"The object of the present paper is to study K-paracontact manifold admitting parallel Cotton tensor, vanishing Cotton tensor and to study Bach flatness on K-paracontact manifold. In that we prove for a K-paracontact metric manifold M^{2n+1} has parallel Cotton tensor if and only if M^{2n+1} is an η-Einstein manifold and r=-2n(2n+1). Further we show that if g is an η-Einstein K-paracontact metric and if g is Bach flat then g is an Einstein. Also we study vanishing Cotton tensor on (k,μ)-paracontact manifold for both k>-1 and k<-1. Finally, we prove that if M^{2n+1} is a (k,μ)-paracontact manifold for k ≠ -1 and if M^{2n+1} has vanishing Cotton tensor for μ ≠ k, then M^{2n+1} is an η-Einstein manifold."
{"title":"A study on K-paracontact and (k,μ)-paracontact manifold admitting vanishing Cotton tensor and Bach tensor","authors":"V. Venkatesha, N. Bhanumathi, C. Shruthi","doi":"10.52846/ami.v49i1.1336","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1336","url":null,"abstract":"\"The object of the present paper is to study K-paracontact manifold admitting parallel Cotton tensor, vanishing Cotton tensor and to study Bach flatness on K-paracontact manifold. In that we prove for a K-paracontact metric manifold M^{2n+1} has parallel Cotton tensor if and only if M^{2n+1} is an η-Einstein manifold and r=-2n(2n+1). Further we show that if g is an η-Einstein K-paracontact metric and if g is Bach flat then g is an Einstein. Also we study vanishing Cotton tensor on (k,μ)-paracontact manifold for both k>-1 and k<-1. Finally, we prove that if M^{2n+1} is a (k,μ)-paracontact manifold for k ≠ -1 and if M^{2n+1} has vanishing Cotton tensor for μ ≠ k, then M^{2n+1} is an η-Einstein manifold.\"","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77118529","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}
"Let $D=(V,A)$ be a finite simple digraph. A signed double Roman dominating function (SDRD-function) on the digraph $D$ is a function $f:V(D)rightarrow{-1,1,2, 3}$ satisfying the following conditions: (i) $sum_{xin N^-[v]}f(x)ge 1$ for each $vin V(D)$, where $N^-[v]$ consist of $v$ and all in-neighbors of $v$, and (ii) if $f(v)=-1$, then the vertex $v$ must have at least two in-neighbors assigned 2 under $f$ or one in-neighbor assigned 3, while if $f(v)=1$, then the vertex $v$ must have at least one in-neighbor assigned 2 or 3. The weight of a SDRD-function $f$ is the value $sum_{xin V(D)}f(x)$. The signed double Roman domination number (SDRD-number) $gamma_{sdR}(D)$ of a digraph $D$ is the minimum weight of a SDRD-function on $D$. In this paper we study the SDRD-number of digraphs, and we present lower and upper bounds for $gamma_{sdR}(D)$ in terms of the order, maximum degree and chromatic number of a digraph. In addition, we determine the SDRD-number of some classes of digraphs."
{"title":"Signed double Roman domination numbers in digraphs","authors":"J. Amjadi, F. Pourhosseini","doi":"10.52846/ami.v48i1.1305","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1305","url":null,"abstract":"\"Let $D=(V,A)$ be a finite simple digraph. A signed double Roman dominating function (SDRD-function) on the digraph $D$ is a function $f:V(D)rightarrow{-1,1,2, 3}$ satisfying the following conditions: (i) $sum_{xin N^-[v]}f(x)ge 1$ for each $vin V(D)$, where $N^-[v]$ consist of $v$ and all in-neighbors of $v$, and (ii) if $f(v)=-1$, then the vertex $v$ must have at least two in-neighbors assigned 2 under $f$ or one in-neighbor assigned 3, while if $f(v)=1$, then the vertex $v$ must have at least one in-neighbor assigned 2 or 3. The weight of a SDRD-function $f$ is the value $sum_{xin V(D)}f(x)$. The signed double Roman domination number (SDRD-number) $gamma_{sdR}(D)$ of a digraph $D$ is the minimum weight of a SDRD-function on $D$. In this paper we study the SDRD-number of digraphs, and we present lower and upper bounds for $gamma_{sdR}(D)$ in terms of the order, maximum degree and chromatic number of a digraph. In addition, we determine the SDRD-number of some classes of digraphs.\"","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78597232","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}
A total edge Steiner set of G is an edge Steiner set W such that the subgraph induced by has no isolated vertex. The minimum cardinality of a total edge Steiner set of G is the total edge Steiner number of G and is denoted by ste(G). Some general properties satisfied by this concept are studied. The total edge Steiner numbers of certain classes of graphs is studied. Connected graphs of order p with total edge Steiner number 2 or 3 are characterized. Necessary conditions for total edge Steiner number to be p or p − 1 is given. It is shown that for every pair a and b of integers with 2 ≤ a < b and b > a+ 1, there exists a connected graph G such that se(G) = a and ste(G) = b. Also it shown that for every pair a and b of integers with 4 ≤ a < b and b > a + 1, there exists a connected graph G such that st(G) = a and ste(G) = b.
{"title":"The total edge Steiner number of a graph","authors":"J. John","doi":"10.52846/ami.v48i1.1361","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1361","url":null,"abstract":"A total edge Steiner set of G is an edge Steiner set W such that the subgraph induced by has no isolated vertex. The minimum cardinality of a total edge Steiner set of G is the total edge Steiner number of G and is denoted by ste(G). Some general properties satisfied by this concept are studied. The total edge Steiner numbers of certain classes of graphs is studied. Connected graphs of order p with total edge Steiner number 2 or 3 are characterized. Necessary conditions for total edge Steiner number to be p or p − 1 is given. It is shown that for every pair a and b of integers with 2 ≤ a < b and b > a+ 1, there exists a connected graph G such that se(G) = a and ste(G) = b. Also it shown that for every pair a and b of integers with 4 ≤ a < b and b > a + 1, there exists a connected graph G such that st(G) = a and ste(G) = b.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84589449","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}
The aim of this research note is firstly to introduce certain fundamental information in relation with various operators of fractional-order calculus in the complex plane, then create some comprehensive results associating with certain analytic functions as implications of those operators, and also present numerous conclusions and recommendations for the related researchers.
{"title":"Characterizations of some fractional-order operators in complex domains and their extensive implications to certain analytic functions","authors":"H. Irmak","doi":"10.52846/ami.v48i1.1481","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1481","url":null,"abstract":"The aim of this research note is firstly to introduce certain fundamental information in relation with various operators of fractional-order calculus in the complex plane, then create some comprehensive results associating with certain analytic functions as implications of those operators, and also present numerous conclusions and recommendations for the related researchers.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85159928","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}
Parallel curves (or offset curves) and parallel surfaces (or offset surfaces) have a big importance for CAD/CAM, robotics, cam design and many industrial applications, especially for mathematical modelling of cutting paths milling machines. Any vector space has a corresponding dual vector space that consists of all linear functions on vector space. Dual spaces are used in mathematics such as describing measures, distributions, and Hilbert spaces. Consequently, the dual space is an important concept in functional analysis. This paper proposes a novel definition of generalized and standard dual parallel curves and surfaces. Additionally, we give some properties of generalized dual parallel curves and surfaces using this novel definition. We also express the variation of the generalized dual parallel curves, the first and second variation of area change of the standard dual parallel surfaces and the first variation of area change of the generalized dual parallel surfaces.
{"title":"Exchange variations of generalized dual parallel curves and surfaces","authors":"Vahide Bulut","doi":"10.52846/ami.v48i1.1413","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1413","url":null,"abstract":"Parallel curves (or offset curves) and parallel surfaces (or offset surfaces) have a big importance for CAD/CAM, robotics, cam design and many industrial applications, especially for mathematical modelling of cutting paths milling machines. Any vector space has a corresponding dual vector space that consists of all linear functions on vector space. Dual spaces are used in mathematics such as describing measures, distributions, and Hilbert spaces. Consequently, the dual space is an important concept in functional analysis. This paper proposes a novel definition of generalized and standard dual parallel curves and surfaces. Additionally, we give some properties of generalized dual parallel curves and surfaces using this novel definition. We also express the variation of the generalized dual parallel curves, the first and second variation of area change of the standard dual parallel surfaces and the first variation of area change of the generalized dual parallel surfaces.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77318062","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}
In this article, we present some operator inequalities via arbitrary operator means and unital positive linear maps. For instance, we show that if $A,B in {mathbb B}({mathscr H}) $ are two positive invertible operators such that $ 0 < m leq A,B leq M $ and $sigma$ is an arbitrary operator mean, then begin{align*} Phi^{p}(Asigma B) leq K^{p}(h) Phi^{p}(Bsigma^{perp} A), end{align*} where $sigma^{perp}$ is dual $sigma$, $pgeq0$ and $K(h)=frac{(M+m)^{2}}{4 Mm}$ is the classical Kantorovich constant. We also generalize the above inequality for two arbitrary means $sigma_{1},sigma_{2}$ which lie between $sigma$ and $sigma^{perp}$.
本文给出了任意算子均值和一元正线性映射的算子不等式。例如，如果$A,B in {mathbb B}({mathscr H}) $是两个正可逆算子，使得$ 0 < m leq A,B leq M $和$sigma$是任意算子均值，则begin{align*} Phi^{p}(Asigma B) leq K^{p}(h) Phi^{p}(Bsigma^{perp} A), end{align*}其中$sigma^{perp}$是对偶的$sigma$, $pgeq0$和$K(h)=frac{(M+m)^{2}}{4 Mm}$是经典的Kantorovich常数。我们还将上述不等式推广到$sigma$和$sigma^{perp}$之间的两个任意均值$sigma_{1},sigma_{2}$。
{"title":"New generalized inequalities using arbitrary operator means and their duals","authors":"Leila Nasiri, M. Bakherad","doi":"10.52846/ami.v48i1.1179","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1179","url":null,"abstract":"In this article, we present some operator inequalities via arbitrary operator means and unital positive linear maps. For instance, we show that if $A,B in {mathbb B}({mathscr H}) $ are two positive invertible operators such that $ 0 < m leq A,B leq M $ and $sigma$ is an arbitrary operator mean, then begin{align*} Phi^{p}(Asigma B) leq K^{p}(h) Phi^{p}(Bsigma^{perp} A), end{align*} where $sigma^{perp}$ is dual $sigma$, $pgeq0$ and $K(h)=frac{(M+m)^{2}}{4 Mm}$ is the classical Kantorovich constant. We also generalize the above inequality for two arbitrary means $sigma_{1},sigma_{2}$ which lie between $sigma$ and $sigma^{perp}$.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82391041","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}
To prevent an exhaustive key-search attack of the key-exchange protocol using real quadratic fields, we need to ensure that the number l of reduced principal ideals in K is sufficiently large. In this paper we present an example of a family which are not valid for this protocol.
{"title":"On the key-exchange protocol using real quadratic fields","authors":"A. Azizi, Jamal Benamara, M. C. Ismaili","doi":"10.52846/ami.v48i1.1331","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1331","url":null,"abstract":"To prevent an exhaustive key-search attack of the key-exchange protocol using real quadratic fields, we need to ensure that the number l of reduced principal ideals in K is sufficiently large. In this paper we present an example of a family which are not valid for this protocol.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86424496","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}
In this paper, we study the boundary feedback stabilization problem of a hybrid system consisting of a flexible beam attached to the platform moving a long a straight rail and carrying at the free end a load which is deplaced in a horizontal plan. The model proposed in this paper fits a large real applications such as an overhead crane with beam. Using the Riesz basis approach of general second-differential equation systems with non separated boundary conditions, it is shown that the Riesz basis property holds for the system and as consequence, the exponential stability is concluded. To verify the theoritical developments, numerical study of the spectrum is performed by Legendre approximation, also thenumerical simulations are presented to show the effectivnesse of the proposed control.
{"title":"Boundary stabilization of an overhead crane with beam model","authors":"M. D. Aouragh, Samir Khallouq, M’hamed Segaoui","doi":"10.52846/ami.v48i1.1345","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1345","url":null,"abstract":"In this paper, we study the boundary feedback stabilization problem of a hybrid system consisting of a flexible beam attached to the platform moving a long a straight rail and carrying at the free end a load which is deplaced in a horizontal plan. The model proposed in this paper fits a large real applications such as an overhead crane with beam. Using the Riesz basis approach of general second-differential equation systems with non separated boundary conditions, it is shown that the Riesz basis property holds for the system and as consequence, the exponential stability is concluded. To verify the theoritical developments, numerical study of the spectrum is performed by Legendre approximation, also thenumerical simulations are presented to show the effectivnesse of the proposed control.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81801801","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}
Spatial data mining is a special type of data mining. The main difference between data mining and spatial data mining is that in spatial data mining tasks we use not only non-spatial attributes but also spatial attributes. Spatial data mining techniques have strong relationship with GIS (Geographical Information System) and are widely used in GIS for inferring association among spatial attributes, clustering and classifying information with respect to spatial attributes. In this paper we use the statistical package Weka on two models, which consist of two parcels plans from the Olt area of Romania. In our experimentation, we compare the results of the vector models depending on the values of the training datasets. Using these models with GIS data from the domain of Cadaster we analyze the performance of the Artificial Neural Networks in context of spatial data mining.
{"title":"New approaches to processing GIS Data using Artificial Neural Networks models","authors":"Dana Mihai","doi":"10.52846/ami.v48i1.1551","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1551","url":null,"abstract":"Spatial data mining is a special type of data mining. The main difference between data mining and spatial data mining is that in spatial data mining tasks we use not only non-spatial attributes but also spatial attributes. Spatial data mining techniques have strong relationship with GIS (Geographical Information System) and are widely used in GIS for inferring association among spatial attributes, clustering and classifying information with respect to spatial attributes. In this paper we use the statistical package Weka on two models, which consist of two parcels plans from the Olt area of Romania. In our experimentation, we compare the results of the vector models depending on the values of the training datasets. Using these models with GIS data from the domain of Cadaster we analyze the performance of the Artificial Neural Networks in context of spatial data mining.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80308668","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}
In this article, we unify the multi-quadratic mappings as a single functional equation. We also apply a fixed point theorem to provide the Hyers-Ulam stability for this new multi-quadratic functional equation in non-Archimedean normed spaces.
{"title":"Approximation for multi-quadratic mappings in non-Archimedean spaces","authors":"A. Bodaghi, Somaye Salimi, Ghasem Abbasi","doi":"10.52846/ami.v48i1.1364","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1364","url":null,"abstract":"In this article, we unify the multi-quadratic mappings as a single functional equation. We also apply a fixed point theorem to provide the Hyers-Ulam stability for this new multi-quadratic functional equation in non-Archimedean normed spaces.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77144922","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：