Pub Date : 2024-05-14DOI: 10.22342/jims.30.1.1401.110-120
Hubbi Muhammad, Rambu Maya Imung Maharani, Sri Nurhayati, Mira Wadu, Yeni Susanti
We introduce the non-braid graph of a group G, denoted by ζ(G), as a graph with vertex set G B(G), where B(G) is the braider of G, defined as the set {x ∈ G | (∀y ∈ G)xyx = yxy}, and two distinct vertices x and y are joined by an edge if and only if xyx ̸ = yxy. In this paper particularly we give the independent number, the vertex chromatic number, the clique number, and the minimum vertex cover of non-braid graph of dihedral group Dn
我们将群 G 的无辫图（用 ζ(G)表示）引入为具有顶点集 G B(G) 的图，其中 B(G) 是 G 的辫图，定义为集合 {x∈G | (∀y∈G)xyx = yxy}，并且当且仅当 xyx ̸ = yxy 时，两个不同的顶点 x 和 y 通过边连接。本文特别给出了二面角组 Dn 的非辫子图的独立数、顶点色度数、小群数和最小顶点覆盖率。
{"title":"THE NON-BRAID GRAPH OF DIHEDRAL GROUP Dn","authors":"Hubbi Muhammad, Rambu Maya Imung Maharani, Sri Nurhayati, Mira Wadu, Yeni Susanti","doi":"10.22342/jims.30.1.1401.110-120","DOIUrl":"https://doi.org/10.22342/jims.30.1.1401.110-120","url":null,"abstract":"We introduce the non-braid graph of a group G, denoted by ζ(G), as a graph with vertex set G B(G), where B(G) is the braider of G, defined as the set {x ∈ G | (∀y ∈ G)xyx = yxy}, and two distinct vertices x and y are joined by an edge if and only if xyx ̸ = yxy. In this paper particularly we give the independent number, the vertex chromatic number, the clique number, and the minimum vertex cover of non-braid graph of dihedral group Dn","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140979614","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 : 2024-05-14DOI: 10.22342/jims.30.1.1432.121-138
Roji Bala Singla, Vinod Mishra
In this paper, we introduces Narayana sequence in two parameters, namely, (k, t)-Narayana sequence, which is generalization of classical Narayana sequence and provide some identities and matrix expressions. Further, we find relations between (k, t)-Narayana numbers and determinants and permanents of some Hessenberg matrices. We study recurrence relations and the sum of the first n terms of this sequence. We obtain some properties from matrices. Additionally, we define (k, t)−Narayana sequence for negative subscripts and derive some relations.
{"title":"Generalised (k, t)-Narayana sequence","authors":"Roji Bala Singla, Vinod Mishra","doi":"10.22342/jims.30.1.1432.121-138","DOIUrl":"https://doi.org/10.22342/jims.30.1.1432.121-138","url":null,"abstract":"In this paper, we introduces Narayana sequence in two parameters, namely, (k, t)-Narayana sequence, which is generalization of classical Narayana sequence and provide some identities and matrix expressions. Further, we find relations between (k, t)-Narayana numbers and determinants and permanents of some Hessenberg matrices. We study recurrence relations and the sum of the first n terms of this sequence. We obtain some properties from matrices. Additionally, we define (k, t)−Narayana sequence for negative subscripts and derive some relations.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140978195","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 : 2024-04-09DOI: 10.22342/jims.30.1.1443.100-109
Nandhini Chandrasekar, K. K. Myithili
A hypergraph is an extension of a graph in which one edge can connect any number of vertices. In contrary, an edge connects exactly two vertices in a graph.In this paper we introduce hub-hyperpath, hubset and hubnumber of a hypergraph. Also we defined the hubnumber of a different types of hypergraphs and analyze some of its properties. Then the hub number of a hypergraph is compared with its dual hypergraph. Hubset can be useful for various tasks, such as targeted marketing and social networks. Additionally, finding the hub number of a graph is useful in network security, as it helps in identifying nodes that, if compromised, could have a significant impact on the overall network.
{"title":"Hub Parameters of Hypergraph","authors":"Nandhini Chandrasekar, K. K. Myithili","doi":"10.22342/jims.30.1.1443.100-109","DOIUrl":"https://doi.org/10.22342/jims.30.1.1443.100-109","url":null,"abstract":"A hypergraph is an extension of a graph in which one edge can connect any number of vertices. In contrary, an edge connects exactly two vertices in a graph.In this paper we introduce hub-hyperpath, hubset and hubnumber of a hypergraph. Also we defined the hubnumber of a different types of hypergraphs and analyze some of its properties. Then the hub number of a hypergraph is compared with its dual hypergraph. Hubset can be useful for various tasks, such as targeted marketing and social networks. Additionally, finding the hub number of a graph is useful in network security, as it helps in identifying nodes that, if compromised, could have a significant impact on the overall network.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140727771","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 : 2024-04-09DOI: 10.22342/jims.30.1.1604.89-99
S. E. Atani
Let £ be a bounded distributive lattice and S a join-subset of £. In this paper, we introduce the concept of S-prime elements (resp. weakly S-prime elements) of £. Let p be an element of £ with S ∧p = 0 (i.e. s∧p = 0 for all s ∈ S). We say that p is an S-prime element (resp. a weakly S-prime element) of £ if there is an element s ∈ S such that for all x, y ∈ £ if p ≤ x ∨ y (resp. p ≤ x ∨ y 6= 1), then p ≤ x ∨ s or p ≤ y ∨ s. We extend the notion of S-prime property in commutative rings to S-prime property in lattices.
设 £ 是有界分布网格，S 是 £ 的连接子集。在本文中，我们引入了 S-prime 元素（即弱 S-prime 元素）的概念。设 p 是 £ 的元素，且 S ∧p = 0（即对于所有 s∈ S，s∧p = 0）。如果有一个元素 s∈S 使得对于所有 x, y∈ £ 如果 p ≤ x ∨ y （或者 p≤ x ∨ y 6= 1），那么 p ≤ x ∨ s 或者 p ≤ y ∨ s，我们就说 p 是 £ 的 S-prime 元素（或者弱 S-prime 元素）。
{"title":"On Weakly S-Prime Elements of Lattices","authors":"S. E. Atani","doi":"10.22342/jims.30.1.1604.89-99","DOIUrl":"https://doi.org/10.22342/jims.30.1.1604.89-99","url":null,"abstract":"Let £ be a bounded distributive lattice and S a join-subset of £. In this paper, we introduce the concept of S-prime elements (resp. weakly S-prime elements) of £. Let p be an element of £ with S ∧p = 0 (i.e. s∧p = 0 for all s ∈ S). We say that p is an S-prime element (resp. a weakly S-prime element) of £ if there is an element s ∈ S such that for all x, y ∈ £ if p ≤ x ∨ y (resp. p ≤ x ∨ y 6= 1), then p ≤ x ∨ s or p ≤ y ∨ s. We extend the notion of S-prime property in commutative rings to S-prime property in lattices.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140723391","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 : 2024-04-07DOI: 10.22342/jims.30.1.1396.63-76
I. Gede, Adhitya Wisnu Wardhana, Pudji Astuti, Intan Muchtadi-Alamsyah
In most cases, almost prime submodules are equivalent to prime submodules, but in a finitely generated module, it is not necessarily equivalent. Based on the fact that a finitely generated module over a principal ideal domain can be decomposed into a free part and a torsion part, we give a new approach to the characteristic of almost prime submodules in the finitely generated module, especially we point out the cases when the submodules are almost prime but not prime.
{"title":"The Characterization of Almost Prime Submodule on the 6 Finitely Generated Module over Principal Ideal Domain","authors":"I. Gede, Adhitya Wisnu Wardhana, Pudji Astuti, Intan Muchtadi-Alamsyah","doi":"10.22342/jims.30.1.1396.63-76","DOIUrl":"https://doi.org/10.22342/jims.30.1.1396.63-76","url":null,"abstract":"In most cases, almost prime submodules are equivalent to prime submodules, but in a finitely generated module, it is not necessarily equivalent. Based on the fact that a finitely generated module over a principal ideal domain can be decomposed into a free part and a torsion part, we give a new approach to the characteristic of almost prime submodules in the finitely generated module, especially we point out the cases when the submodules are almost prime but not prime.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140733272","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}
This investigation is an approach to setup an analytical solution of steady plane allied MHD fluid flow having infinite electrical conductivity in a rotating frame through porous media by Martin’s method. The governing non-linearequations of the fluid flow are transformed into a new form called Martin’s form by employing differential geometry where the curvilinear co-ordinates (Φ, Ψ) in the plane of flow shows that, the co-ordinate lines Ψ are the streamlines of flow and the co-ordinate lines Φ are arbitrary constants. Exact solution is obtained and velocity,vorticity, current density magnetic field and pressure distribution are found out. Also, the diagrams have been plotted to sketch the streamline patterns and to study variation of pressure function with angular velocity.
{"title":"Analytical Solution of Equations Governing Aligned Plane Rotating Magnetohydrodynamic Fluid Through Porous Media by Martin’s Method","authors":"Birendra Kumar Vishwakarma Birendra, Sayantan Sil, Manoj Kumar","doi":"10.22342/jims.30.1.1356.40-62","DOIUrl":"https://doi.org/10.22342/jims.30.1.1356.40-62","url":null,"abstract":"This investigation is an approach to setup an analytical solution of steady plane allied MHD fluid flow having infinite electrical conductivity in a rotating frame through porous media by Martin’s method. The governing non-linearequations of the fluid flow are transformed into a new form called Martin’s form by employing differential geometry where the curvilinear co-ordinates (Φ, Ψ) in the plane of flow shows that, the co-ordinate lines Ψ are the streamlines of flow and the co-ordinate lines Φ are arbitrary constants. Exact solution is obtained and velocity,vorticity, current density magnetic field and pressure distribution are found out. Also, the diagrams have been plotted to sketch the streamline patterns and to study variation of pressure function with angular velocity.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140744851","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.29.2.1581.245-258
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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