In this paper, we introduce screen generic lightlike submanifolds of semi-Riemannian product manifolds. We investigate the integrability of various distributions and geometry of such lightlike submanifolds. Finally, we find a condition for minimal screen generic lightlike submanifolds. We also give examples.
{"title":"Screen generic lightlike submanifolds of semi-Riemannian product manifolds","authors":"N. Poyraz","doi":"10.15672/hujms.1168604","DOIUrl":"https://doi.org/10.15672/hujms.1168604","url":null,"abstract":"In this paper, we introduce screen generic lightlike submanifolds of semi-Riemannian product manifolds. We investigate the integrability of various distributions and geometry of such lightlike submanifolds. Finally, we find a condition for minimal screen generic lightlike submanifolds. We also give examples.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"74 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74802059","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, there has been a considerable effort to obtain new solutions to the Rhoades' open problem on the existence of contractive mappings that admit discontinuity at the fixed point. An extended version of this problem is also stated using a geometric approach. In this paper, we obtain new solutions to this extended version of the Rhoades' open problem. A related problem, the fixed-circle problem (resp. fixed-disc problem) is also studied. Both of these problems are related to the geometric properties of the fixed point set of a self-mapping on a metric space. Furthermore, a new result about metric completeness and a short discussion on the activation functions used in the study of neural networks are given. By providing necessary examples, we show that our obtained results are effective.
{"title":"On the Geometry of Fixed Points and Discontinuity","authors":"R. Pant, N. Özgür, Bharti Joshi, M. Ram","doi":"10.15672/hujms.1149843","DOIUrl":"https://doi.org/10.15672/hujms.1149843","url":null,"abstract":"Recently, there has been a considerable effort to obtain new solutions to the Rhoades' open problem on the existence of contractive mappings that\u0000admit discontinuity at the fixed point. An extended version of this problem is also stated using a geometric approach. In this paper, we obtain new\u0000solutions to this extended version of the Rhoades' open problem. A related problem, the fixed-circle problem (resp. fixed-disc problem) is also\u0000studied. Both of these problems are related to the geometric properties of the fixed point set of a self-mapping on a metric space. Furthermore, a new\u0000result about metric completeness and a short discussion on the activation functions used in the study of neural networks are given. By providing\u0000necessary examples, we show that our obtained results are effective.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"21 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82772414","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 multiple regression, different techniques are available to deal with the situation where the predictors are large in number, and multicollinearity exists among them. Some of these approaches rely on correlation and others depend on principal components. To cope with the influential observations (outliers, leverage, or both) in the data matrix for regression purposes, two techniques are proposed in this paper. These are Robust Correlation Based Regression (RCBR) and Robust Correlation Scaled Principal Component Regression (RCSPCR). These proposed methods are compared with the existing methods, i.e., traditional Principal Component Regression (PCR), Correlation Scaled Principal Component Regression (CSPCR), and Correlation Based Regression (CBR). Also, Macro (Missingness and cellwise and row-wise outliers) RCSPCR is proposed to cope with the problem of multicollinearity, the high dimensionality of the dataset, outliers, and missing observations simultaneously. The proposed techniques are assessed by considering several simulated scenarios with appropriate levels of contamination. The results indicate that the suggested techniques seem to be more reliable for analyzing the data with missingness and outlyingness. Additionally, real-life data applications are also used to illustrate the performance of the proposed methods.
{"title":"Robust correlation scaled principal component regression","authors":"Aiman Tahi̇r, Dr. Maryam Ilyas","doi":"10.15672/hujms.1122113","DOIUrl":"https://doi.org/10.15672/hujms.1122113","url":null,"abstract":"In multiple regression, different techniques are available to deal with the situation where the predictors are large in number, and multicollinearity exists among them. Some of these approaches rely on correlation and others depend on principal components. To cope with the influential observations (outliers, leverage, or both) in the data matrix for regression purposes, two techniques are proposed in this paper. These are Robust Correlation Based Regression (RCBR) and Robust Correlation Scaled Principal Component Regression (RCSPCR). These proposed methods are compared with the existing methods, i.e., traditional Principal Component Regression (PCR), Correlation Scaled Principal Component Regression (CSPCR), and Correlation Based Regression (CBR). Also, Macro (Missingness and cellwise and row-wise outliers) RCSPCR is proposed to cope with the problem of multicollinearity, the high dimensionality of the dataset, outliers, and missing observations simultaneously. The proposed techniques are assessed by considering several simulated scenarios with appropriate levels of contamination. The results indicate that the suggested techniques seem to be more reliable for analyzing the data with missingness and outlyingness. Additionally, real-life data applications are also used to illustrate the performance of the proposed methods.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"17 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75615873","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 recent years, the intrinsic metrics have been formulated on the classical fractals. In particular, Sierpinski-like triangles such as equilateral, isosceles, scalene, added and mod-3 Sierpinski triangle have been considered in many different studies. The intrinsic metrics can be defined in different ways. One of the methods applied to obtain the intrinsic metric formulas is to use the code representations of the points on these self-similar sets. To define the intrinsic metrics via the code representations of the points on fractals make also possible to investigate different geometrical, topological properties and geodesics of these sets. In this paper, we investigate some circles and closed sets of the added Sierpinski triangle and express them as the code sets by using its intrinsic metric.
{"title":"On the computation of some code sets of the added Sierpinski triangle","authors":"Aslıhan İklim Şen, M. Saltan","doi":"10.15672/hujms.1194872","DOIUrl":"https://doi.org/10.15672/hujms.1194872","url":null,"abstract":"In recent years, the intrinsic metrics have been formulated on the classical fractals. In particular, Sierpinski-like triangles such as equilateral, isosceles, scalene, added and mod-3 Sierpinski triangle have been considered in many different studies. The intrinsic metrics can be defined in different ways. One of the methods applied to obtain the intrinsic metric formulas is to use the code representations of the points on these self-similar sets. To define the intrinsic metrics via the code representations of the points on fractals make also possible to investigate different geometrical, topological properties and geodesics of these sets. In this paper, we investigate some circles and closed sets of the added Sierpinski triangle and express them as the code sets by using its intrinsic metric.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"35 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76605669","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 extend the method of canonical form for congruence of bilinear forms to give the classification of some subclasses of 7-dimensional nilpotent Leibniz algebras. Odd-nilpotent Leibniz algebras are defined as that its even dimensional ideals in lower central series are all zero and the classification of 7-dimensional complex odd-nilpotent Leibniz algebras with one dimensional Leib ideal is obtained by applying the aforementioned method.
{"title":"On classification of 7-dimensional odd-nilpotent Leibniz algebras","authors":"İsmail Demi̇r","doi":"10.15672/hujms.1185538","DOIUrl":"https://doi.org/10.15672/hujms.1185538","url":null,"abstract":"In this paper we extend the method of canonical form for congruence of bilinear forms to give the classification of some subclasses of 7-dimensional nilpotent Leibniz algebras. Odd-nilpotent Leibniz algebras are defined as that its even dimensional ideals in lower central series are all zero and the classification of 7-dimensional complex odd-nilpotent Leibniz algebras with one dimensional Leib ideal is obtained by applying the aforementioned method.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"9 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74777763","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-statistics represent a fundamental class of statistics from modeling quantities of interest defined by multi-subject responses. U-statistics generalise the empirical mean of a random variable X to sums over every m-tuple of distinct observations of X. Stute [Conditional U -statistics, Ann. Probab., 1991] introduced a class of estimators called conditional U-statistics. In the present work, we provide a new class of estimators of conditional U-statistics. More precisely, we investigate the conditional U-statistics based on copula representation. We establish the uniform-in-bandwidth consistency for the proposed estimator. In addition, uniform consistency is also established over φ ∈ Ƒ for a suitably restricted class Ƒ, in both cases bounded and unbounded, satisfying some moment conditions. Our theorems allow data-driven local bandwidths for these statistics. Moreover, in the same context, we show the uniform bandwidth consistency for the nonparametric Inverse Probability of Censoring Weighted estimators of the regression function under random censorship, which is of its own interest. We also consider the weak convergence of the conditional U-statistics processes. We discuss the wild bootstrap of the conditional U-statistics processes. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis class of functions and some mild conditions on the model.
{"title":"On the weak convergence and the uniform-in-bandwidth consistency of the general conditional U -processes based on the copula representation: multivariate setting","authors":"S. Bouzebda","doi":"10.15672/hujms.1134334","DOIUrl":"https://doi.org/10.15672/hujms.1134334","url":null,"abstract":"U-statistics represent a fundamental class of statistics from modeling quantities of interest\u0000defined by multi-subject responses. U-statistics generalise the empirical mean of a random\u0000variable X to sums over every m-tuple of distinct observations of X. Stute [Conditional U -statistics, Ann. Probab., 1991] introduced a class of estimators called conditional U-statistics. In the present work, we provide a new class of estimators of conditional U-statistics. More precisely, we investigate the conditional U-statistics based on copula representation. We establish the uniform-in-bandwidth consistency for the proposed estimator. In addition, uniform consistency is also established over φ ∈ Ƒ for a suitably restricted class Ƒ, in both cases bounded and unbounded, satisfying some moment conditions. Our theorems allow data-driven local bandwidths for these statistics. Moreover, in the same context, we show the uniform bandwidth consistency for the nonparametric Inverse Probability of Censoring Weighted estimators of the regression function under random censorship, which is of its own interest. We also consider the weak convergence of the conditional U-statistics processes. We discuss the wild bootstrap of the conditional U-statistics processes. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis class of functions and some mild conditions on the model.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"97 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85894626","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}
This article studies H∞ control problem based on the event–triggered scheme with time delays for the synchronization of an chaotic system represented by delayed Takagi–Sugeno models. Firstly, this method depending on two scenarios: a) Each local subsystem in- tegrated that the delayed T–S fuzzy model for the same value of input matrices for the networked system and b) This is near steady-state zero-error diversification has to all be the same local subsystems. Generally, in the case of fuzzy regulation, these in lieu of generating the fuzzy regulator as a result of linear local controllers, circumstances were adjusted by addressing the issue of fuzzy regulation for the delayed Takagi–Sugeno models fuzzy model. Then, a delayed Takagi–Sugeno uses a fuzzy system to model the non–linear regulator. On the other hand, communication delays are a vital factor that cannot be ig- nored. To tackle the networked induced delay initially, author attempt to implement the event–triggered scheme for output regulation which reduce the cost of network transmis- sion. By constructing a Lyapunov functional and making use of event–triggered method, some suitable circumstances that ensure asymptotic stability of H∞ performance index for the resulting model were derived. Additionally, as the variations of the aforementioned results, two scenarios were presented. Our developed approaches are demonstrated by a final example illustrating their superiority, usefulness and reliability.
{"title":"Output regulation for time–delayed Takagi–Sugeno fuzzy model with networked control system","authors":"M. S. Aslam, Zhenhua Ma","doi":"10.15672/hujms.1017898","DOIUrl":"https://doi.org/10.15672/hujms.1017898","url":null,"abstract":"This article studies H∞ control problem based on the event–triggered scheme with time delays for the synchronization of an chaotic system represented by delayed Takagi–Sugeno models. Firstly, this method depending on two scenarios: a) Each local subsystem in- tegrated that the delayed T–S fuzzy model for the same value of input matrices for the networked system and b) This is near steady-state zero-error diversification has to all be the same local subsystems. Generally, in the case of fuzzy regulation, these in lieu of generating the fuzzy regulator as a result of linear local controllers, circumstances were adjusted by addressing the issue of fuzzy regulation for the delayed Takagi–Sugeno models fuzzy model. Then, a delayed Takagi–Sugeno uses a fuzzy system to model the non–linear regulator. On the other hand, communication delays are a vital factor that cannot be ig- nored. To tackle the networked induced delay initially, author attempt to implement the event–triggered scheme for output regulation which reduce the cost of network transmis- sion. By constructing a Lyapunov functional and making use of event–triggered method, some suitable circumstances that ensure asymptotic stability of H∞ performance index for the resulting model were derived. Additionally, as the variations of the aforementioned results, two scenarios were presented. Our developed approaches are demonstrated by a final example illustrating their superiority, usefulness and reliability.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"700 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76890731","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}
By making use of known identities of terminating well-poised $q$-series, we shall demonstrate several remarkable summation formulae involving products of two Fibonomial/Lucanomial coefficients or quotients of two such coefficients over a third one.
{"title":"Fibonomial and Lucanomial sums through well-poised $q$-series","authors":"W. Chu, E. Kılıç","doi":"10.15672/hujms.1066540","DOIUrl":"https://doi.org/10.15672/hujms.1066540","url":null,"abstract":"By making use of known identities of terminating well-poised $q$-series,\u0000we shall demonstrate several remarkable summation formulae involving\u0000products of two Fibonomial/Lucanomial coefficients or quotients\u0000of two such coefficients over a third one.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"15 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73227925","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}
Bükre Yıldırım Külekci, Uğur Karabey, Sevtap SELCUK-KESTEL
Several extreme events in history have shown that the low probability and high impact extreme values may result in catastrophic losses. In this paper, we propose the use of extreme value theory with a time-varying framework to model the bivariate dependent insurance occurrences and provide more reliable risk measures, such as value at risk and expected shortfall. In this paper three models are considered; time series for the underlying volatility of the data, extreme value theory for the tail estimation, and copula to model the dependence structure are combined. The performance of the proposed generalized Pareto-GARCH-Copula model is tested using the violation numbers and backtesting methods. We then aim to assess the combined model in terms of its effectiveness in reducing the ruin probability. Results show that, compared to well-known traditional methods, which may underestimate the extreme risks, the dynamic generalized Pareto-GARCH-Copula model captures better the real-life data's behavior and results in lower ruin probabilities for heavy-tailed and non-conventional dependent insurance data.
{"title":"Assessment of dependent risk using extreme value theory in a time-varying framework","authors":"Bükre Yıldırım Külekci, Uğur Karabey, Sevtap SELCUK-KESTEL","doi":"10.15672/hujms.992699","DOIUrl":"https://doi.org/10.15672/hujms.992699","url":null,"abstract":"Several extreme events in history have shown that the low probability and high impact extreme values may result in catastrophic losses. In this paper, we propose the use of extreme value theory with a time-varying framework to model the bivariate dependent insurance occurrences and provide more reliable risk measures, such as value at risk and expected shortfall. In this paper three models are considered; time series for the underlying volatility of the data, extreme value theory for the tail estimation, and copula to model the dependence structure are combined. The performance of the proposed generalized Pareto-GARCH-Copula model is tested using the violation numbers and backtesting methods. We then aim to assess the combined model in terms of its effectiveness in reducing the ruin probability. Results show that, compared to well-known traditional methods, which may underestimate the extreme risks, the dynamic generalized Pareto-GARCH-Copula model captures better the real-life data's behavior and results in lower ruin probabilities for heavy-tailed and non-conventional dependent insurance data.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"11 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87422260","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 propose a consistent test for testing the distribution of bivariate random samples. The probability of type I, type II errors and probability of making no decisions under null and alternative hypotheses are obtained based on copula functions. The consistency of the proposed test is discussed under some null and alternative hypotheses. An unbiased, consistent estimator is proposed for probability of making no decision. Moreover, a simulation study is performed for showing the consistency of the proposed test for some well-known copulas such as independent, Clayton, Gumbel, Frank and Farlie-Gumbel-Morgenstern.
{"title":"A consistent statistical test based on bivariate random samples","authors":"A. Erem, I. Bayramoglu","doi":"10.15672/hujms.1031959","DOIUrl":"https://doi.org/10.15672/hujms.1031959","url":null,"abstract":"We propose a consistent test for testing the distribution of bivariate random samples. The probability of type I, type II errors and probability of making no decisions under null and alternative hypotheses are obtained based on copula functions. The consistency of the proposed test is discussed under some null and alternative hypotheses. An unbiased, consistent estimator is proposed for probability of making no decision. Moreover, a simulation study is performed for showing the consistency of the proposed test for some well-known copulas such as independent, Clayton, Gumbel, Frank and Farlie-Gumbel-Morgenstern.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"2 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78827958","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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