In this paper we investigate exact $K$-g-frames, weaving of $K$-g-frames and $Q$-dual of g-frames in Hilbert spaces. We present a sufficient condition for a g-Bessel sequence to be an exact $K$-g-frame. Given two woven pairs $(Lambda, Gamma)$ and $(Theta, Delta)$ of $K$-g-frames, we investigate under what conditions can $Lambda$ be $K$-g-woven with $Delta$ if $Gamma$ is $K$-g-woven with $Theta$. Given a $K$-g-frame $Lambda$ and its dual $Gamma$ on $mathcal{U}$, we construct a new pair based on $Lambda$ and $Gamma$ so that they are woven on a subspace $R(K)$ of $mathcal{U}$. Finally, we give an equivalent characterization of $Q$-dual of g-frames.
{"title":"Redundancy, weaving and Q-dual of K-g-frames in Hilbert spaces","authors":"Xiangchun Xiao, Guo Ping Zhao, Guorong Zhou","doi":"10.15672/hujms.1130102","DOIUrl":"https://doi.org/10.15672/hujms.1130102","url":null,"abstract":"In this paper we investigate exact $K$-g-frames, weaving of $K$-g-frames and $Q$-dual of g-frames in Hilbert spaces. We present a sufficient condition for a g-Bessel sequence to be an exact $K$-g-frame. Given two woven pairs $(Lambda, Gamma)$ and $(Theta, Delta)$ of $K$-g-frames, we investigate under what conditions can $Lambda$ be $K$-g-woven with $Delta$ if $Gamma$ is $K$-g-woven with $Theta$. Given a $K$-g-frame $Lambda$ and its dual $Gamma$ on $mathcal{U}$, we construct a new pair based on $Lambda$ and $Gamma$ so that they are woven on a subspace $R(K)$ of $mathcal{U}$. Finally, we give an equivalent characterization of $Q$-dual of g-frames.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"8 43","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440022","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}
S. MEENAKSHİ1, G. Muhiuddin, D. Al-Kadi, B. Elavarasan
The fuzzy set is an excellent solution for dealing with ambiguity and for expressing people’s hesitation in regular life. Soft set theory is an innovative method for solving practical issues. This is useful in resolving a number of problems, and a lot of progress is being made at the moment. In order to develop hybrid structures, Jun et al. fused the fuzzy and soft sets. In this paper, the notion of hybrid bi-ideals in near-subtraction semigroups is proposed and their associated results are discussed. The notion of hybrid intersections is examined. Furthermore, we establish some results related to the homomorphic image and preimage of a hybrid bi-ideal in near-subtraction semigroups.
{"title":"Hybrid bi-ideals in Near- Subtraction Semigroups","authors":"S. MEENAKSHİ1, G. Muhiuddin, D. Al-Kadi, B. Elavarasan","doi":"10.15672/hujms.1229332","DOIUrl":"https://doi.org/10.15672/hujms.1229332","url":null,"abstract":"The fuzzy set is an excellent solution for dealing with ambiguity and for expressing people’s hesitation in regular life. Soft set theory is an innovative method for solving practical issues. This is useful in resolving a number of problems, and a lot of progress is being made at the moment. In order to develop hybrid structures, Jun et al. fused the fuzzy and soft sets. In this paper, the notion of hybrid bi-ideals in near-subtraction semigroups is proposed and their associated results are discussed. The notion of hybrid intersections is examined. Furthermore, we establish some results related to the homomorphic image and preimage of a hybrid bi-ideal in near-subtraction semigroups.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"83 22","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440803","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 $ sigma={sigma_i:iin I} $ be a partition of the set $ mathbb{P} $ of all primes. A finite group $ G $ is called $ sigma $-primary if the prime divisors, if any, of $|G|$ all belong to the same member of $ sigma $. A finite group $ G $ is called $ sigma $-soluble if every chief factor of $ G $ is $ sigma$-primary. A subgroup $H$ of a group $G$ is called $sigma$-subnormal in $G$ if there is a chain of subgroups $H=H_0leq H_1leqcdotsleq H_n=G$ such that either $ H_{i-1} $ is normal in $ H_i $ or $ H_{i}/(H_{i-1})_{H_{i}} $ is $ sigma $-primary for all $ i=1,dots,n $; A subgroup $H$ of a group $G$ is called $sigma$-$c$-subnormal in $G$ if there is a subnormal subgroup $T$ of $G$ such that $G=HT$ and $Hcap Tleq H_{sigma G}$, where the subgroup $H_{sigma G}$ is generated by all $sigma$-subnormal subgroups of $G$ contained in $H$. In this paper, we investigate the influence of $sigma$-$c$-subnormality of some kinds of maximal subgroups on $sigma$-solubility of finite groups, which generalize some known results.
{"title":"On $sigma$-$c$-subnormal subgroups of finite groups","authors":"Jiahui Li̇u, Sh. Qiao","doi":"10.15672/hujms.1342339","DOIUrl":"https://doi.org/10.15672/hujms.1342339","url":null,"abstract":"Let $ sigma={sigma_i:iin I} $ be a partition of the set $ mathbb{P} $ of all primes. A finite group $ G $ is called $ sigma $-primary if the prime divisors, if any, of $|G|$ all belong to the same member of $ sigma $. A finite group $ G $ is called $ sigma $-soluble if every chief factor of $ G $ is $ sigma$-primary. A subgroup $H$ of a group $G$ is called $sigma$-subnormal in $G$ if there is a chain of subgroups $H=H_0leq H_1leqcdotsleq H_n=G$ such that either $ H_{i-1} $ is normal in $ H_i $ or $ H_{i}/(H_{i-1})_{H_{i}} $ is $ sigma $-primary for all $ i=1,dots,n $; A subgroup $H$ of a group $G$ is called $sigma$-$c$-subnormal in $G$ if there is a subnormal subgroup $T$ of $G$ such that $G=HT$ and $Hcap Tleq H_{sigma G}$, where the subgroup $H_{sigma G}$ is generated by all $sigma$-subnormal subgroups of $G$ contained in $H$. In this paper, we investigate the influence of $sigma$-$c$-subnormality of some kinds of maximal \u0000subgroups on $sigma$-solubility of finite groups, which generalize some known results.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"11 6","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439803","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 the present article is to provide geometric sufficient conditions for discrete points to be a sampling sequence for a generalized Hilbert Bargmann-Fock space in several complex variables.
本文旨在为离散点成为多个复变的广义希尔伯特-巴格曼-福克空间的采样序列提供几何充分条件。
{"title":"On a Sampling Problem for a Bargmann-Fock Space","authors":"Mohammed EL AIDI","doi":"10.15672/hujms.1339373","DOIUrl":"https://doi.org/10.15672/hujms.1339373","url":null,"abstract":"The purpose of the present article is to provide geometric sufficient conditions for discrete points to be a sampling sequence for a generalized Hilbert Bargmann-Fock space in several complex variables.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"3 12","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440179","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}
Solving some systems of operator equations, new kinds of generalized inverses are introduced. Since these new inverses can be expressed by inner and gMP inverses, they are called inner-gMP and gMP-inner inverses. In this way, the concepts of gMP, 1MP and MP1 inverses are generalized. Various representations and characterizations of inner-gMP and gMP-inner inverses are presented. Using the inner and *gMP inverse, we define the inner-*gMP and *gMP-inner inverses which are new extensions of 1MP, MP1 and *gMP inverses. We apply inner-gMP and gMP-inner inverses as well as inner-*gMP and *gMP-inner inverses to solve several kinds of linear equations. Consequently, we obtain solvability of the normal equation which is connected to the least--squares solution. Numerical examples are given to illustrate our results.
{"title":"Inner-gMP and gMP-inner inverses","authors":"Dunja Stojanovi̇c, D. Mosić","doi":"10.15672/hujms.1351762","DOIUrl":"https://doi.org/10.15672/hujms.1351762","url":null,"abstract":"Solving some systems of operator equations, new kinds of generalized inverses are introduced. \u0000Since these new inverses can be expressed by inner and gMP inverses, they are called inner-gMP and gMP-inner inverses. \u0000In this way, the concepts of gMP, 1MP and MP1 inverses are generalized. Various representations and characterizations of inner-gMP and gMP-inner inverses are presented. Using the inner and *gMP inverse, we define the inner-*gMP and *gMP-inner inverses which are new extensions of 1MP, MP1 and *gMP inverses. \u0000We apply inner-gMP and gMP-inner inverses as well as inner-*gMP and *gMP-inner inverses to solve several kinds of linear equations. Consequently, we obtain solvability of the normal equation which is connected to the least--squares solution. Numerical examples are given to illustrate our results.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"92 9","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440227","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 completely classify Ricci bi-conformal vector fields on connected, simply-connected five-dimensional two-step nilpotent Lie groups and we show which of them are the Killing vector fields and gradient vector fields.
{"title":"ًRicci bi-conformal vector fields on Lorentzian five dimensional two-step nilpotent Lie groups","authors":"S. Azami, U.c. De","doi":"10.15672/hujms.1294973","DOIUrl":"https://doi.org/10.15672/hujms.1294973","url":null,"abstract":"In this paper, we completely classify Ricci bi-conformal vector fields on connected, simply-connected five-dimensional two-step nilpotent Lie groups and we show which of them are the Killing vector fields and gradient vector fields.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"88 15","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440495","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 compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Heston's option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.
本文比较了针对赫斯顿期权定价模型的侵入式适当正交分解（POD）、Galerkin 投影和数据驱动的动态模式分解（DMD）。全阶模型是通过空间的非连续 Galerkin 离散化和时间的反向欧拉离散化获得的。蝶式价差、欧式和数字看涨期权的数值结果表明，一般来说，在相同精度水平下，DMD 比 POD 模式需要更多的模式。然而，由于 DMD 的非侵入性，DMD 的加速因子要比 POD 高得多。
{"title":"Reduced-Order Modeling for Heston Stochastic Volatility Model","authors":"Sinem Kozpinar, M. Uzunca, B. Karasözen","doi":"10.15672/hujms.1066143","DOIUrl":"https://doi.org/10.15672/hujms.1066143","url":null,"abstract":"In this paper, we compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Heston's option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438779","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 a ring with identity. The comaximal graph of $R$, denoted by $Gamma(R)$, is a simple graph with vertex set $R$ and two different vertices $a$ and $b$ are adjacent if and only if $aR+bR=R$. Let $Gamma_{2}(R)$ be a subgraph of $Gamma(R)$ induced by $Rbackslash{U(R)cup J(R)}$. In this paper, we investigate the genus of the line graph $L(Gamma(R))$ of $Gamma(R)$ and the line graph $L(Gamma_{2}(R))$ of $Gamma_2(R)$. All finite commutative rings whose genus of $L(Gamma(R))$ and $L(Gamma_{2}(R))$ are 0, 1, 2 are completely characterized, respectively.
{"title":"Finite commutative rings whose line graphs of comaximal graphs have genus at most two","authors":"Huadong Su","doi":"10.15672/hujms.1256413","DOIUrl":"https://doi.org/10.15672/hujms.1256413","url":null,"abstract":"Let $R$ be a ring with identity. The comaximal graph of $R$, denoted by $Gamma(R)$, is a simple graph with vertex set $R$ and two different vertices $a$ and $b$ are adjacent if and only if $aR+bR=R$. Let $Gamma_{2}(R)$ be a subgraph of $Gamma(R)$ induced by $Rbackslash{U(R)cup J(R)}$. In this paper, we investigate the genus of the line graph $L(Gamma(R))$ of $Gamma(R)$ and the line graph $L(Gamma_{2}(R))$ of $Gamma_2(R)$. All finite commutative rings whose genus of $L(Gamma(R))$ and $L(Gamma_{2}(R))$ are 0, 1, 2 are completely characterized, respectively.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"6 9","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440195","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 Bochner–Schoenberg–Eberlein module property on commutative Banach algebras is a property related to extensions of multipliers on Banach algebras to module morphisms from Banach algebras into Banach modules. In this paper, we answer the problem (1) raised in [J. Algebra Appl., 21(8) (2022), 2250155, DOI: 10.1142/S0219498822501559]. We show that the Banach $ArtimesU$-module $Xtimes Y$ ($X$ is a Banach $A,U$-module and $Y$ is a Banach $U$-module) has a BSE-module property if and only if $X$ is a BSE Banach $A,U$-module and $Y$ is a BSE Banach $U$-module.
{"title":"The Bochner–Schoenberg–Eberlein module property for amalgamated duplication of Banach algebras","authors":"M. Abolfathi, Ali Ebadian, Ali Jabbari̇","doi":"10.15672/hujms.1261110","DOIUrl":"https://doi.org/10.15672/hujms.1261110","url":null,"abstract":"The Bochner–Schoenberg–Eberlein module property on commutative Banach algebras is a property related to extensions of multipliers on Banach algebras to module morphisms from Banach algebras into Banach modules. In this paper, we answer the problem (1) raised in [J. Algebra Appl., 21(8) (2022), 2250155, DOI: 10.1142/S0219498822501559]. We show that the Banach $ArtimesU$-module $Xtimes Y$ ($X$ is a Banach $A,U$-module and $Y$ is a Banach $U$-module) has a BSE-module property if and only if $X$ is a BSE Banach $A,U$-module and $Y$ is a BSE Banach $U$-module.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"73 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440566","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, researchers have focused on exploring different forms of statistical convergence in Riesz spaces, such as statistical order convergence and statistical unbounded order convergence. This study aims to present the concept of deferred statistical convergence within Riesz spaces, specifically concerning its relationship with order convergence. Furthermore, we delve into the interconnections between deferred statistical order convergence and various other types of statistical convergence. Moreover, we explore in depth the intricate connections between deferred statistical order convergence and other notable forms of statistical convergence. We provide valuable insights into the broader framework of statistical convergence theory in Riesz spaces.
{"title":"Deferred statistical order convergence in Riesz spaces","authors":"M. Küçükaslan, Abdullah Aydin","doi":"10.15672/hujms.1322652","DOIUrl":"https://doi.org/10.15672/hujms.1322652","url":null,"abstract":"In recent years, researchers have focused on exploring different forms of statistical convergence in Riesz spaces, such as statistical order convergence and statistical unbounded order convergence. This study aims to present the concept of deferred statistical convergence within Riesz spaces, specifically concerning its relationship with order convergence. Furthermore, we delve into the interconnections between deferred statistical order convergence and various other types of statistical convergence. Moreover, we explore in depth the intricate connections between deferred statistical order convergence and other notable forms of statistical convergence. We provide valuable insights into the broader framework of statistical convergence theory in Riesz spaces.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438789","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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