In this study, we consider an unbalanced fully rough interval transportation problem, where all the parameters and decision variables are represented by rough interval numbers. A method named as split and separation method has been proposed in the literature to find the optimal solution of balanced fully rough interval transportation problem. As per our knowledge, no method exists in the literature to solve an unbalanced fully rough interval transportation problem. Therefore, a new method is proposed in this study to solve such problem. Using proposed methodology, firstly the unbalanced problem is converted into a balanced one and then the optimal solution of the balanced problem is obtained. To show the applicability of the proposed methodology, a numerical example is solved. Finally, the study’s conclusions and future research directions are discussed.
{"title":"An approach for unbalanced fully rough interval transportation problem","authors":"S. SHİVANİ, Deepika RANİ, Ali EBRAHİMNRJAD","doi":"10.15672/hujms.980108","DOIUrl":"https://doi.org/10.15672/hujms.980108","url":null,"abstract":"In this study, we consider an unbalanced fully rough interval transportation problem, where all the parameters and decision variables are represented by rough interval numbers. A method named as split and separation method has been proposed in the literature to find the optimal solution of balanced fully rough interval transportation problem. As per our knowledge, no method exists in the literature to solve an unbalanced fully rough interval transportation problem. Therefore, a new method is proposed in this study to solve such problem. Using proposed methodology, firstly the unbalanced problem is converted into a balanced one and then the optimal solution of the balanced problem is obtained. To show the applicability of the proposed methodology, a numerical example is solved. Finally, the study’s conclusions and future research directions are discussed.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"87 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135765535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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 a new almost convergent sequence space by means of a matrix involving Catalan and Motzkin numbers. It is demonstrated that this novel sequence space and the space of all almost convergent sequences are linearly isomorphic and the beta- dual of this new space is deduced. In addition, by defining Catalan-Motzkin core of a complex-valued sequence, certain inclusion relations are derived for it.
{"title":"Certain topological properties for almost convergent Catalan-Motzkin sequence space","authors":"Muhammet Cihat DAĞLI","doi":"10.15672/hujms.1298097","DOIUrl":"https://doi.org/10.15672/hujms.1298097","url":null,"abstract":"The purpose of this paper is to introduce a new almost convergent sequence space by means of a matrix involving Catalan and Motzkin numbers. It is demonstrated that this novel sequence space and the space of all almost convergent sequences are linearly isomorphic and the beta- dual of this new space is deduced. In addition, by defining Catalan-Motzkin core of a complex-valued sequence, certain inclusion relations are derived for it.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136337019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give closed-form evaluation formulas for the real and imaginary parts of the series $sum_{m,n=1}^{infty}frac{e^{2pi ileft( mx-nyright) }} {m^{p}n^{r}left( mc+nright) ^{q}},$ $cinmathbb{N},$ in terms of certain zeta values.textbf{ }Particular choices of $x$ and $y$ lead evaluation formulas for some Tornheim type $sum_{m,n=1}^{infty}frac{1}{m^{p}% n^{r}left( mc+nright) ^{q}}$ and Euler type $sum_{m,n=1}^{infty}frac {1}{n^{p}left( mc+nright) ^{q}}$ double series and their alternating analogues.
{"title":"Evaluation formulas for Tornheim and Euler type double series","authors":"Emre ÇAY, Mümün CAN, Levent KARGIN","doi":"10.15672/hujms.1165578","DOIUrl":"https://doi.org/10.15672/hujms.1165578","url":null,"abstract":"We give closed-form evaluation formulas for the real and imaginary parts of the series $sum_{m,n=1}^{infty}frac{e^{2pi ileft( mx-nyright) }} {m^{p}n^{r}left( mc+nright) ^{q}},$ $cinmathbb{N},$ in terms of certain zeta values.textbf{ }Particular choices of $x$ and $y$ lead evaluation formulas for some Tornheim type $sum_{m,n=1}^{infty}frac{1}{m^{p}% n^{r}left( mc+nright) ^{q}}$ and Euler type $sum_{m,n=1}^{infty}frac {1}{n^{p}left( mc+nright) ^{q}}$ double series and their alternating analogues.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136337022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The estimation of parameters for a distribution function is a significant and prominent field within statistical inference. This particular problem holds great relevance in various domains, including industries, stock markets, image processing, and reliability studies. There are two recognized approaches to estimation: point estimation and interval estimation, also known as confidence intervals. In this study, our primary focus lies in the point estimation of parameters associated with an exponential dispersion distribution function. In this process, we consider one of the parameters as a random variable that requires estimation. To tackle this, we adopt a Bayesian inference approach utilizing a one-parameter dispersion distribution. We explore non-informative priors, such as uniform and Jeffrey’s priors, and provide evidence of the effectiveness of our method through simulation studies.
{"title":"Non-informative Bayesian estimation in dispersion models","authors":"Ibrahim SADOK, Mourad ZRİBİ, Afif MASMOUDİ","doi":"10.15672/hujms.1053432","DOIUrl":"https://doi.org/10.15672/hujms.1053432","url":null,"abstract":"The estimation of parameters for a distribution function is a significant and prominent field within statistical inference. This particular problem holds great relevance in various domains, including industries, stock markets, image processing, and reliability studies. There are two recognized approaches to estimation: point estimation and interval estimation, also known as confidence intervals. In this study, our primary focus lies in the point estimation of parameters associated with an exponential dispersion distribution function. In this process, we consider one of the parameters as a random variable that requires estimation. To tackle this, we adopt a Bayesian inference approach utilizing a one-parameter dispersion distribution. We explore non-informative priors, such as uniform and Jeffrey’s priors, and provide evidence of the effectiveness of our method through simulation studies.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"221 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135492925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present a new analogue of the Filbert and Lilbert matrices whose the indices have different asymmetric and nonlinear rules according to their row numbers. Explicit formulæ are derived for the LU-decompositions, their inverses and the inverse of main matrix as well as its determinant. To prove the claimed results we use backward induction method. The asymmetric variants of the Filbert and Lilbert matrices are obtained from our results for a particular q value.
{"title":"Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices","authors":"Didem ERSANLI, Emrah KILIÇ","doi":"10.15672/hujms.1264983","DOIUrl":"https://doi.org/10.15672/hujms.1264983","url":null,"abstract":"In this paper, we present a new analogue of the Filbert and Lilbert matrices whose the indices have different asymmetric and nonlinear rules according to their row numbers. Explicit formulæ are derived for the LU-decompositions, their inverses and the inverse of main matrix as well as its determinant. To prove the claimed results we use backward induction method. The asymmetric variants of the Filbert and Lilbert matrices are obtained from our results for a particular q value.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135398159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Işıl BAYDAR, Burcu ÜNGÖR, Sait HALİCİOGLU, Abdullah HARMANCI
In this paper we extend the concept of fusibility to the module theoretic setting by introducing fusible modules. Let $R$ be a ring with identity, $M$ a right $R$-module and $0neq min M$. Then $m$ is called {it fusible} if it can be expressed as the sum of a torsion element and a torsion-free element in $M$. The module $M$ is said to be {it fusible} if every non-zero element of $M$ is fusible. We investigate some properties of fusible modules. It is proved that the class fusible modules is situated between the classes of torsion-free modules and nonsingular modules.
本文通过引入易熔模块，将易熔性的概念扩展到模块理论的设定中。设$R$是一个带单位元的环，$M$是一个右$R$-模，$0neq M 在M$中。如果$m$可以表示为$m$中的一个扭转单元和一个无扭转单元的和，则$m$称为{it fusible}。如果模块$M$的每个非零元素都是可熔的，则称模块$M$是可熔的。研究了易熔模块的一些性质。证明了可熔模类介于无扭模类和非奇异模类之间。
{"title":"Fusible Modules","authors":"Işıl BAYDAR, Burcu ÜNGÖR, Sait HALİCİOGLU, Abdullah HARMANCI","doi":"10.15672/hujms.1206395","DOIUrl":"https://doi.org/10.15672/hujms.1206395","url":null,"abstract":"In this paper we extend the concept of fusibility to the module theoretic setting by introducing fusible modules. Let $R$ be a ring with identity, $M$ a right $R$-module and $0neq min M$. Then $m$ is called {it fusible} if it can be expressed as the sum of a torsion element and a torsion-free element in $M$. The module $M$ is said to be {it fusible} if every non-zero element of $M$ is fusible. We investigate some properties of fusible modules. It is proved that the class fusible modules is situated between the classes of torsion-free modules and nonsingular modules.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134919324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A ring $R$ is called a left Ikeda-Nakayama ring (left IN-ring) if the right annihilator of the intersection of any two left ideals is the sum of the two right annihilators. As a generalization of left IN-rings, a ring $R$ is called a right SA-ring if the sum of right annihilators of two ideals is a right annihilator of an ideal of $R$. It is natural to ask if IN and SA property can be extended from $R$ to $R[x; alpha, delta]$. In this note, the results concerning the conditions will allow these properties to transfer from $R$ to skew polynomials $R[x;alpha,delta]$ are obtained. In addition, for an $(alpha,delta)$-compatible ring $R$, it is shown that: (i) If $S = R[x;alpha,delta]$ is a left IN-ring with ${rm{Idm}}(R) ={rm{Idm}}(R[x;alpha, delta])$, then $R$ is left McCoy. (ii) Every reduced left IN-ring with finitely many minimal prime ideals is a semiprime left Goldie ring. (iii) Every commutative principal ideal ring (PIR) $R$, is an IN-ring and so is $R[x]$. (iv) If $R$ be a reduced ring and $n$ a positive integer, then $R$ is right SA if and only if $R[x]/(x^{n+1})$ is right SA.
{"title":"ON SUM ANNIHILATOR IDEALS IN ORE EXTENSIONS","authors":"M. Paykani̇an, E. Hashemi, A. Alhevaz","doi":"10.15672/hujms.1037521","DOIUrl":"https://doi.org/10.15672/hujms.1037521","url":null,"abstract":"A ring $R$ is called a left Ikeda-Nakayama ring (left IN-ring) if the right annihilator of\u0000 the intersection of any two left ideals is the sum of the two right annihilators.\u0000 As a generalization of left IN-rings, a ring $R$ is called a right SA-ring if the sum of\u0000 right annihilators of two ideals is a right annihilator of an ideal of $R$.\u0000 It is natural to ask if IN and SA property can be extended from $R$ to\u0000 $R[x; alpha, delta]$.\u0000 In this note, the results concerning the conditions will allow these properties\u0000to transfer from $R$ to skew polynomials $R[x;alpha,delta]$ are obtained.\u0000 In addition, for an $(alpha,delta)$-compatible ring $R$, it is shown that:\u0000 (i) If $S = R[x;alpha,delta]$ is a left IN-ring with ${rm{Idm}}(R) ={rm{Idm}}(R[x;alpha, delta])$, then $R$ is left McCoy.\u0000 (ii) Every reduced left IN-ring with finitely many minimal\u0000prime ideals is a semiprime left Goldie ring.\u0000 (iii) Every commutative principal ideal ring (PIR) $R$, is an IN-ring and so is $R[x]$.\u0000 (iv) If $R$ be a reduced ring and $n$ a positive integer, then $R$ is right\u0000SA if and only if $R[x]/(x^{n+1})$ is right SA.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"42 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88081591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this introductory review, we study Hankel and Toeplitz opera- tors considering them as acting on certain spaces of analytic functions, namely Hardy spaces and compare their spectral properties such as their compactness criteria. In contrast to Toeplitz operators, the symbol of a Hankel operator is not uniquely determined by the operator. We also connect Toeplitz operators with Fredholm operators and give some of the most beautiful properties of Toeplitz operators such as the essential spectrum of Toeplitz operator with continuous symbol and the index of Toeplitz operator introducing Fredholm operators firstly.
{"title":"A COMPARATIVE STUDY FOR THE SPECTRAL PROPERTIES OF TOEPLITZ AND HANKEL OPERATORS","authors":"Ayşe Güven Sarıhan","doi":"10.15672/hujms.1241656","DOIUrl":"https://doi.org/10.15672/hujms.1241656","url":null,"abstract":"In this introductory review, we study Hankel and Toeplitz opera-\u0000tors considering them as acting on certain spaces of analytic functions, namely\u0000Hardy spaces and compare their spectral properties such as their compactness\u0000criteria. In contrast to Toeplitz operators, the symbol of a Hankel operator is\u0000not uniquely determined by the operator. We also connect Toeplitz operators\u0000with Fredholm operators and give some of the most beautiful properties of\u0000Toeplitz operators such as the essential spectrum of Toeplitz operator with\u0000continuous symbol and the index of Toeplitz operator introducing Fredholm\u0000operators firstly.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"91 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85540073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
U. Shahzad, I. Ahmad, I. Almanjahie, Nadia H. AL – NOOR, M. Hanif
In nonparametric regression research, estimation of regression function is a prime concern. Recently, researchers developed some modified Nadaraya-Watson (N-W) regression estimators utilizing robust mean, median and harmonic mean. In this paper, we propose to utilize the additive combination of non-traditional measures i.e. (Hodges-Lehmann, Mid-Range, Tri-Mean, Quartile-Deviation) with the robust minimum covariance determinant (MCD) scale estimator in (N-W) regression estimator. Utilizing these measures, we get some new versions of (N-W) regression estimator. We also attempted to derive the properties of the proposed versions, such as bias, variance, mean square error (MSE), and mean integrated square error (MISE). The proposed estimators are compared with some of the existing estimators available in literature through a simulation study, utilizing two artificial populations. We also incorporated real-life application by taking British food data set denoted as Engel95, and assess the predictive ability of nonparametric regression, based on proposed and existing N-W estimators.
{"title":"Adaptive Nadaraya-Watson kernel regression estimators utilizing some non-traditional and robust measures: a numerical application of British food data","authors":"U. Shahzad, I. Ahmad, I. Almanjahie, Nadia H. AL – NOOR, M. Hanif","doi":"10.15672/hujms.1167617","DOIUrl":"https://doi.org/10.15672/hujms.1167617","url":null,"abstract":"In nonparametric regression research, estimation of regression function is a prime concern. Recently, researchers developed some modified Nadaraya-Watson (N-W) regression estimators utilizing robust mean, median and harmonic mean. In this paper, we propose to utilize the additive combination of non-traditional measures i.e. (Hodges-Lehmann, Mid-Range, Tri-Mean, Quartile-Deviation) with the robust minimum covariance determinant (MCD) scale estimator in (N-W) regression estimator. Utilizing these measures, we get some new versions of (N-W) regression estimator. We also attempted to derive the properties of the proposed versions, such as bias, variance, mean square error (MSE), and mean integrated square error (MISE). The proposed estimators are compared with some of the existing estimators available in literature through a simulation study, utilizing two artificial populations. We also incorporated real-life application by taking British food data set denoted as Engel95, and assess the predictive ability of nonparametric regression, based on proposed and existing N-W estimators.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75126015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we aim to construct $n$ dimensional Jensen, Hardy and Hermite-Hadamard type inequalities for multiple diamond-alpha integral on time scales. The cases of Hardy type inequality with a weighted function and Hermite-Hadamard type inequality of three variables are also considered minutely.
{"title":"On Hardy and Hermite-Hadamard inequalities for N-tuple diamond-alpha integral","authors":"Zhongjian Mao, Wen-bin Zhang, Jing-feng Ti̇an","doi":"10.15672/hujms.1191725","DOIUrl":"https://doi.org/10.15672/hujms.1191725","url":null,"abstract":"In this paper, we aim to construct $n$ dimensional Jensen, Hardy and Hermite-Hadamard type inequalities for multiple diamond-alpha integral on time scales. The cases of Hardy type inequality with a weighted function and Hermite-Hadamard type inequality of three variables are also considered minutely.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"14 9 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139357068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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：