Pub Date : 2023-07-31DOI: 10.22342/jims.29.2.1581.245-258
Randi Deautama, Kurnia Novita Sari
The 2019 Indonesian Mortality Table IV (TMI IV) involved 52 life insurance companies in Indonesia during the study period from 2013 to 2017. From the data, there may be differences in the characteristics of company customers so that the use of TMI IV is not in accordance with these characteristics. In life insurance companies, there are types of coverage (causes), namely: NDPA, which means death due to illness or accident; PAD, which means reimbursement of medical expenses, and SRD, which is the cancellation of the policy so that the coverage ends. The Companies can construct a Life Table involving multiple causes called a Multiple Decrement (MD) Table. This table is modified into a Modified Multiple Decrement Table (MDT) by adding factors to the causes in the form of regions. The clustering of factors needs to be done to reduce the complexity of the calculation. Using the K-means method, the grouping of regions R1R9 is divided into the following: PAD causes (3 groups) and SRD (2 groups). MDT is obtained from the relationship between MD and the Associated Single Decrement (ASD). The Annual Exposure Method was used to calculate the probability of causes. Furthermore, extrapolation is performed on the probability of cause, for which there is no value, and graduation is performed on the less smooth probability of cause. Then, credibility theory is used to determine the credibility level of the industry. The industry-credible probability of cause has a value between the observed value and the industry value (TMI IV).
{"title":"Modified Multiple Decrement Table and Its Credibility Based on Factor Characteristics","authors":"Randi Deautama, Kurnia Novita Sari","doi":"10.22342/jims.29.2.1581.245-258","DOIUrl":"https://doi.org/10.22342/jims.29.2.1581.245-258","url":null,"abstract":"The 2019 Indonesian Mortality Table IV (TMI IV) involved 52 life insurance companies in Indonesia during the study period from 2013 to 2017. From the data, there may be differences in the characteristics of company customers so that the use of TMI IV is not in accordance with these characteristics. In life insurance companies, there are types of coverage (causes), namely: NDPA, which means death due to illness or accident; PAD, which means reimbursement of medical expenses, and SRD, which is the cancellation of the policy so that the coverage ends. The Companies can construct a Life Table involving multiple causes called a Multiple Decrement (MD) Table. This table is modified into a Modified Multiple Decrement Table (MDT) by adding factors to the causes in the form of regions. The clustering of factors needs to be done to reduce the complexity of the calculation. Using the K-means method, the grouping of regions R1R9 is divided into the following: PAD causes (3 groups) and SRD (2 groups). MDT is obtained from the relationship between MD and the Associated Single Decrement (ASD). The Annual Exposure Method was used to calculate the probability of causes. Furthermore, extrapolation is performed on the probability of cause, for which there is no value, and graduation is performed on the less smooth probability of cause. Then, credibility theory is used to determine the credibility level of the industry. The industry-credible probability of cause has a value between the observed value and the industry value (TMI IV).","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"40 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139353581","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 : 2023-07-31DOI: 10.22342/jims.29.2.1371.197-216
Ayoub Basheer
The Janko sporadic simple group J2 has an automorphism group 2. Using the electronic Atlas of Wilson [22], the group J2:2 has an absolutely irreducible module of dimension 12 over F2. It follows that a split extension group of the form 2^12:(J2:2) := G exists. In this article we study this group, where we compute its conjugacy classes and character table using the coset analysis technique together with Clifford-Fischer Theory. The inertia factor groups of G will be determined by analysing the maximal subgroups of J2:2 and maximal of the maximal subgroups of J2:2 together with various other information. It turns out that the character table of G is a 64×64 real valued matrix, while the Fischer matrices are all integer valued matrices with sizes ranging from 1 to 6.
{"title":"On A Group Involving The Automorphism of The Janko Group J2","authors":"Ayoub Basheer","doi":"10.22342/jims.29.2.1371.197-216","DOIUrl":"https://doi.org/10.22342/jims.29.2.1371.197-216","url":null,"abstract":"The Janko sporadic simple group J2 has an automorphism group 2. Using the electronic Atlas of Wilson [22], the group J2:2 has an absolutely irreducible module of dimension 12 over F2. It follows that a split extension group of the form 2^12:(J2:2) := G exists. In this article we study this group, where we compute its conjugacy classes and character table using the coset analysis technique together with Clifford-Fischer Theory. The inertia factor groups of G will be determined by analysing the maximal subgroups of J2:2 and maximal of the maximal subgroups of J2:2 together with various other information. It turns out that the character table of G is a 64×64 real valued matrix, while the Fischer matrices are all integer valued matrices with sizes ranging from 1 to 6.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135358352","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 : 2023-07-31DOI: 10.22342/jims.29.2.1584.259-270
Ahmad Hadra Zuhri, Yudi Soeharyadi, Jalina Widjaja
We consider a system of differential equations on a Banach space X given by: x'(t) = Ax(t) + u(t)f(t, x(t)), x(0) = x0, where A is an infinitesimal generator of a C0-semigroup, f : R0+ × X → X is a locally Lipschitz function, and u ∈ Lp([0, T], R) is a control defined on [0, T] with 1 < p ≤ ∞. Using the Compactness Principle and the generalization of Gronwalls Lemma, the system is shown to be controllable for a γ-bounded function f. Another result of this study is the local existence and the uniqueness of the solution of the system for locally bounded function f through weighted ω-norm.
我们考虑巴拿赫空间 X 上的微分方程系统，其给定方程为x'(t) = Ax(t) + u(t)f(t, x(t)), x(0) = x0，其中 A 是 C0 半群的无穷小生成器，f ：f : R0+ × X → X 是局部 Lipschitz 函数，u∈ Lp([0, T], R) 是定义在 [0, T] 上的控制，1 < p ≤ ∞。利用紧凑性原理和 Gronwalls Lemma 的广义，证明该系统对于一个 γ 有界函数 f 是可控的。本研究的另一个结果是通过加权 ω 准则证明该系统的解对于局部有界函数 f 的局部存在性和唯一性。
{"title":"On Conditions for Controllability and Local Regularity of A System of Differential Equations","authors":"Ahmad Hadra Zuhri, Yudi Soeharyadi, Jalina Widjaja","doi":"10.22342/jims.29.2.1584.259-270","DOIUrl":"https://doi.org/10.22342/jims.29.2.1584.259-270","url":null,"abstract":"We consider a system of differential equations on a Banach space X given by: x'(t) = Ax(t) + u(t)f(t, x(t)), x(0) = x0, where A is an infinitesimal generator of a C0-semigroup, f : R0+ × X → X is a locally Lipschitz function, and u ∈ Lp([0, T], R) is a control defined on [0, T] with 1 < p ≤ ∞. Using the Compactness Principle and the generalization of Gronwalls Lemma, the system is shown to be controllable for a γ-bounded function f. Another result of this study is the local existence and the uniqueness of the solution of the system for locally bounded function f through weighted ω-norm.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"2016 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139353622","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 : 2023-07-31DOI: 10.22342/jims.29.2.988.217-234
S Monikandan, V Manikandan
A split graph is a graph in which the vertices can be partitioned into an independent set and a clique. A graph is split if and only if it has no induced subgraph isomorphic to C5, C4 or 2K2, which is a well-known characterization for split graph. A property of a graph G is recognizable if it can be recognized from the collection of all maximal proper induced subgraphs of G. We show that any nonsplit graph can have at most five split maximal induced subgraphs. Also we list out all C5-free nonsplit graphs having split maximal induced subgraphs, which is the main and, in fact, tedious result of this paper
{"title":"Nonsplit Graphs with Split Maximal Induced Subgraphs","authors":"S Monikandan, V Manikandan","doi":"10.22342/jims.29.2.988.217-234","DOIUrl":"https://doi.org/10.22342/jims.29.2.988.217-234","url":null,"abstract":"A split graph is a graph in which the vertices can be partitioned into an independent set and a clique. A graph is split if and only if it has no induced subgraph isomorphic to C5, C4 or 2K2, which is a well-known characterization for split graph. A property of a graph G is recognizable if it can be recognized from the collection of all maximal proper induced subgraphs of G. We show that any nonsplit graph can have at most five split maximal induced subgraphs. Also we list out all C5-free nonsplit graphs having split maximal induced subgraphs, which is the main and, in fact, tedious result of this paper","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135358351","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 : 2023-07-30DOI: 10.22342/jims.29.2.1448.235-244
Sri Gemawati, None Mashadi, Musraini M, Elsi Fitria
First, this article presents the definition of left-right derivation and right-left derivation in BP-algebra, and their characteristic are explored. Then, we define the concept of inside and outside fq-derivation of BP-algebras. Finally, their properties are explored. Furthermore, the notion of fq-derivation within BP-algebra is synonymous with B-algebra; however, they do exhibit variations in their respective characteristics.
{"title":"fq-Derivation of BP-Algebras","authors":"Sri Gemawati, None Mashadi, Musraini M, Elsi Fitria","doi":"10.22342/jims.29.2.1448.235-244","DOIUrl":"https://doi.org/10.22342/jims.29.2.1448.235-244","url":null,"abstract":"First, this article presents the definition of left-right derivation and right-left derivation in BP-algebra, and their characteristic are explored. Then, we define the concept of inside and outside fq-derivation of BP-algebras. Finally, their properties are explored. Furthermore, the notion of fq-derivation within BP-algebra is synonymous with B-algebra; however, they do exhibit variations in their respective characteristics.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135398093","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 : 2023-07-26DOI: 10.22342/jims.29.2.1319.166-176
Yeni Susanti, Niswah Qonita
Let G be a finite group. Associate a simple undirected graph Γ_G with G, called bipartite graph associated to elements and cosets of subgroups of G, as follows : Take G ∪ S_G as the vertices of Γ_G, with S_G is the set of all subgroups of a group G and join two vertices a ∈ G and H ∈ S_G if and only if aH = Ha. In this paper, hamiltonicity and eulerianity of Γ_G for some finite groups G are studied. In particular, it is obtained that for any cyclic group G, Γ_G is hamiltonian if and only if |G| = 2 and Γ_G is eulerian if and only if |G| is even non-perfect square number. Also, we prove that Γ_Dn is eulerian if k is even and n = 2k and for some other cases of n, Γ_Dn is not eulerian.
{"title":"Hamiltonicity and Eulerianity of Some Bipartite Graphs Associated to Finite Groups","authors":"Yeni Susanti, Niswah Qonita","doi":"10.22342/jims.29.2.1319.166-176","DOIUrl":"https://doi.org/10.22342/jims.29.2.1319.166-176","url":null,"abstract":"Let G be a finite group. Associate a simple undirected graph Γ_G with G, called bipartite graph associated to elements and cosets of subgroups of G, as follows : Take G ∪ S_G as the vertices of Γ_G, with S_G is the set of all subgroups of a group G and join two vertices a ∈ G and H ∈ S_G if and only if aH = Ha. In this paper, hamiltonicity and eulerianity of Γ_G for some finite groups G are studied. In particular, it is obtained that for any cyclic group G, Γ_G is hamiltonian if and only if |G| = 2 and Γ_G is eulerian if and only if |G| is even non-perfect square number. Also, we prove that Γ_Dn is eulerian if k is even and n = 2k and for some other cases of n, Γ_Dn is not eulerian.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48616885","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 : 2023-07-19DOI: 10.22342/jims.29.2.1321.156-165
R. W. N. Wijaya, J. Ryan, T. Kalinowski
For a simple graph G = (V (G), E(G)), a total labeling ∂ is called an edge irregular total k-labeling of G if ∂ : V (G) ∪ E(G) → {1, 2, . . . , k} such that for any two different edges uv and u'v' in E(G), we have wt∂(uv) not equal to wt∂(u'v') where wt∂(uv) = ∂(u) + ∂(v) + ∂(uv). The minimum k for which G has an edge irregulartotal k-labeling is called the total edge irregularity strength, denoted by tes(G). It is known that ceil((|E(G)|+2)/3) is a lower bound for the total edge irregularity strength of a graph G. In this paper we prove that if G is a bipartite graph for which this bound is tight then this is also true for Cartesian product of G with any path.
{"title":"Total Edge Irregularity Strength of the Cartesian Product of Bipartite Graphs and Paths","authors":"R. W. N. Wijaya, J. Ryan, T. Kalinowski","doi":"10.22342/jims.29.2.1321.156-165","DOIUrl":"https://doi.org/10.22342/jims.29.2.1321.156-165","url":null,"abstract":"For a simple graph G = (V (G), E(G)), a total labeling ∂ is called an edge irregular total k-labeling of G if ∂ : V (G) ∪ E(G) → {1, 2, . . . , k} such that for any two different edges uv and u'v' in E(G), we have wt∂(uv) not equal to wt∂(u'v') where wt∂(uv) = ∂(u) + ∂(v) + ∂(uv). The minimum k for which G has an edge irregulartotal k-labeling is called the total edge irregularity strength, denoted by tes(G). It is known that ceil((|E(G)|+2)/3) is a lower bound for the total edge irregularity strength of a graph G. In this paper we prove that if G is a bipartite graph for which this bound is tight then this is also true for Cartesian product of G with any path.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44673228","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 : 2023-07-18DOI: 10.22342/jims.29.2.1246.150-155
Ni Wayan, Switrayni, Gede Adhitya, Wisnu Wardhana, Q. Aini
Some methods have been used to express a finitely generated module over a principal ideal domain as a finite direct sum of its cyclic submodules. In this paper, we give an alternative technique to decompose a free module with finite rank over a principal ideal domain using eigen spaces of its endomorphism ring.
{"title":"A Note on Free Module Decomposition over A Principal Ideal Domain","authors":"Ni Wayan, Switrayni, Gede Adhitya, Wisnu Wardhana, Q. Aini","doi":"10.22342/jims.29.2.1246.150-155","DOIUrl":"https://doi.org/10.22342/jims.29.2.1246.150-155","url":null,"abstract":"Some methods have been used to express a finitely generated module over a principal ideal domain as a finite direct sum of its cyclic submodules. In this paper, we give an alternative technique to decompose a free module with finite rank over a principal ideal domain using eigen spaces of its endomorphism ring.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44707777","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 : 2023-07-17DOI: 10.22342/jims.29.2.1122.135-149
B. B., Goutam Veerapur
In this paper, we introduce the higher-order Sombor index of a molecular graph. In addtition, we compute the second order Sombor index of some standard class of graphs and line graph of subdivision graph of 2D-lattice, nanotube and nanotorus of TUC_4C_8[p,q] and also we obtain the expressions of the second order Sombor index of the line graph of subdivision graph of tadpole graph, wheel graph, ladder graph and chain silicate network CSn. Further, we study the linear regression analysis of the second order Sombor index with the entropy, acentric factor, enthalpy of vaporization and standard enthalpy of vaporization of an octane isomers.
{"title":"Chemical Applicability of Second Order Sombor Index","authors":"B. B., Goutam Veerapur","doi":"10.22342/jims.29.2.1122.135-149","DOIUrl":"https://doi.org/10.22342/jims.29.2.1122.135-149","url":null,"abstract":"In this paper, we introduce the higher-order Sombor index of a molecular graph. In addtition, we compute the second order Sombor index of some standard class of graphs and line graph of subdivision graph of 2D-lattice, nanotube and nanotorus of TUC_4C_8[p,q] and also we obtain the expressions of the second order Sombor index of the line graph of subdivision graph of tadpole graph, wheel graph, ladder graph and chain silicate network CSn. Further, we study the linear regression analysis of the second order Sombor index with the entropy, acentric factor, enthalpy of vaporization and standard enthalpy of vaporization of an octane isomers.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41690488","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 : 2023-03-30DOI: 10.22342/jims.29.1.1062.75-92
T. Menagadevi, P. Maragatha Meenakshi, N. Rajesh
The aim of this paper is to introduce and study the concepts of intuitionistic r-fuzzy regular open sets and their related notions in topological spaces.
本文的目的是介绍和研究拓扑空间中直觉r-模糊正则开集的概念及其相关概念。
{"title":"Regular Open Sets on The Intuitionistic Fuzzy Topological Spaces in Sostak's Sense","authors":"T. Menagadevi, P. Maragatha Meenakshi, N. Rajesh","doi":"10.22342/jims.29.1.1062.75-92","DOIUrl":"https://doi.org/10.22342/jims.29.1.1062.75-92","url":null,"abstract":"The aim of this paper is to introduce and study the concepts of intuitionistic r-fuzzy regular open sets and their related notions in topological spaces.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44127832","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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