"Analysts like Renyi (1961), Csiszar (1963, 1966), Bregman (1967), Burba-Rao (1982), Jain and Saraswat (2012), etc., have introduced and analyzed the different functional discriminating measures for comparing two discrete probability distributions. But in this article, a new functional discriminating measure has been proposed that will compare finite (more than two) discrete probability distributions simultaneously. Further, some intra-relations among the measures at different values of the parameters have been discussed. Also, an interesting connection with Csiszar’s generalized functional measure has been created. Some new inequalities compared to variational discrimination and Chi-square discrimination have been discussed as well. "
{"title":"Generalized Functional Discriminating Measure For Finite Probability Distributions","authors":"P. Chhabra","doi":"10.37193/cmi.2023.01.03","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.03","url":null,"abstract":"\"Analysts like Renyi (1961), Csiszar (1963, 1966), Bregman (1967), Burba-Rao (1982), Jain and Saraswat (2012), etc., have introduced and analyzed the different functional discriminating measures for comparing two discrete probability distributions. But in this article, a new functional discriminating measure has been proposed that will compare finite (more than two) discrete probability distributions simultaneously. Further, some intra-relations among the measures at different values of the parameters have been discussed. Also, an interesting connection with Csiszar’s generalized functional measure has been created. Some new inequalities compared to variational discrimination and Chi-square discrimination have been discussed as well. \"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115577187","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}
$H$-line graph, denoted by $HL(G)$, is a generalization of line graph. Let $G$ and $H$ be two graphs such that $H$ has at least 3 vertices and is connected. The $H$-line graph of $G$, denoted by $HL(G)$, is that graph whose vertices are the edges of $G$ and two vertices of $HL(G)$ are adjacent if they are adjacent in $G$ and lie in a common copy of $H$. In this paper, we show that $H$-line graphs do not admit a forbidden subgraph characterization.
{"title":"Non-existence of forbidden subgraph characterization of $H$-line graphs","authors":"S. Varghese","doi":"10.37193/cmi.2023.01.11","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.11","url":null,"abstract":"$H$-line graph, denoted by $HL(G)$, is a generalization of line graph. Let $G$ and $H$ be two graphs such that $H$ has at least 3 vertices and is connected. The $H$-line graph of $G$, denoted by $HL(G)$, is that graph whose vertices are the edges of $G$ and two vertices of $HL(G)$ are adjacent if they are adjacent in $G$ and lie in a common copy of $H$. In this paper, we show that $H$-line graphs do not admit a forbidden subgraph characterization.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123028103","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 introduced the notion of intuitionistic fuzzy prime radical of an intuitionistic fuzzy ideal in $Gamma$-rings. We also characterise intuitionistic fuzzy primary ideal of $Gamma$-rings. We also analyse homomorphic behaviour of intuitionistic fuzzy primary ideal and intuitionistic fuzzy prime radical of $Gamma$-rings.
{"title":"Intuitionistic Fuzzy Prime Radical and Intuitionistic Fuzzy Primary Ideal Of $Gamma$-Ring","authors":"P. K. Sharma, Hem Lata, Nitin Bharadwaj","doi":"10.37193/cmi.2023.01.08","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.08","url":null,"abstract":"In this paper, we introduced the notion of intuitionistic fuzzy prime radical of an intuitionistic fuzzy ideal in $Gamma$-rings. We also characterise intuitionistic fuzzy primary ideal of $Gamma$-rings. We also analyse homomorphic behaviour of intuitionistic fuzzy primary ideal and intuitionistic fuzzy prime radical of $Gamma$-rings.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114868669","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 Hausdorff series provides a solution to the equation $w=log(e^ue^v)$ given by a recursive formula which can be expressed as nested commutators of $u$ and $v$. Evolutions of the Haussdorff series in various algebras and rings has been considered in obtaining a closed form of this formula. We consider the rectangular band $L_mtimes R_n$ determined by the left zero semigroup $L_m$ and the right zero semigroup $R_n$ of order $m$ and $n$, respectively. Let $mathbb Rlangle L_mtimes R_nrangle$ be the semigroup ring spanned on $L_mtimes R_n$ together with the identity element $1$. We provide a closed form of the formula for solving the equation in $mathbb Rlangle L_mtimes R_nrangle$."
Hausdorff级数提供了方程$w=log(e^ue^v)$的一个解，该解由一个递归公式给出，该递归公式可以表示为$u$和$v$的嵌套对易子。在得到该公式的封闭形式时，考虑了Haussdorff级数在各种代数和环中的演化。我们考虑矩形带$L_m乘以R_n$分别由$m$阶和$n$阶的左零半群$L_m$和右零半群$R_n$决定。设$mathbb R rangle L_m乘以R_nrangle$是在$L_m乘以R_n$上张成的半群环和单位元$1$。我们提供了一个封闭形式的公式来求解$mathbb Rlangle L_m乘以R_nrangle$。
{"title":"Hausdorff series in semigroup rings of rectangular bands","authors":"O. Kelekci","doi":"10.37193/cmi.2023.01.06","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.06","url":null,"abstract":"\"The Hausdorff series provides a solution to the equation $w=log(e^ue^v)$ given by a recursive formula which can be expressed as nested commutators of $u$ and $v$. Evolutions of the Haussdorff series in various algebras and rings has been considered in obtaining a closed form of this formula. We consider the rectangular band $L_mtimes R_n$ determined by the left zero semigroup $L_m$ and the right zero semigroup $R_n$ of order $m$ and $n$, respectively. Let $mathbb Rlangle L_mtimes R_nrangle$ be the semigroup ring spanned on $L_mtimes R_n$ together with the identity element $1$. We provide a closed form of the formula for solving the equation in $mathbb Rlangle L_mtimes R_nrangle$.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126214534","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 the present paper, we define the $Pw$-contraction by considering the inequality called $P$-contraction in metric space together with the $w$ -distance. We then present fixed point theorems for both single-valued and multivalued $Pw$-contractions. We also support our results with suitable examples."
{"title":"Fixed point results for $P$-contractions via $w$-distance","authors":"I. Altun, H. A. Hançer, Ümran Bașar","doi":"10.37193/cmi.2023.01.02","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.02","url":null,"abstract":"\"In the present paper, we define the $Pw$-contraction by considering the inequality called $P$-contraction in metric space together with the $w$ -distance. We then present fixed point theorems for both single-valued and multivalued $Pw$-contractions. We also support our results with suitable examples.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132761245","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 new inertial iterative algorithm for approximating solution of split equality fixed point problem (SEFPP) for quasi-$phi$- nonexpansive mappings is introduced and studied in $p$-uniformly convex and uniformly smooth real Banach spaces, $p>1$. A strong convergence theorem is proved without imposing any compactness-type condition on the mappings. Our theorems complement several important recent results that have been proved in 2-uniformly convex and uniformly smooth real Banach spaces. It is well known that these spaces do not include $L_p, l_p $ and the Sobolev spaces ${W^m}_p(Omega)$, for $2< p < infty$. Our theorems, in particular, are applicable in these spaces. Furthermore, application of our theorem to split equality variational inclusion problem is presented. Finally, numerical examples are presented to illustrate the convergence of our algorithms."
在$p$ -一致凸和一致光滑实Banach空间$p>1$中，研究了拟- $phi$ -非扩张映射的分裂相等不动点问题(SEFPP)近似解的一种新的惯性迭代算法。在不加紧性条件的情况下证明了一个强收敛定理。我们的定理补充了最近在2-一致凸和一致光滑实巴拿赫空间中证明的几个重要结果。众所周知，对于$2< p < infty$，这些空间不包括$L_p, l_p $和Sobolev空间${W^m}_p(Omega)$。我们的定理，特别地，适用于这些空间。进一步，给出了该定理在分裂等式变分包含问题中的应用。最后通过数值算例说明了算法的收敛性。
{"title":"An iterative method involving a class of quasi-phi-nonexpansive mappings for solving split equality fixed point problems","authors":"C. Chidume, Aisha A. Adam, A. Adamu","doi":"10.37193/cmi.2023.01.04","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.04","url":null,"abstract":"\"A new inertial iterative algorithm for approximating solution of split equality fixed point problem (SEFPP) for quasi-$phi$- nonexpansive mappings is introduced and studied in $p$-uniformly convex and uniformly smooth real Banach spaces, $p>1$. A strong convergence theorem is proved without imposing any compactness-type condition on the mappings. Our theorems complement several important recent results that have been proved in 2-uniformly convex and uniformly smooth real Banach spaces. It is well known that these spaces do not include $L_p, l_p $ and the Sobolev spaces ${W^m}_p(Omega)$, for $2< p < infty$. Our theorems, in particular, are applicable in these spaces. Furthermore, application of our theorem to split equality variational inclusion problem is presented. Finally, numerical examples are presented to illustrate the convergence of our algorithms.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126122554","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 present paper studies the existence and uniqueness of solutions to a boundary value problem (BVP) of fractional order involving the Caputo fractional derivative and also discusses some other properties of the solutions. An example in support of all established results is given."
{"title":"\"Existence and Uniqueness of Solutions of a Boundary Value Problem of Fractional Order via S-Iteration\"","authors":"H. L. Tidke, G. Patil","doi":"10.37193/cmi.2023.01.10","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.10","url":null,"abstract":"\"The present paper studies the existence and uniqueness of solutions to a boundary value problem (BVP) of fractional order involving the Caputo fractional derivative and also discusses some other properties of the solutions. An example in support of all established results is given.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115022555","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 consider the Fibonacci and Padovan sequences. We introduce the quinary Fibonacci-Padovan sequences whose compounds are the Fibonacci and Padovan sequences. We derive the Binet-like formulas, the generating functions and exponential generating functions of these sequences. Also, we obtain some binomial identities, series and sums for them.
{"title":"On the Quinary Fibonacci-Padovan Sequences","authors":"Orhan Dişkaya, H. Menken","doi":"10.37193/cmi.2023.01.05","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.05","url":null,"abstract":"In this paper, we consider the Fibonacci and Padovan sequences. We introduce the quinary Fibonacci-Padovan sequences whose compounds are the Fibonacci and Padovan sequences. We derive the Binet-like formulas, the generating functions and exponential generating functions of these sequences. Also, we obtain some binomial identities, series and sums for them.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124479876","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 purpose of this paper is to introduce the class of $mathfrak{R}$-enriched interpolative Kannan pair and proved a common fixed point result in the context of $mathfrak{R}$-complete convex metric spaces. Some examples are presented to support the concepts introduced herein. Moreover, we study the well-posedness, limit shadowing property and Ulam-Hyers stability of the mappings introduced herein. Our result extend and generalize several comparable results in the existing literature."
{"title":"\"Fixed point results Oof $mathfrak{R}$ Enriched Interpolative Kannan pair in $mathfrak{R}$-convex metric spaces\"","authors":"M. Abbas, Rizwana Anjum, Shakeela Riasat","doi":"10.37193/cmi.2023.01.01","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.01","url":null,"abstract":"\"The purpose of this paper is to introduce the class of $mathfrak{R}$-enriched interpolative Kannan pair and proved a common fixed point result in the context of $mathfrak{R}$-complete convex metric spaces. Some examples are presented to support the concepts introduced herein. Moreover, we study the well-posedness, limit shadowing property and Ulam-Hyers stability of the mappings introduced herein. Our result extend and generalize several comparable results in the existing literature.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"311 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122825500","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 exact values for the projective dimension of edge ideals associated to some star related graphs and product graphs $G square P_2$, when $G= C_n, K_n$ and upper bounds for the projective dimension when $G= P_n, W_n$, are obtained. We have proved that $pd(C_{n+1} square P_2)= 2big(n-leftlfloor frac{n}{4}rightrfloorbig)$, $pd(K_n square P_2)= 2n-2$ and $pd(P_{n+1} square P_2)le n+3+leftlfloor frac{n-3}{2}rightrfloor$, $pd(W_n square P_2)leq n+1+lceilfrac{2n-1}{3}rceil$. These values are functions of the number of vertices in the corresponding graphs.
{"title":"Projective Dimension of Some Graphs","authors":"Reji Thankachan, Ruby Rosemary, Sneha Balakrishnan","doi":"10.37193/cmi.2023.01.09","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.09","url":null,"abstract":"In this paper exact values for the projective dimension of edge ideals associated to some star related graphs and product graphs $G square P_2$, when $G= C_n, K_n$ and upper bounds for the projective dimension when $G= P_n, W_n$, are obtained. We have proved that $pd(C_{n+1} square P_2)= 2big(n-leftlfloor frac{n}{4}rightrfloorbig)$, $pd(K_n square P_2)= 2n-2$ and $pd(P_{n+1} square P_2)le n+3+leftlfloor frac{n-3}{2}rightrfloor$, $pd(W_n square P_2)leq n+1+lceilfrac{2n-1}{3}rceil$. These values are functions of the number of vertices in the corresponding graphs.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128679254","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：