This paper is concerned with the study of stability analysis to a complicated recovered fracturing fluid model (RFFM, for short), which consists of a stationary incompressible Stokes equation involving multivalued and nonmonotone boundary conditions, and a reaction-diffusion equation with Neumann boundary conditions. Firstly, we introduce a family of perturbated problems corresponding to (RFFM) and deliver the variational formulation of perturbated problem which is a hemivariational inequality coupled with a variational equation. Then, we prove that the existence of solutions to perturbated problems and the solution sequence to perturbated problems are uniformly bounded. Finally, via employing Mosco convergent approach and the theory of nonsmooth, a stability result to (RFFM) is established.
{"title":"Stability analysis for a recovered fracturing fluid model in the wellbore of shale gas reservoir","authors":"Jinxia Cen, Nicuşor Costea, Chao Min, J. Yao","doi":"10.15672/hujms.1193699","DOIUrl":"https://doi.org/10.15672/hujms.1193699","url":null,"abstract":"This paper is concerned with the study of stability analysis to a complicated recovered fracturing fluid model (RFFM, for short), which consists of a stationary incompressible Stokes equation involving multivalued and nonmonotone boundary conditions, and a reaction-diffusion equation with Neumann boundary conditions. Firstly, we introduce a family of perturbated problems corresponding to (RFFM) and deliver the variational formulation of perturbated problem which is a hemivariational inequality coupled with a variational equation. Then, we prove that the existence of solutions to perturbated problems and the solution sequence to perturbated problems are uniformly bounded. Finally, via employing Mosco convergent approach and the theory of nonsmooth, a stability result to (RFFM) is established.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"14 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82567582","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}
M. Baratnia, Abdolhamid REZAEİ ROKNABADY, M. Doostparast
The discrete Pareto distribution can be considered as a lifetime distribution and then is widely used in practice. It follows the power law tails property which makes it as a candidate model for natural phenomena. This paper deals with comparison of discrete Pareto populations by proposing a non-linear fixed effects model. Estimators for the factor effects are derived in explicit expressions. Stochastic properties of the estimators are studied in details. A test for assessing the homogeneity of populations is proposed. Illustrative examples are also given. The proposed model is an alternative model for analyzing data sets in which the linear models have poor performance.
{"title":"Comparing discrete Pareto populations under a fixed effects model","authors":"M. Baratnia, Abdolhamid REZAEİ ROKNABADY, M. Doostparast","doi":"10.15672/hujms.820849","DOIUrl":"https://doi.org/10.15672/hujms.820849","url":null,"abstract":"The discrete Pareto distribution can be considered as a lifetime distribution and then is widely used in practice. It follows the power law tails property which makes it as a candidate model for natural phenomena. This paper deals with comparison of discrete Pareto populations by proposing a non-linear fixed effects model. Estimators for the factor effects are derived in explicit expressions. Stochastic properties of the estimators are studied in details. A test for assessing the homogeneity of populations is proposed. Illustrative examples are also given. The proposed model is an alternative model for analyzing data sets in which the linear models have poor performance.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"17 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81785660","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}
Emel KIZILOK KARA, Sibel AÇIK KEMALOĞLU, O. Evkaya
The increase of the product variety in the financial markets requires a clear understanding of the dependence between such instruments for the decision-makers. For a few decades, such dependence structures were often modeled with symmetric copula families. However, financial data may reveal an asymmetric structure, which can be determined via directional dependence measures in the context of copulas. Previously, some asymmetric copula models were proposed in different ways using Khoudraji’s device. But they are merely used for financial time series data in a broader sense. In this study, a new set of asymmetric copulas were defined by using one parameter of Archimedean copula families. For this aim, widely used copula families were studied and the corresponding directional dependence measures were analyzed. To illustrate the efficiency of the parameter estimation method, a small simulation scenario consisting of an asymmetric dependence pattern was carried out. Thereafter, the proposed asymmetric bi-variate copulas with directional dependence coefficients were investigated for two different stock market data. The study’s primary findings suggested that the newly generated asymmetric models might be useful for directional dependence. Especially, the estimated directional dependence coefficients can serve as an indicator to explain the variability of one stock in terms of the other.
{"title":"Analysis of asymmetric financial data with directional dependence measures","authors":"Emel KIZILOK KARA, Sibel AÇIK KEMALOĞLU, O. Evkaya","doi":"10.15672/hujms.1141392","DOIUrl":"https://doi.org/10.15672/hujms.1141392","url":null,"abstract":"The increase of the product variety in the financial markets requires a clear understanding of the dependence between such instruments for the decision-makers. For a few decades, such dependence structures were often modeled with symmetric copula families. However, financial data may reveal an asymmetric structure, which can be determined via directional dependence measures in the context of copulas. Previously, some asymmetric copula models were proposed in different ways using Khoudraji’s device. But they are merely used for financial time series data in a broader sense. In this study, a new set of asymmetric copulas were defined by using one parameter of Archimedean copula families. For this aim, widely used copula families were studied and the corresponding directional dependence measures were analyzed. To illustrate the efficiency of the parameter estimation method, a small simulation scenario consisting of an asymmetric dependence pattern was carried out. Thereafter, the proposed asymmetric bi-variate copulas with directional dependence coefficients were investigated for two different stock market data. The study’s primary findings suggested that the newly generated asymmetric models might be useful for directional dependence. Especially, the estimated directional dependence coefficients can serve as an indicator to explain the variability of one stock in terms of the other.","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":"83713384","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 $mathcal P_n cong H^{*}big(BE_n; mathbb F_2 big)$ be the graded polynomial algebra over the prime field of two elements $mathbb F_2$, where $E_n$ is an elementary abelian 2-group of rank $n,$ and $BE_n$ is the classifying space of $E_n.$ We study the {it hit problem}, set up by Frank Peterson, of finding a minimal set of generators for the polynomial algebra $mathcal P_{n},$ viewed as a module over the mod-2 Steenrod algebra $mathcal{A}$. This problem remains unsolvable for $n>4,$ even with the aid of computers in the case of $n=5.$ By considering $mathbb F_2$ as a trivial $mathcal A$-module, then the hit problem is equivalent to the problem of finding a basis of $mathbb F_2$-graded vector space $mathbb F_2 {otimes}_{mathcal{A}}mathcal P_{n}.$ This paper aims to explicitly determine an admissible monomial basis of the $ mathbb{F}_{2}$-vector space $mathbb{F}_{2}{otimes}_{mathcal{A}}mathcal P_{n}$ in the generic degree $n(2^{r}-1)+2cdot 2^{r},$ where $r$ is an arbitrary non-negative integer, and in the case of $n=6.$ As an application of these results, we obtain the dimension results for the polynomial algebra $mathcal P_n$ in degrees $(n-1)cdot(2^{n+u-1}-1)+ellcdot2^{n+u},$ where $u$ is an arbitrary non-negative integer, $ell =13,$ and $n=7.$ Moreover, for any integer $r>1,$ the behavior of the sixth Singer algebraic transfer in degree $6(2^{r}-1)+2cdot2^r$ is also discussed at the end of this paper. Here, the Singer algebraic transfer is a homomorphism from the homology of the Steenrod algebra to the subspace of $mathbb{F}_{2}{otimes}_{mathcal{A}}mathcal P_{n}$ consisting of all the $GL_n(mathbb F_2)$-invariant classes. It is a useful tool in describing the homology groups of the Steenrod algebra, $text{Tor}^{mathcal A}_{n, n+*}(mathbb F_2,mathbb F_2).$
{"title":"On a minimal set of generators for the algebra $H^*(BE_6; mathbb F_2)$ as a module over the Steenrod algebra and applications","authors":"Nguyen Khac Tin","doi":"10.15672/hujms.1127140","DOIUrl":"https://doi.org/10.15672/hujms.1127140","url":null,"abstract":"Let $mathcal P_n cong H^{*}big(BE_n; mathbb F_2 big)$ be the graded polynomial algebra over the prime field of two elements $mathbb F_2$, where $E_n$ is an elementary abelian 2-group of rank $n,$ and $BE_n$ is the classifying space of $E_n.$ We study the {it hit problem}, set up by Frank Peterson, of finding a minimal set of generators for the polynomial algebra $mathcal P_{n},$ viewed as a module over the mod-2 Steenrod algebra $mathcal{A}$. This problem remains unsolvable for $n>4,$ even with the aid of computers in the case of $n=5.$ By considering $mathbb F_2$ as a trivial $mathcal A$-module, then the hit problem is equivalent to the problem of finding a basis of $mathbb F_2$-graded vector space $mathbb F_2 {otimes}_{mathcal{A}}mathcal P_{n}.$ This paper aims to explicitly determine an admissible monomial basis of the $ mathbb{F}_{2}$-vector space $mathbb{F}_{2}{otimes}_{mathcal{A}}mathcal P_{n}$ in the generic degree $n(2^{r}-1)+2cdot 2^{r},$ where $r$ is an arbitrary non-negative integer, and in the case of $n=6.$ As an application of these results, we obtain the dimension results for the polynomial algebra $mathcal P_n$ in degrees $(n-1)cdot(2^{n+u-1}-1)+ellcdot2^{n+u},$ where $u$ is an arbitrary non-negative integer, $ell =13,$ and $n=7.$ Moreover, for any integer $r>1,$ the behavior of the sixth Singer algebraic transfer in degree $6(2^{r}-1)+2cdot2^r$ is also discussed at the end of this paper. Here, the Singer algebraic transfer is a homomorphism from the homology of the Steenrod algebra to the subspace of $mathbb{F}_{2}{otimes}_{mathcal{A}}mathcal P_{n}$ consisting of all the $GL_n(mathbb F_2)$-invariant classes. It is a useful tool in describing the homology groups of the Steenrod algebra, $text{Tor}^{mathcal A}_{n, n+*}(mathbb F_2,mathbb F_2).$","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":"74223880","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 the present study, a mathematical model of non-steady partial differential equation from the process of oxygen mass transport in the human pulmonary circulation is proposed. Mathematical modelling of this kind of problems lead to a non-steady partial differential equation and for its numerical simulation, we have used finite differences. The aim of the process is the exact numerical analysis of the study, wherein consistency, stability and convergence is proposed. The necessity of doing the process is that, we would like to increase the order of numerical solution to a higher order scheme. An increment in the order of numerical solution makes the numerical simulation more accurate, also makes the numerical simulation being more complicated. In addition, the process of numerical analysis of the study in this order of solution needs more research work.
{"title":"Stability analysis and numerical simulation of non-steady partial differential model in the human pulmonary capillaries using finite differences technique","authors":"M. Derakhshan, Azim Ami̇ataei̇","doi":"10.15672/hujms.1095502","DOIUrl":"https://doi.org/10.15672/hujms.1095502","url":null,"abstract":"In the present study, a mathematical model of non-steady partial differential equation from the process of oxygen mass transport in the human pulmonary circulation is proposed. Mathematical modelling of this kind of problems lead to a non-steady partial differential equation and for its numerical simulation, we have used finite differences. The aim of the process is the exact numerical analysis of the study, wherein consistency, stability and convergence is proposed. The necessity of doing the process is that, we would like to increase the order of numerical solution to a higher order scheme. An increment in the order of numerical solution makes the numerical simulation more accurate, also makes the numerical simulation being more complicated. In addition, the process of numerical analysis of the study in this order of solution needs more research work.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"388 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84994942","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}
An important bias can occur when estimating coefficients by maximizing the known partial likelihood function in the Cox regression model with the measurement error covariate. We focus here on Bayesian methods in order to adjust measurement error and aim to propose an adjusting Bayesian method. Constructing simulation studies using Markov Chain Monte Carlo simulation techniques to investigate the performance of models. We compare the proposed method with the existing method that used partial likelihood function, Bayesian Cox regression model ignoring measurement error, the adjusted Bayesian Cox regression model that exists in the literature by a simulation study which consists of different sample sizes, censoring rates, reliability levels, and regression coefficients. Simulation studies indicate that the proposed method outperformed others given some scenarios. A real data set is analyzed for an illustration of the findings.
{"title":"A new adjusted Bayesian method in Cox regression model with covariate subject to measurement error","authors":"H. Isik, Duru Karasoy, Uğur Karabey","doi":"10.15672/hujms.1120196","DOIUrl":"https://doi.org/10.15672/hujms.1120196","url":null,"abstract":"An important bias can occur when estimating coefficients by maximizing the known partial likelihood function in the Cox regression model with the measurement error covariate. We focus here on Bayesian methods in order to adjust measurement error and aim to propose an adjusting Bayesian method. Constructing simulation studies using Markov Chain Monte Carlo simulation techniques to investigate the performance of models. We compare the proposed method with the existing method that used partial likelihood function, Bayesian Cox regression model ignoring measurement error, the adjusted Bayesian Cox regression model that exists in the literature by a simulation study which consists of different sample sizes, censoring rates, reliability levels, and regression coefficients. Simulation studies indicate that the proposed method outperformed others given some scenarios. A real data set is analyzed for an illustration of the findings.","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":"90123323","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 Beta Regression Model (BRM) is commonly used when analyzing data in which the dependent variable is restricted to the interval [0,1] for example proportion or probability. The Maximum Likelihood Estimator (MLE) is used to estimate the regression coefficients of BRMs. But in the presence of multicollinearity, MLE is very sensitive to high correlation among the explanatory variables. For this reason, we introduce a new biased estimator called the Beta Liu-Type Estimator (BLTE) to overcome the multicollinearity problem in which the dependent variable has Beta distribution. The proposed estimator is a general estimator which includes other biased estimators, such as the Ridge Estimator, Liu Estimator, and the estimators with two biasing parameters as special cases in BRM. The performance of the proposed new estimator is compared to the MLE and other biased estimators depending on the Estimated Mean Squared Error (EMSE) criterion by conducting a simulation study. Finally, a numerical example is given to show the benefit of the proposed estimator over existing estimators.
{"title":"The beta Liu-type estimator: simulation and application","authors":"Ali Erkoç, Esra Ertan, Z. Algamal, K. Akay","doi":"10.15672/hujms.1145607","DOIUrl":"https://doi.org/10.15672/hujms.1145607","url":null,"abstract":"The Beta Regression Model (BRM) is commonly used when analyzing data in which the dependent variable is restricted to the interval [0,1] for example proportion or probability. The Maximum Likelihood Estimator (MLE) is used to estimate the regression coefficients of BRMs. But in the presence of multicollinearity, MLE is very sensitive to high correlation among the explanatory variables. For this reason, we introduce a new biased estimator called the Beta Liu-Type Estimator (BLTE) to overcome the multicollinearity problem in which the dependent variable has Beta distribution. The proposed estimator is a general estimator which includes other biased estimators, such as the Ridge Estimator, Liu Estimator, and the estimators with two biasing parameters as special cases in BRM. The performance of the proposed new estimator is compared to the MLE and other biased estimators depending on the Estimated Mean Squared Error (EMSE) criterion by conducting a simulation study. Finally, a numerical example is given to show the benefit of the proposed estimator over existing estimators.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"151 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76854654","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, the canonical property of the solutions and the inverse problem for a system of differential equations having a singularity and turning point of even or odd order are investigated. First, we study the infinite product representation of the solutions of the system in turning case, and derive the corresponding dual equations. Then, by a replacement, we transform the system of differential equations to a second-order differential equation with a singularity and find the canonical product representation of its solution, and provide a procedure for constructing the solution of the inverse problem. We present a new approach to solve the inverse problems having a singularity inside the interval.
{"title":"Inverse problem for differential systems having a singularity and turning point of even or odd order","authors":"S. Mosazadeh","doi":"10.15672/hujms.1050832","DOIUrl":"https://doi.org/10.15672/hujms.1050832","url":null,"abstract":"In this paper, the canonical property of the solutions and the inverse problem for a system of differential equations having a singularity and turning point of even or odd order are investigated. First, we study the infinite product representation of the solutions of the system in turning case, and derive the corresponding dual equations. Then, by a replacement, we transform the system of differential equations to a second-order differential equation with a singularity and find the canonical product representation of its solution, and provide a procedure for constructing the solution of the inverse problem. We present a new approach to solve the inverse problems having a singularity inside the interval.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"18 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84495294","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 make use of generalized derivations to scrutinize the deportment of prime ideal satisfying certain algebraic $*$-identities in rings with involution. In specific cases, the structure of the quotient ring $mathscr{R}/mathscr{P}$ will be resolved, where $mathscr{R}$ is an arbitrary ring and $mathscr{P}$ is a prime ideal of $mathscr{R}$ and we also find the behaviour of derivations associated with generalized derivations satisfying algebraic $*$-identities involving prime ideals. Finally, we conclude our paper with applications of the previous section's results.
{"title":"Actions of generalized derivations on prime ideals in $*$-rings with applications","authors":"A. Abbasi̇, A. Khan, Mohammad Salahuddin Khan","doi":"10.15672/hujms.1119353","DOIUrl":"https://doi.org/10.15672/hujms.1119353","url":null,"abstract":"In this paper, we make use of generalized derivations to scrutinize the deportment of prime ideal satisfying certain algebraic $*$-identities in rings with involution. In specific cases, the structure of the quotient ring $mathscr{R}/mathscr{P}$ will be resolved, where $mathscr{R}$ is an arbitrary ring and $mathscr{P}$ is a prime ideal of $mathscr{R}$ and we also find the behaviour of derivations associated with generalized derivations satisfying algebraic $*$-identities involving prime ideals. Finally, we conclude our paper with applications of the previous section's results.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"52 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89662621","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 the vertical generalized Berger type deformed Sasaki metric on the tangent bundle $TM$ over an anti-paraK"{a}hler manifold as a new natural metric. Firstly, we investigate the Levi-Civita connection of this metric and then calculate all forms of the Riemannian curvature tensors. Also, we present some results concerning curvature properties. Finally, we study the geometry of $varphi $-unit tangent bundle equipped with vertical generalized Berger type deformed Sasaki metric.
{"title":"A study on tangent bundles with vertical generalized Berger type deformed Sasaki metric","authors":"Saadia Chaoui̇, A. Zagane, A. Gezer, N. Djaa","doi":"10.15672/hujms.1091758","DOIUrl":"https://doi.org/10.15672/hujms.1091758","url":null,"abstract":"In this paper, we introduce the vertical generalized Berger type deformed Sasaki metric on the tangent bundle $TM$ over an anti-paraK\"{a}hler manifold as a new natural metric. Firstly, we investigate the Levi-Civita connection of this metric and then calculate all forms of the Riemannian curvature tensors. Also, we present some results concerning curvature properties. Finally, we study the geometry of $varphi $-unit tangent bundle equipped with vertical generalized Berger type deformed Sasaki metric.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"9 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79850980","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：