Pub Date : 2022-07-30DOI: 10.22342/jims.28.2.1064.158-163
Jonald P. Fenecios, A. Racca
Let $X$ be a complete separable metric space and $Y$ be a separable Banach space. We provide a proof of equivalence by linking explicitly the following statements: noindent textbf{textit{Lebesgue's Theorem.}} For every $epsilon>0$ there exists a countable collection of closed sets $leftlbrace C_nrightrbrace $ of $X$ such that $$X=bigcup_{n=1}^{infty}C_n;;text{and};; omega_fleft( C_nright)
{"title":"Equivalence of Lebesgue's Theorem and Baire Characterization Theorem","authors":"Jonald P. Fenecios, A. Racca","doi":"10.22342/jims.28.2.1064.158-163","DOIUrl":"https://doi.org/10.22342/jims.28.2.1064.158-163","url":null,"abstract":"Let $X$ be a complete separable metric space and $Y$ be a separable Banach space. We provide a proof of equivalence by linking explicitly the following statements: noindent textbf{textit{Lebesgue's Theorem.}} For every $epsilon>0$ there exists a countable collection of closed sets $leftlbrace C_nrightrbrace $ of $X$ such that $$X=bigcup_{n=1}^{infty}C_n;;text{and};; omega_fleft( C_nright)<epsilon;; text{for each} ;; n.$$ textbf{textit{Baire Characterization Theorem.}} For every nonempty perfect set $Ksubset X$, the function $f|_K$ has at least one point of continuity in $K$. In fact, $C(f|_K)$ is dense in $K$. indent Moreover, replacing ``closed'' by ``open'' in the Lebesgue's Theorem, we obtain a characterization of continuous functions on space $X$.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47862063","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 : 2022-07-27DOI: 10.22342/jims.28.2.1052.107-121
Sami H. Altoum, A. Msmali, M. Elamin
This paper deals with the theory of V. Kondratiev which allows to study the regularity of elliptical problems in corner domains. After having introduced the Mellin transform and the Sobolev spaces to weight, we recall the links with Sobolev spaces. The Mellin transform represent an important key to study the H^s regularity in corner domains.
{"title":"Solution of Laplace’s Equation in A Singular Domain Using Mellin Transform","authors":"Sami H. Altoum, A. Msmali, M. Elamin","doi":"10.22342/jims.28.2.1052.107-121","DOIUrl":"https://doi.org/10.22342/jims.28.2.1052.107-121","url":null,"abstract":"This paper deals with the theory of V. Kondratiev which allows to study the regularity of elliptical problems in corner domains. After having introduced the Mellin transform and the Sobolev spaces to weight, we recall the links with Sobolev spaces. The Mellin transform represent an important key to study the H^s regularity in corner domains.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46949893","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 : 2022-03-31DOI: 10.22342/jims.28.1.1058.84-95
G.F. Wankap Nono, A. Ntyam, Emmanuel Hinamari Mang-Massou
For a Golden-structure ζ on a smooth manifold M and any covariant functor which assigns to M its bundle MA of infinitely near points of A-king, we define the Golden structure ζ^A on M^A and prove that ζ is integrable if and only if so is ζ^A. We also investigate the integrability, parallelism, half parallelism and anti-half parallelism of the Golden-structure ζ^A and their associated distributions on M^A.
{"title":"Prolongations of Golden Structure to Bundles of Infinitely Near Points","authors":"G.F. Wankap Nono, A. Ntyam, Emmanuel Hinamari Mang-Massou","doi":"10.22342/jims.28.1.1058.84-95","DOIUrl":"https://doi.org/10.22342/jims.28.1.1058.84-95","url":null,"abstract":"For a Golden-structure ζ on a smooth manifold M and any covariant functor which assigns to M its bundle MA of infinitely near points of A-king, we define the Golden structure ζ^A on M^A and prove that ζ is integrable if and only if so is ζ^A. We also investigate the integrability, parallelism, half parallelism and anti-half parallelism of the Golden-structure ζ^A and their associated distributions on M^A.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49019340","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 : 2022-03-30DOI: 10.22342/jims.28.1.991.75-83
P. Karmakar, A. Bhattacharyya
In this paper we analyse briefly some properties of hemi-slant sub-manifold of (LCS)n-manifold. Here we discuss about some necessary and sufficient conditions for distributions to be integrable and obtain some results in this direction. We also study the geometry of leaves of hemi-slant submanifold of (LCS)n-manifold. At last we give an example of a hemi-slant submanifold of an (LCS)n-manifold.
{"title":"Hemi-Slant Submanifold of (LCS)n-Manifold","authors":"P. Karmakar, A. Bhattacharyya","doi":"10.22342/jims.28.1.991.75-83","DOIUrl":"https://doi.org/10.22342/jims.28.1.991.75-83","url":null,"abstract":"In this paper we analyse briefly some properties of hemi-slant sub-manifold of (LCS)n-manifold. Here we discuss about some necessary and sufficient conditions for distributions to be integrable and obtain some results in this direction. We also study the geometry of leaves of hemi-slant submanifold of (LCS)n-manifold. At last we give an example of a hemi-slant submanifold of an (LCS)n-manifold.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41271273","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 : 2022-03-28DOI: 10.22342/jims.28.1.1032.69-74
S. Sujitha, Mary Jenitha Lazer
An edge subset F of a connected graph G is a super edge cut if G − F is disconnected and every component of G−F has atleast two vertices. The minimum cardinality of super edge cut is called super edge connectivity number and it is denoted by λ'(G). Every arithmetic graph G = Vn, n not equal to p1 × p2 has super edge cut. In this paper, the authors study super edge connectivity number of an arithmetic graphs G = Vn, n = p_1^a_1 × p_2^a_2 , a1 > 1, a2 ≥ 1, and G = Vn, n = p_1^a_1 × p_2^a_2 × · · · ×p_r^a_r , r > 2, ai ≥ 1, 1 ≤ i ≤ r.
连通图G的边子集F是一个超边切，如果G−F是不连通的，并且G−F的每个分量至少有两个顶点。超边切的最小基数称为超边连通性数，用λ’(G)表示。每个算术图G = Vn, n不等于p1 × p2都有超切边。本文研究了一类算术图G = Vn, n = p_1^a_1 × p_2^a_2, a1 > 1, a2≥1，以及G = Vn, n = p_1^a_1 × p_2^a_2 ×··×p_r^a_r, r > 2, ai≥1,1≤i≤r的超边连通性数。
{"title":"Super Edge Connectivity Number of an Arithmetic Graph","authors":"S. Sujitha, Mary Jenitha Lazer","doi":"10.22342/jims.28.1.1032.69-74","DOIUrl":"https://doi.org/10.22342/jims.28.1.1032.69-74","url":null,"abstract":"An edge subset F of a connected graph G is a super edge cut if G − F is disconnected and every component of G−F has atleast two vertices. The minimum cardinality of super edge cut is called super edge connectivity number and it is denoted by λ'(G). Every arithmetic graph G = Vn, n not equal to p1 × p2 has super edge cut. In this paper, the authors study super edge connectivity number of an arithmetic graphs G = Vn, n = p_1^a_1 × p_2^a_2 , a1 > 1, a2 ≥ 1, and G = Vn, n = p_1^a_1 × p_2^a_2 × · · · ×p_r^a_r , r > 2, ai ≥ 1, 1 ≤ i ≤ r.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47213427","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 : 2022-03-25DOI: 10.22342/jims.28.1.992.44-51
G. Malleswari, S. Sreenivasulu, G. Shobhalatha
Let R be a semiprime ring, I a non-zero ideal of R and α be an automorphism of R. A map F : R to R is said to be a multiplicative (generalized)(α, 1)-derivation associated with a map d : R to R such that F (xy) = F (x) α (y) + xd (y), for all x, y in R. In the present paper, we shall prove that R contains a non-zero central ideal if any one of the following holds: (i) F [x, y] ± [x,y] =0; (ii) F (xoy)±α(xoy) = 0; (iii) F [x, y] = [F (x) , y]α;1 ; (iv) F [x, y] =(F (x) oy)α;1 ; (v) F (xoy) = [F(x) , y]α;1 and (vi)F (xoy) = (F (x) oy)α;1, for all x, y in I.
{"title":"Some Identities Involving Multiplicative (Generalized)(α; 1)-Derivations in Semiprime Rings","authors":"G. Malleswari, S. Sreenivasulu, G. Shobhalatha","doi":"10.22342/jims.28.1.992.44-51","DOIUrl":"https://doi.org/10.22342/jims.28.1.992.44-51","url":null,"abstract":"Let R be a semiprime ring, I a non-zero ideal of R and α be an automorphism of R. A map F : R to R is said to be a multiplicative (generalized)(α, 1)-derivation associated with a map d : R to R such that F (xy) = F (x) α (y) + xd (y), for all x, y in R. In the present paper, we shall prove that R contains a non-zero central ideal if any one of the following holds: (i) F [x, y] ± [x,y] =0; (ii) F (xoy)±α(xoy) = 0; (iii) F [x, y] = [F (x) , y]α;1 ; (iv) F [x, y] =(F (x) oy)α;1 ; (v) F (xoy) = [F(x) , y]α;1 and (vi)F (xoy) = (F (x) oy)α;1, for all x, y in I.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44697658","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 : 2022-03-25DOI: 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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.28.1.1025.1-7
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":null,"pages":null},"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}
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