T-convergence structures serve as an important tool to describe fuzzy topology and deserve more and more attention. This paper aims to give further investigations onT-convergence structures. Firstly, several types of $top$-convergence structures are introduced, including Kent T-convergence structures, T-limit structures and principal T-convergence structures, and their mutual categorical relationships as well as their own categorical properties are studied. Secondly, by changing of the underlying lattice, the ``change of base" approach is applied to T-convergence structures and the relationships between T-convergence structures with respect to different underlying lattices are demonstrated.
t收敛结构作为描述模糊拓扑的重要工具，越来越受到人们的重视。本文旨在对t收敛结构作进一步的研究。首先，介绍了几种$top$-收敛结构，包括Kent t -收敛结构、t -极限结构和主t -收敛结构，并研究了它们之间的相互范畴关系和各自的范畴性质。其次，通过改变底层晶格，将“基的改变”方法应用于t收敛结构，并证明了t收敛结构相对于不同底层晶格之间的关系。
{"title":"Subcategories of the category of T-convergence spaces","authors":"Yuan Gao, B. Pang","doi":"10.15672/hujms.1205089","DOIUrl":"https://doi.org/10.15672/hujms.1205089","url":null,"abstract":"T-convergence structures serve as an important tool to describe fuzzy topology and deserve more and more attention. This paper aims to give further investigations onT-convergence structures. Firstly, several types of $top$-convergence structures are introduced, including Kent T-convergence structures, T-limit structures and principal T-convergence structures, and their mutual categorical relationships as well as their own categorical properties are studied. Secondly, by changing of the underlying lattice, the ``change of base\" approach is applied to T-convergence structures and the relationships between T-convergence structures with respect to different underlying lattices are demonstrated.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"60 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90436944","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 introduce new expansion classes, namely weakly $ (k,n) $-absorbing hyperideals and weakly $ (k,n) $-absorbing primary hyperideals of a Krasner $ (m,n) $-hyperring, including $ (k,n) $-absorbing hyperideal and $ (k,n) $-absorbing primary hyperideal. Therefore, we give generalizations of $ (k,n) $-absorbing hyperideal and $ (k,n) $-absorbing primary hyperideal. Also, we examine the relations between classical hyperideals and the new hyperideals and explore some ways to connect them. Additionally, some main results and examples are given to explain the structures of these concepts. Finally, we study a version of Nakayama's lemma on a commutative Krasner $ (m,n) $-hyperring.
{"title":"weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring","authors":"B. Davvaz, G. Ulucak, Ünsal Tekir","doi":"10.15672/hujms.1199437","DOIUrl":"https://doi.org/10.15672/hujms.1199437","url":null,"abstract":"In this paper, we introduce new expansion classes, namely weakly $ (k,n) $-absorbing hyperideals and weakly $ (k,n) $-absorbing primary hyperideals of a Krasner $ (m,n) $-hyperring, including $ (k,n) $-absorbing hyperideal and $ (k,n) $-absorbing primary hyperideal. Therefore, we give generalizations of $ (k,n) $-absorbing hyperideal and $ (k,n) $-absorbing primary hyperideal. Also, we examine the relations between classical hyperideals and the new hyperideals and explore some ways to connect them. Additionally, some main results and examples are given to explain the structures of these concepts. Finally, we study a version of Nakayama's lemma on a commutative Krasner $ (m,n) $-hyperring.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"28 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87744898","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 analyze a parabolic-elliptic chemo-repulsion system, with superlinear production term in two-dimensional domains. Under the injection/extract chemical substance on a subdomain $omegasubsetOmega$, we prove the existence and uniqueness of global-in-time strong solutions at finite time.
{"title":"A parabolic-elliptic chemo-repulsion system in 2D domains with nonlinear production","authors":"Alex ANCOMA-HUARACHİ, E. Mallea-Zepeda","doi":"10.15672/hujms.1133453","DOIUrl":"https://doi.org/10.15672/hujms.1133453","url":null,"abstract":"In this paper we analyze a parabolic-elliptic chemo-repulsion system, with superlinear production term in two-dimensional domains. Under the injection/extract chemical substance on a subdomain $omegasubsetOmega$, we prove the existence and uniqueness of global-in-time strong solutions at finite time.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"61 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88039805","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 cause-specific hazard function plays an important role in developing the regression models for competing risks survival data. Proportional hazards and additive hazards are the commonly used regression approaches in survival analysis. Mostly, in literature, the proportional hazards model was used for parametric regression modelling of survival data. In this article, we introduce a parametric additive hazards regression model for survival analysis with competing risks. For employing a parametric model we consider the modified Weibull distribution as a baseline model which is capable to model survival data with non-monotonic behaviour of hazard rate. The estimation process is carried out via maximum likelihood and Bayesian approaches. In addition to Bayesian methods, a class of non-informative types of prior is introduced with squared error (symmetric) and linear-exponential (asymmetric) loss functions. The relative performance of the different estimators is assessed using Monte Carlo simulation. Finally, using the proposed methodology, a real data analysis is performed.
{"title":"Analysis and modelling of competing risks survival data using modified Weibull additive hazards regression approach","authors":"H. Rehman, N. Chandra, A. Abuzaid","doi":"10.15672/hujms.1066111","DOIUrl":"https://doi.org/10.15672/hujms.1066111","url":null,"abstract":"The cause-specific hazard function plays an important role in developing the regression models for competing risks survival data. Proportional hazards and additive hazards are the commonly used regression approaches in survival analysis. Mostly, in literature, the proportional hazards model was used for parametric regression modelling of survival data. In this article, we introduce a parametric additive hazards regression model for survival analysis with competing risks. For employing a parametric model we consider the modified Weibull distribution as a baseline model which is capable to model survival data with non-monotonic behaviour of hazard rate. The estimation process is carried out via maximum likelihood and Bayesian approaches. In addition to Bayesian methods, a class of non-informative types of prior is introduced with squared error (symmetric) and linear-exponential (asymmetric) loss functions. The relative performance of the different estimators is assessed using Monte Carlo simulation. Finally, using the proposed methodology, a real data analysis is performed.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"27 3 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80013511","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 examine the resulting dynamics when Newton's method is applied to perturbations of polynomials that have a multiple root. Specifically, we consider the case where Newton's method is applied to the polynomial family $(z^2 + c)(z-1)$.
{"title":"SINGULAR PERTURBATIONS ARISING IN COMPLEX NEWTON'S METHOD","authors":"Fi̇gen Çi̇li̇ngi̇r","doi":"10.15672/hujms.1132257","DOIUrl":"https://doi.org/10.15672/hujms.1132257","url":null,"abstract":"We examine the resulting dynamics when Newton's method is applied to perturbations of polynomials that have a multiple root. Specifically, we consider the case where Newton's method is applied to the polynomial family $(z^2 + c)(z-1)$.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79918575","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 generalize the Brown$^{^,}$s topology on the fundamental groupoids. For a locally path connected space $X$ and a totally disconnected normal subgroupoid $M$ of $pi X$, we define a topology on the quotient groupoid $dfrac{pi X}{M}$ which is a generalization of what introduced by Brown for locally path connected and semilocally simply connected spaces. We prove that $dfrac{pi X}{M}$ equipped with this topology is a topological groupoid. Also, we will find a class of subgroupoids of topological groupoids whose their related quotient groupoids will be topological groupoids. By using this, we show that our topology on $dfrac{pi X}{M}$ is equivalent to the quotient of the Lasso topology on the topological fundamental groupoids, $dfrac{pi^L X}{M}$ cite{PS}.
{"title":"Topological Fundamental Groupoids: Brown$^{^,}$s Topology","authors":"A. Pakdaman, Fereshteh Shahi̇ni̇","doi":"10.15672/hujms.1205441","DOIUrl":"https://doi.org/10.15672/hujms.1205441","url":null,"abstract":"In this paper, we generalize the Brown$^{^,}$s topology on the fundamental groupoids. For a locally path connected space $X$ and a totally disconnected normal subgroupoid $M$ of $pi X$, we define a topology on the quotient groupoid $dfrac{pi X}{M}$ which is a generalization of what introduced by Brown for locally path connected and semilocally simply connected spaces. We prove that $dfrac{pi X}{M}$ equipped with this topology is a topological groupoid. Also, we will find a class of subgroupoids of topological groupoids whose their related quotient groupoids will be topological groupoids. By using this, we show that our topology on $dfrac{pi X}{M}$ is equivalent to the quotient of the Lasso topology on the topological fundamental groupoids, $dfrac{pi^L X}{M}$ cite{PS}.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"22 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75574831","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}
Recently, the beta regression model has been used in several fields of science to model data in the form of rate or proportion. In this paper, we propose some novel and improved methods to estimate parameters in the beta regression model. We consider a sub-space on the regression coefficients of the beta regression model and combine the unrestricted and restricted estimators then we present Stein-type and preliminary estimators. We develop the expressions for the proposed estimators' asymptotic biases and their quadratic risks. Numerical studies through Monte Carlo simulations are used to evaluate the performance of the proposed estimators in terms of their simulated relative efficiency. The results show that the proposed estimators outperform the unrestricted estimator when the restrictions hold. Finally, an empirical application is provided to demonstrate the practical usefulness of the proposed estimators.
{"title":"James-Stein type estimators in beta regression model: simulation and application","authors":"S. Seifollahi, Hossein BEVRANİ","doi":"10.15672/hujms.1122207","DOIUrl":"https://doi.org/10.15672/hujms.1122207","url":null,"abstract":"Recently, the beta regression model has been used in several fields of science to model data in the form of rate or proportion. In this paper, we propose some novel and improved methods to estimate parameters in the beta regression model. We consider a sub-space on the regression coefficients of the beta regression model and combine the unrestricted and restricted estimators then we present Stein-type and preliminary estimators. We develop the expressions for the proposed estimators' asymptotic biases and their quadratic risks. Numerical studies through Monte Carlo simulations are used to evaluate the performance of the proposed estimators in terms of their simulated relative efficiency. The results show that the proposed estimators outperform the unrestricted estimator when the restrictions hold. Finally, an empirical application is provided to demonstrate the practical usefulness of the proposed estimators.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90199082","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 article, simultaneous identification of the timewise lowest and source terms in a two-dimensional (2D) parabolic equation from knowledge of additional measurements is studied. Existence and uniqueness of the solution is proved by means of the contraction mapping on a small time interval. Since the problem is yet ill- posed (very small errors in the time-average temperature input may cause large errors in the output source and potential functions), we need to regularize the solution. Hence, regularization is needed for the retrieval of unknown terms. The 2D equation is computationally solved using the ADE scheme and reshaped as non-linear optimization of the Tikhonov regularization function. This is numerically studied by means of the MATLAB $lsqnonlin$ subroutine. Finally, we present a numerical example to demonstrate the accuracy and efficiency of the proposed method. Our numerical results show that the ADE is an efficient and unconditionally stable scheme for reconstructing the potential and source coefficients from minimal data which makes the solution of the inverse problem (IP) unique.
{"title":"An inverse problem of identifying the time-dependent potential and source terms in a two-dimensional parabolic equation","authors":"M. J. Huntul, İbrahim Teki̇n","doi":"10.15672/hujms.1118138","DOIUrl":"https://doi.org/10.15672/hujms.1118138","url":null,"abstract":"In this article, simultaneous identification of the timewise lowest and source terms in a two-dimensional (2D) parabolic equation from knowledge of additional measurements is studied. Existence and uniqueness of the solution is proved by means of the contraction mapping on a small time interval. Since the problem is yet ill- posed (very small errors in the time-average temperature input may cause large errors in the output source and potential functions), we need to regularize the solution. Hence, regularization is needed for the retrieval of unknown terms. The 2D equation is computationally solved using the ADE scheme and reshaped as non-linear optimization of the Tikhonov regularization function. This is numerically studied by means of the MATLAB $lsqnonlin$ subroutine. Finally, we present a numerical example to demonstrate the accuracy and efficiency of the proposed method. Our numerical results show that the ADE is an efficient and unconditionally stable scheme for reconstructing the potential and source coefficients from minimal data which makes the solution of the inverse problem (IP) unique.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"5 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72644961","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}
Let $A=R_{+}times R$ be an affine group with right Haar measure $dmu$ and $Phi_i$, $i=1,2$, be Young functions. We show that there exists an isometric isomorphism between the multiplier of the pair $(L^{Phi_1}(A),L^{Phi_2}(A))$ and $(L^{Psi_2}(A),L^{Psi_1}(A))$ where $Psi_i$ are complementary pairs of $Phi_i$, $i=1,2$, respectively. Moreover we show that under some conditions there is no nonzero multiplier for the pair $(L^{Phi_1}(A),L^{Phi_2}(A))$, i.e., for an affine group $A$ only the spaces $M(L^{Phi_1}(A),L^{Phi_2}(A))$, with a concrete condition, are of any interest.
{"title":"A criterion for nonzero multipliers for Orlicz spaces of an affine group $R_{+}times R$","authors":"Rüya Üster","doi":"10.15672/hujms.1175682","DOIUrl":"https://doi.org/10.15672/hujms.1175682","url":null,"abstract":"Let $A=R_{+}times R$ be an affine group with right Haar measure $dmu$ and $Phi_i$, $i=1,2$, be Young functions. We show that there exists an isometric isomorphism between the multiplier of the pair $(L^{Phi_1}(A),L^{Phi_2}(A))$ and $(L^{Psi_2}(A),L^{Psi_1}(A))$ where $Psi_i$ are complementary pairs of $Phi_i$, $i=1,2$, respectively. Moreover we show that under some conditions there is no nonzero multiplier for the pair $(L^{Phi_1}(A),L^{Phi_2}(A))$, i.e., for an affine group $A$ only the spaces $M(L^{Phi_1}(A),L^{Phi_2}(A))$, with a concrete condition, are of any interest.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"11 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88692774","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}
Let $R$ be an associative ring. $R$ is called right CSP if the sum of any two closed right ideals of $R$ is also a closed right ideal of $R$. Left CSP rings can be defined similarly. It is shown that a matrix ring over a right CSP ring may not be right CSP. And $mathbb{M}_{2}(R)$ is right CSP if and only if $R$ is right self-injective and von Neumann regular. This informs that a left CSP ring may not be right CSP. At last, an equivalent characterization is given for the trivial extension $Rpropto R$ of $R$ to be right CSP.
设$R$是一个结合环。如果R$的任意两个封闭右理想的和也是R$的封闭右理想，则R$称为右CSP。左CSP环可以类似地定义。证明了右CSP环上的矩阵环可能不是右CSP环。并且$mathbb{M}_{2}(R)$是正确的CSP当且仅当$R$是正确的自内射和冯·诺伊曼正则。这说明左CSP环可能不是右CSP环。最后，给出了$R$的平凡扩展$R proto R$为右CSP的等价刻画。
{"title":"A note on CSP rings","authors":"Haitao Ma, L. Shen","doi":"10.15672/hujms.1213444","DOIUrl":"https://doi.org/10.15672/hujms.1213444","url":null,"abstract":"Let $R$ be an associative ring. $R$ is called right CSP if the sum of any two closed right ideals of $R$ is also a closed right ideal of $R$. Left CSP rings can be defined similarly. It is shown that a matrix ring over a right CSP ring may not be right CSP. And $mathbb{M}_{2}(R)$ is right CSP if and only if $R$ is right self-injective and von Neumann regular. This informs that a left CSP ring may not be right CSP. At last, an equivalent characterization is given for the trivial extension $Rpropto R$ of $R$ to be right CSP.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"516 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77108560","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}
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