for the copper material properties. The numerical results are illustrated graphically by using mathematical software SCILAB.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42289856","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 : 2022-03-13DOI: 10.22342/jims.28.1.1025.1-7
K. Jeya Daisey, R. Santrin Sabibha, P. Jeyanthi, M. Youssef
Let f be a map from V (G) to {0, 1, ..., k − 1} where k is an integer, 1 ≤ k ≤ |V (G)|. For each edge uv assign the label f(u)f(v)(mod k). f is called a k-product cordial labeling if |vf (i) − vf (j)| ≤ 1, and |ef (i) − ef (j)| ≤ 1, i, j ∈ {0, 1, ..., k − 1}, where vf (x) and ef (x) denote the number of vertices and edges respectively labeled with x (x = 0, 1, ..., k − 1). In this paper, we investigate the k-product cordial behaviour of union of graphs
{"title":"k-Product Cordial Behaviour of Union of Graphs","authors":"K. Jeya Daisey, R. Santrin Sabibha, P. Jeyanthi, M. Youssef","doi":"10.22342/jims.28.1.1025.1-7","DOIUrl":"https://doi.org/10.22342/jims.28.1.1025.1-7","url":null,"abstract":"Let f be a map from V (G) to {0, 1, ..., k − 1} where k is an integer, 1 ≤ k ≤ |V (G)|. For each edge uv assign the label f(u)f(v)(mod k). f is called a k-product cordial labeling if |vf (i) − vf (j)| ≤ 1, and |ef (i) − ef (j)| ≤ 1, i, j ∈ {0, 1, ..., k − 1}, where vf (x) and ef (x) denote the number of vertices and edges respectively labeled with x (x = 0, 1, ..., k − 1). In this paper, we investigate the k-product cordial behaviour of union of graphs","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44603851","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 : 2022-01-01DOI: 10.22342/jims.28.3.1158.272-303
Y. Akama, Atina Husnaqilati
We consider a $p$-dimensional, centered normal population such that all variables have a positive variance and any correlation coefficient between different variables is a given nonnegative constant $rho<1$. Suppose that both the sample size $n$ and population dimension $p$ tend to infinity with $p/n to c>0$. We prove that the limiting spectral distributions of the sample covariance matrices and the sample correlation matrices are Marv{c}enko-Pastur distribution of index $c$ and scale parameter $1-rho$.By the limiting spectral distributions, we rigorously show the limiting behavior of widespread stopping rules Guttman-Kaiser criterion and cumulative-percentage-of-variation rule in PCA and EFA.As a result, we establish the following dichotomous behavior of Guttman-Kaiser criterion when both $n$ and $p$ are large, but $p/n$ is small: (1) the criterion retains a small number of variables for $rho>0$, as suggested by Kaiser, Humphreys, and Tucker [Kaiser, H. F. (1992). On Cliff's formula, the Kaiser-Guttman rule and the number of factors. emph{Percept. Mot. Ski.} 74]; and(2) the criterion retains $p/2$ variables for $rho=0$, as in a simulation study [Yeomans, K. A. and Golder, P. A. (1982). The Guttman-Kaiser criterion as a predictor of the number of common factors. emph{J. Royal Stat. Soc. Series D} 31(3)].
我们考虑一个$p$维、居中的正态总体，这样所有变量都有正方差，不同变量之间的任何相关系数都是给定的非负常数$rho0$。我们证明了样本协方差矩阵和样本相关矩阵的极限谱分布是指数$c$和尺度参数$1-rho$的Mar v{c} enko-Pastur分布。通过极限谱分布，我们严格地证明了PCA和EFA中广泛停止规则Guttman-Kaiser准则和累积变异百分比规则的极限行为。因此，当$n$和$p$都很大，但$p/n$很小时，我们建立了以下Guttman-Kaiser准则的二分类行为:(1)根据Kaiser, Humphreys和Tucker [Kaiser, H. F.(1992)]的建议，该准则保留了$rho>0$的少量变量。克里夫公式，凯撒-古特曼法则和因子数。emph{感知。不是。}[74];(2)标准保留$rho=0$的$p/2$变量，如模拟研究[Yeomans, K. a .和Golder, P. a .(1982)]。Guttman-Kaiser标准作为共同因素数量的预测因子。emph{皇家司法学院D系列}31(3)]。
{"title":"A Dichotomous Behavior of Guttman-Kaiser Criterion from Equi-Correlated Normal Population","authors":"Y. Akama, Atina Husnaqilati","doi":"10.22342/jims.28.3.1158.272-303","DOIUrl":"https://doi.org/10.22342/jims.28.3.1158.272-303","url":null,"abstract":"We consider a $p$-dimensional, centered normal population such that all variables have a positive variance and any correlation coefficient between different variables is a given nonnegative constant $rho<1$. Suppose that both the sample size $n$ and population dimension $p$ tend to infinity with $p/n to c>0$. We prove that the limiting spectral distributions of the sample covariance matrices and the sample correlation matrices are Marv{c}enko-Pastur distribution of index $c$ and scale parameter $1-rho$.By the limiting spectral distributions, we rigorously show the limiting behavior of widespread stopping rules Guttman-Kaiser criterion and cumulative-percentage-of-variation rule in PCA and EFA.As a result, we establish the following dichotomous behavior of Guttman-Kaiser criterion when both $n$ and $p$ are large, but $p/n$ is small: (1) the criterion retains a small number of variables for $rho>0$, as suggested by Kaiser, Humphreys, and Tucker [Kaiser, H. F. (1992). On Cliff's formula, the Kaiser-Guttman rule and the number of factors. emph{Percept. Mot. Ski.} 74]; and(2) the criterion retains $p/2$ variables for $rho=0$, as in a simulation study [Yeomans, K. A. and Golder, P. A. (1982). The Guttman-Kaiser criterion as a predictor of the number of common factors. emph{J. Royal Stat. Soc. Series D} 31(3)].","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68348512","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 : 2021-12-10DOI: 10.22342/jims.27.3.989.249-261
B. B., Shruti Policepatil
The mathematical chemistry deals with applications of graph theory to study the physicochemical properties of molecules theoretically. A topological index of a graph is a numeric quantity obtained from the graph mathematically. A cactus graph is a connected graph in which no edges lie in more than one cycle. In this paper, we compute Gourava and hyper-Gourava indices of some cactus chains.
{"title":"Gourava and Hyper-Gourava Indices of Some Cactus Chains","authors":"B. B., Shruti Policepatil","doi":"10.22342/jims.27.3.989.249-261","DOIUrl":"https://doi.org/10.22342/jims.27.3.989.249-261","url":null,"abstract":"The mathematical chemistry deals with applications of graph theory to study the physicochemical properties of molecules theoretically. A topological index of a graph is a numeric quantity obtained from the graph mathematically. A cactus graph is a connected graph in which no edges lie in more than one cycle. In this paper, we compute Gourava and hyper-Gourava indices of some cactus chains.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46580432","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 : 2021-12-02DOI: 10.22342/jims.27.3.1006.249-260
Anusha Vulimiri, Sireesha Veeramachaneni
This paper proposes an approach to solve Multiple Criteria Decision-making (MCDM) problems when the data given by expert is Interval-Valued Intuitionistic Fuzzy (IVIF) information. A decision-making model is constructed by using the distance measure: Normalized Jaccard distance measure. The robustness of the model is illustrated and validated through numerical example. Further, the problem of choosing best e-learning tool in higher education is considered as a case study.
{"title":"Application of Jaccard Distance Measure for IVIF MCDM Problems","authors":"Anusha Vulimiri, Sireesha Veeramachaneni","doi":"10.22342/jims.27.3.1006.249-260","DOIUrl":"https://doi.org/10.22342/jims.27.3.1006.249-260","url":null,"abstract":"This paper proposes an approach to solve Multiple Criteria Decision-making (MCDM) problems when the data given by expert is Interval-Valued Intuitionistic Fuzzy (IVIF) information. A decision-making model is constructed by using the distance measure: Normalized Jaccard distance measure. The robustness of the model is illustrated and validated through numerical example. Further, the problem of choosing best e-learning tool in higher education is considered as a case study.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44156925","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 : 2021-12-02DOI: 10.22342/jims.27.3.1043.285-296
S. Zahidah, D. Mahanani, Karine Lutfiah Oktaviana
Generalized quarternion group (Q_(4n)) is a group of order $4n$ that is generated by two elements x and y with the properties x^{2n}=y^4=e and xy=yx^{-1}. The coprime graph of Q_{4n}, denoted by Omega_{Q_{4n}}, is a graph with the vertices are elements of Q_{4n} and the edges are generated by two elements that have coprime order. The first result of this paper presented that Omega_{Q_{4n}} is a tripartite graph for n is odd and Omega_{Q_{4n}} is a star graph for n is even. The second one presented the connectivity indices of Omega_{Q_{4n}}. Connectivity indices of a graph is a research area in mathematics that popularly applied in chemistry. There are six indices that are presented in this paper, those are first Zagreb index, second Zagreb index, Wiener index, hyper-Wiener index, Harary index, and Szeged index.Generalized quaternion group (Q4n) is a group of order 4n that is generated by two elements x and y with the properties x 2n = y 4 = e and xy = yx−1 . The coprime graph of Q4n, denoted by ΩQ4n , is a graph with the vertices are elements of Q4n and the edges are formed by two elements that have coprime order. The first result of this paper presents that ΩQ4n is a tripartite graph for n is an odd prime and ΩQ4n is a star graph for n is a power of 2. The second one presents the connectivity indices of ΩQ4n . Connectivity indices of a graph is a research area in mathematics that popularly applied in chemistry. There are six indices that are presented in this paper, those are first Zagreb index, second Zagreb index, Wiener index, hyper-Wiener index, Harary index, and Szeged index.
{"title":"Connectivity Indices of Coprime Graph of Generalized Quarternion Group","authors":"S. Zahidah, D. Mahanani, Karine Lutfiah Oktaviana","doi":"10.22342/jims.27.3.1043.285-296","DOIUrl":"https://doi.org/10.22342/jims.27.3.1043.285-296","url":null,"abstract":"Generalized quarternion group (Q_(4n)) is a group of order $4n$ that is generated by two elements x and y with the properties x^{2n}=y^4=e and xy=yx^{-1}. The coprime graph of Q_{4n}, denoted by Omega_{Q_{4n}}, is a graph with the vertices are elements of Q_{4n} and the edges are generated by two elements that have coprime order. The first result of this paper presented that Omega_{Q_{4n}} is a tripartite graph for n is odd and Omega_{Q_{4n}} is a star graph for n is even. The second one presented the connectivity indices of Omega_{Q_{4n}}. Connectivity indices of a graph is a research area in mathematics that popularly applied in chemistry. There are six indices that are presented in this paper, those are first Zagreb index, second Zagreb index, Wiener index, hyper-Wiener index, Harary index, and Szeged index.Generalized quaternion group (Q4n) is a group of order 4n that is generated by two elements x and y with the properties x 2n = y 4 = e and xy = yx−1 . The coprime graph of Q4n, denoted by ΩQ4n , is a graph with the vertices are elements of Q4n and the edges are formed by two elements that have coprime order. The first result of this paper presents that ΩQ4n is a tripartite graph for n is an odd prime and ΩQ4n is a star graph for n is a power of 2. The second one presents the connectivity indices of ΩQ4n . Connectivity indices of a graph is a research area in mathematics that popularly applied in chemistry. There are six indices that are presented in this paper, those are first Zagreb index, second Zagreb index, Wiener index, hyper-Wiener index, Harary index, and Szeged index.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41482922","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 : 2021-12-02DOI: 10.22342/jims.27.3.1018.261-269
Nastitie Nastitie, G. Rachmaputri
The International Union for the Conservation of Nature and Natural Resource (IUCN) Red List found that there are currently over 8.000 critically endangered species and the number seems likely to rise in the future. One of the species included in the IUCN Red List is Eos histrio, also known as the Red-and-blue lory, a bird endemic to Indonesia that inhabits Nusa Utara Islands, North Sulawesi. It lives in a forest with tall trees as its natural habitat. According to the Central Bureau of Statistics (BPS), the forest area is decreasing every year and has caused the bird to lose their habitats and its population is declining. IUCN also reported that there are 8.230 – 21.400 Eos histrio in 1999, however in 2016, it was only around 5.500 – 14.000. Its population will be declining due to extensive deforestation and poor conservation. Using Pontryagin maximum principle, this study found that one of the methods to protect the Eos histrio population is by reducing deforestation in North Sulawesi by at least 10% where the population of the bird could increase within a year.
{"title":"Analysis of Forest Carrying Capacity on Eos histrio in North Sulawesi","authors":"Nastitie Nastitie, G. Rachmaputri","doi":"10.22342/jims.27.3.1018.261-269","DOIUrl":"https://doi.org/10.22342/jims.27.3.1018.261-269","url":null,"abstract":"The International Union for the Conservation of Nature and Natural Resource (IUCN) Red List found that there are currently over 8.000 critically endangered species and the number seems likely to rise in the future. One of the species included in the IUCN Red List is Eos histrio, also known as the Red-and-blue lory, a bird endemic to Indonesia that inhabits Nusa Utara Islands, North Sulawesi. It lives in a forest with tall trees as its natural habitat. According to the Central Bureau of Statistics (BPS), the forest area is decreasing every year and has caused the bird to lose their habitats and its population is declining. IUCN also reported that there are 8.230 – 21.400 Eos histrio in 1999, however in 2016, it was only around 5.500 – 14.000. Its population will be declining due to extensive deforestation and poor conservation. Using Pontryagin maximum principle, this study found that one of the methods to protect the Eos histrio population is by reducing deforestation in North Sulawesi by at least 10% where the population of the bird could increase within a year.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68348503","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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