Pub Date : 2020-04-01DOI: 10.4067/s0719-06462020000100023
S. Pahan
In this paper, we study ( eta )-Ricci solitons on 3-dimensional trans-Sasakian manifolds. Firstly we give conditions for the existence of these geometric structures and then observe that they provide examples of ( eta )-Einstein manifolds. In the case of ( phi )-Ricci symmetric trans-Sasakian manifolds, the η-Ricci soliton condition turns them to Einstein manifolds. Afterward, we study the implications in this geometric context of the important tensorial conditions ( R cdot S = 0), (S cdot R = 0), (W_2cdot S = 0) and (S cdot W_2 = 0).
本文研究了三维反sasakian流形上的( eta ) -Ricci孤子。我们首先给出了这些几何结构存在的条件，然后观察到它们提供了( eta ) -爱因斯坦流形的例子。在( phi ) -Ricci对称反sasaki流形的情况下，η-Ricci孤子条件将它们变成爱因斯坦流形。之后，我们研究了重要张量条件( R cdot S = 0), (S cdot R = 0), (W_2cdot S = 0)和(S cdot W_2 = 0)在这种几何背景下的含义。
{"title":"η-Ricci Solitons on 3-dimensional Trans-Sasakian Manifolds","authors":"S. Pahan","doi":"10.4067/s0719-06462020000100023","DOIUrl":"https://doi.org/10.4067/s0719-06462020000100023","url":null,"abstract":"In this paper, we study ( eta )-Ricci solitons on 3-dimensional trans-Sasakian manifolds. Firstly we give conditions for the existence of these geometric structures and then observe that they provide examples of ( eta )-Einstein manifolds. In the case of ( phi )-Ricci symmetric trans-Sasakian manifolds, the η-Ricci soliton condition turns them to Einstein manifolds. Afterward, we study the implications in this geometric context of the important tensorial conditions ( R cdot S = 0), (S cdot R = 0), (W_2cdot S = 0) and (S cdot W_2 = 0).","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44631809","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 : 2019-08-10DOI: 10.4067/s0719-06462019000200041
M. Siddesha, C. Bagewadi, D. Nirmala
In this paper, we study slant submanifolds of a para-Kenmotsu manifold. We prove that totally umbilical slant submanifold of a para-Kenmotsu manifold is either invariant or anti-invariant or dimension of submanifold is 1 or the mean curvature vector H of the submanifold lies in the invariant normal subbundle.
{"title":"Totally umbilical proper slant submanifolds of para-Kenmotsu manifold","authors":"M. Siddesha, C. Bagewadi, D. Nirmala","doi":"10.4067/s0719-06462019000200041","DOIUrl":"https://doi.org/10.4067/s0719-06462019000200041","url":null,"abstract":"In this paper, we study slant submanifolds of a para-Kenmotsu manifold. We prove that totally umbilical slant submanifold of a para-Kenmotsu manifold is either invariant or anti-invariant or dimension of submanifold is 1 or the mean curvature vector H of the submanifold lies in the invariant normal subbundle.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45434016","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 : 2019-08-10DOI: 10.4067/s0719-06462019000200015
P. Jeyanthi, K. Daisy, A. Semaničová-Feňovčíková
For any non-trivial Abelian group A under addition a graph G is said to be A-magic if there exists a labeling f : E(G) → A − {0} such that, the vertex labeling f+ defined as f+(v) = ∑f(uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Zk-magic graph if the group A is Zk, the group of integers modulo k and these graphs are referred as k-magic graphs. In this paper we prove that the graphs such as path union of cycle, generalized Petersen graph, shell, wheel, closed helm, double wheel, flower, cylinder, total graph of a path, lotus inside a circle and n-pan graph are Zk-magic graphs.
{"title":"Zk-Magic Labeling of Path Union of Graphs","authors":"P. Jeyanthi, K. Daisy, A. Semaničová-Feňovčíková","doi":"10.4067/s0719-06462019000200015","DOIUrl":"https://doi.org/10.4067/s0719-06462019000200015","url":null,"abstract":"For any non-trivial Abelian group A under addition a graph G is said to be A-magic if there exists a labeling f : E(G) → A − {0} such that, the vertex labeling f+ defined as f+(v) = ∑f(uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Zk-magic graph if the group A is Zk, the group of integers modulo k and these graphs are referred as k-magic graphs. In this paper we prove that the graphs such as path union of cycle, generalized Petersen graph, shell, wheel, closed helm, double wheel, flower, cylinder, total graph of a path, lotus inside a circle and n-pan graph are Zk-magic graphs.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47067265","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 : 2019-08-10DOI: 10.4067/s0719-06462019000200065
A. Ammar, A. Jeribi, K. Mahfoudhi
The objective of the study was to investigate a new notion of generalized trace pseudo- spectrum for an matrix pencils. In particular, we prove many new interesting properties of the generalized trace pseudo-spectrum. In addition, we show an analogue of the spectral mapping theorem for the generalized trace pseudo-spectrum in the matrix algebra.
{"title":"Generalized trace pseudo-spectrum of matrix pencils","authors":"A. Ammar, A. Jeribi, K. Mahfoudhi","doi":"10.4067/s0719-06462019000200065","DOIUrl":"https://doi.org/10.4067/s0719-06462019000200065","url":null,"abstract":"The objective of the study was to investigate a new notion of generalized trace pseudo- spectrum for an matrix pencils. In particular, we prove many new interesting properties of the generalized trace pseudo-spectrum. In addition, we show an analogue of the spectral mapping theorem for the generalized trace pseudo-spectrum in the matrix algebra.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45541867","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 : 2019-08-10DOI: 10.4067/s0719-06462019000200077
S. Yadav, Abhishek Kushwaha, D. Narain
We classify quasi-Sasakian 3-manifold with proper η-Ricci soliton and investigate its geometrical properties. Certain results of Yamabe soliton on such manifold are also presented. Finally, we construct an example of non-existence of proper η-Ricci soliton on 3-dimensional quasi-Sasakian manifold to illustrate the results obtained in previous section of the paper.
{"title":"Certain results for η-Ricci Solitons and Yamabe Solitons on quasi-Sasakian 3-Manifolds","authors":"S. Yadav, Abhishek Kushwaha, D. Narain","doi":"10.4067/s0719-06462019000200077","DOIUrl":"https://doi.org/10.4067/s0719-06462019000200077","url":null,"abstract":"We classify quasi-Sasakian 3-manifold with proper η-Ricci soliton and investigate its geometrical properties. Certain results of Yamabe soliton on such manifold are also presented. Finally, we construct an example of non-existence of proper η-Ricci soliton on 3-dimensional quasi-Sasakian manifold to illustrate the results obtained in previous section of the paper.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43927587","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 : 2019-08-10DOI: 10.4067/s0719-06462019000200001
G. Anastassiou
Here we present Caputo fractional Iyengar type inequalities with respect to Lp norms, with 1 ≤ p ≤ ∞. The method is based on the right and left Caputo fractional Taylor’s formulae.
{"title":"Caputo fractional Iyengar type Inequalities","authors":"G. Anastassiou","doi":"10.4067/s0719-06462019000200001","DOIUrl":"https://doi.org/10.4067/s0719-06462019000200001","url":null,"abstract":"Here we present Caputo fractional Iyengar type inequalities with respect to Lp norms, with 1 ≤ p ≤ ∞. The method is based on the right and left Caputo fractional Taylor’s formulae.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49590164","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 : 2019-08-10DOI: 10.4067/s0719-06462019000200051
V. Lampret
For the perimeter (P(a,b)) of an ellipse with the semi-axes (age bge 0) a sequence (Q_n(a,b)) is constructed such that the relative error of the approximation (P(a,b)approx Q_n(a,b)) satisfies the following inequalities (0le -frac{P(a,b)-Q_n(a,b)}{P(a,b)}lefrac{(1-q^2)^{n+1}}{(2n+1)^2}) (le frac{1}{(2n+1)^2},e^{-q^2(n+1)},) true for (nin{mathbb N}) and (q=frac{b}{a}in[0,1]).
{"title":"The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series","authors":"V. Lampret","doi":"10.4067/s0719-06462019000200051","DOIUrl":"https://doi.org/10.4067/s0719-06462019000200051","url":null,"abstract":"For the perimeter (P(a,b)) of an ellipse with the semi-axes (age bge 0) a sequence (Q_n(a,b)) is constructed such that the relative error of the approximation (P(a,b)approx Q_n(a,b)) satisfies the following inequalities \u0000(0le -frac{P(a,b)-Q_n(a,b)}{P(a,b)}lefrac{(1-q^2)^{n+1}}{(2n+1)^2}) \u0000(le frac{1}{(2n+1)^2},e^{-q^2(n+1)},) \u0000 \u0000 \u0000 \u0000true for (nin{mathbb N}) and (q=frac{b}{a}in[0,1]).","PeriodicalId":36416,"journal":{"name":"Cubo","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43910647","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 : 2019-04-01DOI: 10.4067/S0719-06462019000100079
Y. Raffoul, E. Yankson
The existence of multiple positive periodic solutions of the system of difference equations with a parameter x(n + 1) = A(n, x(n))x(n) + λf(n, xn), is studied. In particular, we use the eigenvalue problems of completely continuous operators to obtain our results. We apply our results to a well-known model in population dynamics.
{"title":"Positive periodic solutions of functional discrete systems with a parameter","authors":"Y. Raffoul, E. Yankson","doi":"10.4067/S0719-06462019000100079","DOIUrl":"https://doi.org/10.4067/S0719-06462019000100079","url":null,"abstract":"The existence of multiple positive periodic solutions of the system of difference equations with a parameter \u0000 \u0000 \u0000 \u0000x(n + 1) = A(n, x(n))x(n) + λf(n, xn), \u0000 \u0000 \u0000 \u0000is studied. In particular, we use the eigenvalue problems of completely continuous operators to obtain our results. We apply our results to a well-known model in population dynamics.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47129850","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 : 2019-04-01DOI: 10.4067/S0719-06462019000100061
Khalida Aissani, M. Benchohra, Nadia Benkhettou
In this paper, we prove the existence of mild solution of the fractional integro-differential equations with state-dependent delay with not instantaneous impulses. The existence results are obtained under the conditions in respect of Kuratowski’s measure of non- compactness. An example is also given to illustrate the results.
{"title":"On Fractional Integro-differential Equations with State-Dependent Delay and Non-Instantaneous Impulses","authors":"Khalida Aissani, M. Benchohra, Nadia Benkhettou","doi":"10.4067/S0719-06462019000100061","DOIUrl":"https://doi.org/10.4067/S0719-06462019000100061","url":null,"abstract":"In this paper, we prove the existence of mild solution of the fractional integro-differential equations with state-dependent delay with not instantaneous impulses. The existence results are obtained under the conditions in respect of Kuratowski’s measure of non- compactness. An example is also given to illustrate the results.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4067/S0719-06462019000100061","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47939590","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 : 2019-04-01DOI: 10.4067/S0719-06462019000100049
S. Haq, K. Nisar, A. H. Khan, D.L. Suthar
The aim of this article is to establish some integral transforms of the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function. Some integrals involving trigonometric, generalized Bessel and Struve functions are also indicated as special cases of our main results.
{"title":"Certain integral Transforms of the generalized Lommel-Wright function","authors":"S. Haq, K. Nisar, A. H. Khan, D.L. Suthar","doi":"10.4067/S0719-06462019000100049","DOIUrl":"https://doi.org/10.4067/S0719-06462019000100049","url":null,"abstract":"The aim of this article is to establish some integral transforms of the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function. Some integrals involving trigonometric, generalized Bessel and Struve functions are also indicated as special cases of our main results.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49258384","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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