Pub Date : 2023-09-05DOI: 10.9734/arjom/2023/v19i10740
Rohit Kumar Verma, Jharana Chandrakar
In this paper, we suggest a novel divergence metric on a fuzzy set. Some scholars have used the fuzzy set extension and one that integrated with other theories. Axioms are proven in order to demonstrate the viability of measure. We create a way about decision-making criteria using the suggested measure and provide a workable method. We discuss the divergence metric metric for fuzzy sets in this post. The discussed properties of the proposed proposal. Multicriteria decision making is a very useful technique with a wide range of applications in the real world.
{"title":"On Heterodox Non-KL Generalized Divergence Metric with Characteristics in Fuzzy Environment","authors":"Rohit Kumar Verma, Jharana Chandrakar","doi":"10.9734/arjom/2023/v19i10740","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i10740","url":null,"abstract":"In this paper, we suggest a novel divergence metric on a fuzzy set. Some scholars have used the fuzzy set extension and one that integrated with other theories. Axioms are proven in order to demonstrate the viability of measure. We create a way about decision-making criteria using the suggested measure and provide a workable method. We discuss the divergence metric metric for fuzzy sets in this post. The discussed properties of the proposed proposal. Multicriteria decision making is a very useful technique with a wide range of applications in the real world.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132291581","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 : 2023-08-31DOI: 10.9734/arjom/2023/v19i10738
Mogoi N. E., Apima S. B
Norm-attainable polynomials play a crucial role in various mathematical contexts. This research paper investigates the characterizations and properties of norm-attainable polynomials in different orthogonal polynomial families. We explore their behavior, convexity, and positive definiteness. Additionally, we establish their norm-attainability in specific intervals for various weight functions. The findings contribute to a deeper understanding of norm-attainable polynomials and their applications in approximation theory and mathematical modeling.
{"title":"Norm-Attainable Polynomials: Characterizations and Properties in Orthogonal Polynomial Families","authors":"Mogoi N. E., Apima S. B","doi":"10.9734/arjom/2023/v19i10738","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i10738","url":null,"abstract":"Norm-attainable polynomials play a crucial role in various mathematical contexts. This research paper investigates the characterizations and properties of norm-attainable polynomials in different orthogonal polynomial families. We explore their behavior, convexity, and positive definiteness. Additionally, we establish their norm-attainability in specific intervals for various weight functions. The findings contribute to a deeper understanding of norm-attainable polynomials and their applications in approximation theory and mathematical modeling.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129024882","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 : 2023-08-31DOI: 10.9734/arjom/2023/v19i10739
Yin Chen
Wallis ratio can be expressed as an asymptotic expansion using Stirling series and Bernoulli numbers. We prove the general inequalities for Wallis ratio for arbitrary number of terms in the asymptotic expansion. We show that the coefficients in the asymptotic expansion are the best possible.
{"title":"Some New Optimal Bounds for Wallis Ratio","authors":"Yin Chen","doi":"10.9734/arjom/2023/v19i10739","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i10739","url":null,"abstract":"Wallis ratio can be expressed as an asymptotic expansion using Stirling series and Bernoulli numbers. We prove the general inequalities for Wallis ratio for arbitrary number of terms in the asymptotic expansion. We show that the coefficients in the asymptotic expansion are the best possible.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122101114","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 : 2023-08-30DOI: 10.9734/arjom/2023/v19i10737
Ahmed Yakubu, B. Abubakari, Francis Kwaku Assan
Motivated by the p-analogue of the exponential integral function [1], we introduce a two-parameter generalization of the Incomplete Exponential Integral function. By using the classical H¨older’s and Young’s inequalities, among other analytical techniques, we establish some new inequalities involving the generalized function.
{"title":"Some Properties and Inequalities for a Two-Parameter Generalization of the Incomplete Exponential Integral Function","authors":"Ahmed Yakubu, B. Abubakari, Francis Kwaku Assan","doi":"10.9734/arjom/2023/v19i10737","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i10737","url":null,"abstract":"Motivated by the p-analogue of the exponential integral function [1], we introduce a two-parameter generalization of the Incomplete Exponential Integral function. By using the classical H¨older’s and Young’s inequalities, among other analytical techniques, we establish some new inequalities involving the generalized function.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122682810","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 : 2023-08-29DOI: 10.9734/arjom/2023/v19i10736
T. C. Mujeeburahman, R. J. Hussain, S. Broumi
In this paper, Some bounds, theorems and results on whole edge domination number in bipolar fuzzy graph are established with support of some examples. The concepts of perfect, complete perfect and semi-perfect whole edge domination in bipolar fuzzy graph are discussed and investigated with some of their properties and also results on perfect contributed via the support of some examples.
{"title":"Some Characterizations of Whole Edge Domination in Bipolar Fuzzy Graphs","authors":"T. C. Mujeeburahman, R. J. Hussain, S. Broumi","doi":"10.9734/arjom/2023/v19i10736","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i10736","url":null,"abstract":"In this paper, Some bounds, theorems and results on whole edge domination number in bipolar fuzzy graph are established with support of some examples. The concepts of perfect, complete perfect and semi-perfect whole edge domination in bipolar fuzzy graph are discussed and investigated with some of their properties and also results on perfect contributed via the support of some examples.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"207 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133586763","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 : 2023-08-28DOI: 10.9734/arjom/2023/v19i10735
M. Madukaife
In this paper, a new estimator of the Shannon entropy of a random variable X having a probability density function (mathit{f})((mathit{x})) is obtained based on window size spacings. Under the standard normal, standard exponential and uniform distributions, the estimator is shown to have relative low bias and low RMSE through extensive simulation study at sample sizes 10, 20, and 30. Based on the results, it is recommended as a good estimator of the entropy. Also, the new estimator is applied in goodness-of-fit test to normality. The statistic is affine invariant and consistent and the results show that it is a good statistic for assessing univariate normality of datasets.
{"title":"A New Estimator of Shannon Entropy with Application to Goodness-of-Fit Test to Normal Distribution","authors":"M. Madukaife","doi":"10.9734/arjom/2023/v19i10735","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i10735","url":null,"abstract":"In this paper, a new estimator of the Shannon entropy of a random variable X having a probability density function (mathit{f})((mathit{x})) is obtained based on window size spacings. Under the standard normal, standard exponential and uniform distributions, the estimator is shown to have relative low bias and low RMSE through extensive simulation study at sample sizes 10, 20, and 30. Based on the results, it is recommended as a good estimator of the entropy. Also, the new estimator is applied in goodness-of-fit test to normality. The statistic is affine invariant and consistent and the results show that it is a good statistic for assessing univariate normality of datasets.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"2135 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127469529","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 : 2023-08-28DOI: 10.9734/arjom/2023/v19i10734
I. Demiri, Bilall I. Shaini, S. Rexhepi, E. Iseni
In this paper will be presented some new properties in form of the inequalities related to gamma function, product of two gamma functions and some of them will be presented in the form of infinite series and limit where are included the Euler number and the Euler-Mascheroni constant.
{"title":"On Some New Properties for the Gamma Functions","authors":"I. Demiri, Bilall I. Shaini, S. Rexhepi, E. Iseni","doi":"10.9734/arjom/2023/v19i10734","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i10734","url":null,"abstract":"In this paper will be presented some new properties in form of the inequalities related to gamma function, product of two gamma functions and some of them will be presented in the form of infinite series and limit where are included the Euler number and the Euler-Mascheroni constant.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124681655","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 : 2023-08-26DOI: 10.9734/arjom/2023/v19i10733
M. Ibrahim, S. Isah
In this paper, we investigated anti-excedance statistics in (Gamma)1-non deranged permutations, the permutation which fixes the first element in the permutations. This was accomplished by employing prime integers p (ge) 5 in various calculations using this approach. The anti-excedance on (Gamma)1- non deranged permutations is redefined in this study. The recursive formula for the anti-excedance number and excedance number is generated, we also show that anti-excedance tops sum for any (omega)(mathit{i})-1 (in)Gp(Gamma)1 is equal to the excedance tops sum of (omega)(mathit{i}) (in)Gp(Gamma)1 . Similarly, we observed those anti-excedance bottoms sum for any (omega)(mathit{i})-1 (in)Gp(Gamma)1 is equal to the excedance bottoms sum of (omega)(mathit{i}) (in)Gp(Gamma)1 other properties were also observed.
本文研究了(Gamma) 1-非错乱排列的反超越统计量，这种排列固定了排列中的第一个元素。这是通过在使用这种方法的各种计算中使用素数p (ge) 5来实现的。本文重新定义了(Gamma) 1-非错乱排列的反超越。得到了反超越数和超越数的递推公式，并证明了任意(omega)(mathit{i}) -1 (in) Gp (Gamma) 1的反超越顶和等于(omega)(mathit{i})(in) Gp (Gamma) 1的超越顶和。同样，我们观察到任何(omega)(mathit{i}) -1 (in) Gp (Gamma) 1的反超越底和等于(omega)(mathit{i})(in) Gp (Gamma) 1的超越底和，其他性质也被观察到。
{"title":"Connections between Anti-Excedance and Excedance on the (Gamma)1-non Deranged Permutations","authors":"M. Ibrahim, S. Isah","doi":"10.9734/arjom/2023/v19i10733","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i10733","url":null,"abstract":"In this paper, we investigated anti-excedance statistics in (Gamma)1-non deranged permutations, the permutation which fixes the first element in the permutations. This was accomplished by employing prime integers p (ge) 5 in various calculations using this approach. The anti-excedance on (Gamma)1- non deranged permutations is redefined in this study. The recursive formula for the anti-excedance number and excedance number is generated, we also show that anti-excedance tops sum for any (omega)(mathit{i})-1 (in)Gp(Gamma)1 is equal to the excedance tops sum of (omega)(mathit{i}) (in)Gp(Gamma)1 . Similarly, we observed those anti-excedance bottoms sum for any (omega)(mathit{i})-1 (in)Gp(Gamma)1 is equal to the excedance bottoms sum of (omega)(mathit{i}) (in)Gp(Gamma)1 other properties were also observed.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116644281","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 : 2023-08-24DOI: 10.9734/arjom/2023/v19i10732
V. H. Narendra, P. Mahalakshmi
Topological indices are mathematical techniques used to mathematically correlate the relationship betweenthe chemical structure and various physical attributes, chemical reactivity, or biological activity. In thisresearch studies, the interaction of various chemical compounds(alkanes), their structures, and the eccentricityof the VL-Index., using the First and Second Zagreb, and reformulated First Zagreb indices, we investigatethe (xi)VL index may be considered as an useful tool in predicting the physical properties of lower alkanes.
{"title":"A Theoretical Study on Correlation Analysis Between Eccentricity of VL-index and the Physical Properties of Alkanes","authors":"V. H. Narendra, P. Mahalakshmi","doi":"10.9734/arjom/2023/v19i10732","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i10732","url":null,"abstract":"Topological indices are mathematical techniques used to mathematically correlate the relationship betweenthe chemical structure and various physical attributes, chemical reactivity, or biological activity. In thisresearch studies, the interaction of various chemical compounds(alkanes), their structures, and the eccentricityof the VL-Index., using the First and Second Zagreb, and reformulated First Zagreb indices, we investigatethe (xi)VL index may be considered as an useful tool in predicting the physical properties of lower alkanes.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127506295","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 : 2023-08-24DOI: 10.9734/arjom/2023/v19i10731
Mogoi N. Evans, Samuel B. Apima
In this research paper, we investigate the properties and characterizations of norm-attainable operators in the context of compactness and self-adjointness. We present a series of propositions, a lemma, a theorem, and a corollary that shed light on the nature of these operators and provide insights into their behavior in various settings. Our results contribute to the understanding of norm-attainable operators and their implications in functional analysis.
{"title":"Properties and Characterizations of Norm-Attainable Operators in Compact and Self-Adjoint Settings","authors":"Mogoi N. Evans, Samuel B. Apima","doi":"10.9734/arjom/2023/v19i10731","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i10731","url":null,"abstract":"In this research paper, we investigate the properties and characterizations of norm-attainable operators in the context of compactness and self-adjointness. We present a series of propositions, a lemma, a theorem, and a corollary that shed light on the nature of these operators and provide insights into their behavior in various settings. Our results contribute to the understanding of norm-attainable operators and their implications in functional analysis.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129981296","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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