Pub Date : 2023-01-19DOI: 10.31801/cfsuasmas.1126025
Meriem Mansouria BELHAMITI, Zoubir DAHMANİ, Mehmet Zeki SARIKAYA
In the present paper, we introduce a two-order nonlinear fractional sequential Langevin equation using the derivatives of Atangana-Baleanu and Caputo-Fabrizio. The existence of solutions is proven using a fixed point theorem under a weak topology, and an illustrative example is then given. Furthermore, we present new fractional versions of the Adams-Bashforth three-step approach for the Atangana-Baleanu and Caputo derivatives. New nonlinear chaotic dynamics are performed by numerical simulations.
{"title":"Two fractional order Langevin equation with new chaotic dynamics","authors":"Meriem Mansouria BELHAMITI, Zoubir DAHMANİ, Mehmet Zeki SARIKAYA","doi":"10.31801/cfsuasmas.1126025","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1126025","url":null,"abstract":"In the present paper, we introduce a two-order nonlinear fractional sequential Langevin equation using the derivatives of Atangana-Baleanu and Caputo-Fabrizio. The existence of solutions is proven using a fixed point theorem under a weak topology, and an illustrative example is then given. Furthermore, we present new fractional versions of the Adams-Bashforth three-step approach for the Atangana-Baleanu and Caputo derivatives. New nonlinear chaotic dynamics are performed by numerical simulations.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135392947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-17DOI: 10.31801/cfsuasmas.1133106
Gül TUĞ
The oriented angles between lightlike vectors cannot be defined properly compared to the timelike vectors in the Minkowski spacetime. Therefore, we use the pseudo-angles between any non-lightlike or lightlike vectors to develop the theory of lightlike surfaces having constant angle with a fixed nonlightlike direction. We investigate some geometric properties on these surfaces such as being a tangent developable. Besides, we construct the constant angle lightlike ruled surfaces by means of the null helices. We give several examples to illustrate the obtained surfaces.
{"title":"Constant pseudo-angle lightlike surfaces","authors":"Gül TUĞ","doi":"10.31801/cfsuasmas.1133106","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1133106","url":null,"abstract":"The oriented angles between lightlike vectors cannot be defined properly compared to the timelike vectors in the Minkowski spacetime. Therefore, we use the pseudo-angles between any non-lightlike or lightlike vectors to develop the theory of lightlike surfaces having constant angle with a fixed nonlightlike direction. We investigate some geometric properties on these surfaces such as being a tangent developable. Besides, we construct the constant angle lightlike ruled surfaces by means of the null helices. We give several examples to illustrate the obtained surfaces.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135594615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-30DOI: 10.31801/cfsuasmas.1035344
Olgun Durmaz, Buşra Aktaş, Osman Keçilioğlu
In this paper, the analyticity conditions of dual functions are clearly examined and the properties of the concept derivative are given in detail. Then, using the dual order relation, the dual analytic regions of dual analytic functions are constructed such that a collection of these regions forms a basis on $D^n$. Finally, the equivalent of the inverse function theorem in dual space is given by a theorem and proved.
{"title":"An overview to analyticity of dual functions","authors":"Olgun Durmaz, Buşra Aktaş, Osman Keçilioğlu","doi":"10.31801/cfsuasmas.1035344","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1035344","url":null,"abstract":"In this paper, the analyticity conditions of dual functions are clearly examined and the properties of the concept derivative are given in detail. Then, using the dual order relation, the dual analytic regions of dual analytic functions are constructed such that a collection of these regions forms a basis on $D^n$. Finally, the equivalent of the inverse function theorem in dual space is given by a theorem and proved.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43154189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-30DOI: 10.31801/cfsuasmas.914887
Levent Özbek
Cancer formation is one of the pathologies whose frequency has increased in the recent years. In the literature, the compartment models, which are non-linear, are used for such problems. In nonlinear compartment models, nonlinear state space models and the extended Kalman filter (EKF) are used to estimate the parameter and the state vector. This paper presents a discrete-time Gompertz model (DTGM) for the transfer of optical contrast agent, namely indocyanine green (ICG), in the presence of tumors between the plasma and extracellular extravascular space (EES) compartments. The DTGM, which is proposed for ICG and the estimation of ICG densities used in the vascular invasion of tumor cells of the compartments and in the measurement of migration from the intravascular area to the tissues, is obtained from the experimental data of the study. The ICG values are estimated online (recursive) using the DTGM and the adaptive Kalman filter (AKF) based on the experimental data. By employing the data, the results show that the DTGM in conjunction with the AKF provides a good analysis tool for modeling the ICG in terms of mean square error (MSE), mean absolute percentage error (MAPE), and . When the results obtained from the compartment model used in the reference [9] are compared with the results obtained with the DTGM, the DTGM gives better results in terms of MSE, MAPE and $R^2$ criteria. The DTGM and the AKF compartment model require less numerical processing when compared to the EKF, which indicates that DTGM is a less complicated model. In the literature, EKF is used for such problems.
{"title":"A study on modeling of rat tumors with the discrete-time Gompertz model","authors":"Levent Özbek","doi":"10.31801/cfsuasmas.914887","DOIUrl":"https://doi.org/10.31801/cfsuasmas.914887","url":null,"abstract":"Cancer formation is one of the pathologies whose frequency has increased in the recent years. In the literature, the compartment models, which are non-linear, are used for such problems. In nonlinear compartment models, nonlinear state space models and the extended Kalman filter (EKF) are used to estimate the parameter and the state vector. This paper presents a discrete-time Gompertz model (DTGM) for the transfer of optical contrast agent, namely indocyanine green (ICG), in the presence of tumors between the plasma and extracellular extravascular space (EES) compartments. The DTGM, which is proposed for ICG and the estimation of ICG densities used in the vascular invasion of tumor cells of the compartments and in the measurement of migration from the intravascular area to the tissues, is obtained from the experimental data of the study. The ICG values are estimated online (recursive) using the DTGM and the adaptive Kalman filter (AKF) based on the experimental data. By employing the data, the results show that the DTGM in conjunction with the AKF provides a good analysis tool for modeling the ICG in terms of mean square error (MSE), mean absolute percentage error (MAPE), and . When the results obtained from the compartment model used in the reference [9] are compared with the results obtained with the DTGM, the DTGM gives better results in terms of MSE, MAPE and $R^2$ criteria. The DTGM and the AKF compartment model require less numerical processing when compared to the EKF, which indicates that DTGM is a less complicated model. In the literature, EKF is used for such problems.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42042180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-30DOI: 10.31801/cfsuasmas.1051208
A. Batal
For a simple graph $G$ with vertex set $V(G)={v_1,...,v_n}$, we define the closed neighborhood set of a vertex $u$ as $N[u]={v in V(G) ; | ; v ; text{is adjacent to} ; u ; text{or} ; v=u }$ and the closed neighborhood matrix $N(G)$ as the matrix whose $i$th column is the characteristic vector of $N[v_i]$. We say a set $S$ is odd dominating if $N[u]cap S$ is odd for all $uin V(G)$. We prove that the parity of the cardinality of an odd dominating set of $G$ is equal to the parity of the rank of $G$, where rank of $G$ is defined as the dimension of the column space of $N(G)$. Using this result we prove several corollaries in one of which we obtain a general formula for the nullity of the join of graphs.
{"title":"Parity of an odd dominating set","authors":"A. Batal","doi":"10.31801/cfsuasmas.1051208","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1051208","url":null,"abstract":"For a simple graph $G$ with vertex set $V(G)={v_1,...,v_n}$, we define the closed neighborhood set of a vertex $u$ as $N[u]={v in V(G) ; | ; v ; text{is adjacent to} ; u ; text{or} ; v=u }$ and the closed neighborhood matrix $N(G)$ as the matrix whose $i$th column is the characteristic vector of $N[v_i]$. We say a set $S$ is odd dominating if $N[u]cap S$ is odd for all $uin V(G)$. We prove that the parity of the cardinality of an odd dominating set of $G$ is equal to the parity of the rank of $G$, where rank of $G$ is defined as the dimension of the column space of $N(G)$. Using this result we prove several corollaries in one of which we obtain a general formula for the nullity of the join of graphs.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41527310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-30DOI: 10.31801/cfsuasmas.1123739
Hüseyin Albayrak
In this paper, we investigate the diameters, Chebyshev radii, Chebyshev self-radii and inner radii of a sequence of sets in the normed spaces. We prove that if a sequence of sets is I -Hausdorff convergent to a set, the sequence of Chebyshev radii of that sequence is I-convergent. Similar relations are showed for the sequence of diameters, Chebyshev self-radii and inner radii of that sequence.
{"title":"Ideal convergence of a sequence of Chebyshev radii of sets","authors":"Hüseyin Albayrak","doi":"10.31801/cfsuasmas.1123739","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1123739","url":null,"abstract":"In this paper, we investigate the diameters, Chebyshev radii, Chebyshev self-radii and inner radii of a sequence of sets in the normed spaces. We prove that if a sequence of sets is I -Hausdorff convergent to a set, the sequence of Chebyshev radii of that sequence is I-convergent. Similar relations are showed for the sequence of diameters, Chebyshev self-radii and inner radii of that sequence.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44398590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-30DOI: 10.31801/cfsuasmas.1089480
Bilal Demir, Mustafa Karataş
Fixed points of matrices have many applications in various areas of science and mathematics. Extended modular group ¯¯¯¯ΓΓ¯ is the group of 2×22×2 matrices with integer entries and determinant ±1±1. There are strong connections between extended modular group, continued fractions and Farey graph. Farey graph is a graph with vertex set ^Q=Q∪{∞}Q^=Q∪{∞}. In this study, we consider the elements in ¯¯¯¯ΓΓ¯ that fix rationals. For a given rational number, we use its Farey neighbours to obtain the matrix representation of the element in $overline{Gamma}$ that fixes the given rational. Then we express such elements as words in terms of generators using the relations between the Farey graph and continued fractions. Finally we give the new block reduced form of these words which all blocks have Fibonacci numbers entries.
{"title":"Farey graph and rational fixed points of the extended modular group","authors":"Bilal Demir, Mustafa Karataş","doi":"10.31801/cfsuasmas.1089480","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1089480","url":null,"abstract":"Fixed points of matrices have many applications in various areas of science and mathematics. Extended modular group ¯¯¯¯ΓΓ¯ is the group of 2×22×2 matrices with integer entries and determinant ±1±1. There are strong connections between extended modular group, continued fractions and Farey graph. Farey graph is a graph with vertex set ^Q=Q∪{∞}Q^=Q∪{∞}. In this study, we consider the elements in ¯¯¯¯ΓΓ¯ that fix rationals. For a given rational number, we use its Farey neighbours to obtain the matrix representation of the element in $overline{Gamma}$ that fixes the given rational. Then we express such elements as words in terms of generators using the relations between the Farey graph and continued fractions. Finally we give the new block reduced form of these words which all blocks have Fibonacci numbers entries.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43426327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-30DOI: 10.31801/cfsuasmas.1070240
Samed Özkan, M. Günes
In this paper, we characterize explicitly the separation properties $T_0$ and $T_1$ at a point p in the topological category of quantale-valued preordered spaces and investigate how these characterizations are related. Moreover, we prove that local $T_0$ and $T_1$ quantale-valued preordered spaces are hereditary and productive.
{"title":"Local $T_0$ and $T_1$ quantale-valued preordered spaces","authors":"Samed Özkan, M. Günes","doi":"10.31801/cfsuasmas.1070240","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1070240","url":null,"abstract":"In this paper, we characterize explicitly the separation properties $T_0$ and $T_1$ at a point p in the topological category of quantale-valued preordered spaces and investigate how these characterizations are related. Moreover, we prove that local $T_0$ and $T_1$ quantale-valued preordered spaces are hereditary and productive.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48626458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-30DOI: 10.31801/cfsuasmas.1061084
Berke Kalebog̃az, D. Keskin Tütüncü
In this paper, we first define the notion of $mathcal{F}$-cosmall quotient for an additive exact substructure $mathcal{F}$ of an exact structure $mathcal{E}$ in an additive category $mathcal{A}$. We show that every $mathcal{F}$-cosmall quotient is right minimal in some cases. We also give the definition of $mathcal{F}$-superfluous quotient and we relate it the approximation of modules. As an application, we investigate our results in a pure-exact substructure $mathcal{F}$.
{"title":"On $mathcal{F}$-cosmall morphisms","authors":"Berke Kalebog̃az, D. Keskin Tütüncü","doi":"10.31801/cfsuasmas.1061084","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1061084","url":null,"abstract":"In this paper, we first define the notion of $mathcal{F}$-cosmall quotient for an additive exact substructure $mathcal{F}$ of an exact structure $mathcal{E}$ in an additive category $mathcal{A}$. We show that every $mathcal{F}$-cosmall quotient is right minimal in some cases. We also give the definition of $mathcal{F}$-superfluous quotient and we relate it the approximation of modules. As an application, we investigate our results in a pure-exact substructure $mathcal{F}$.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42696863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-30DOI: 10.31801/cfsuasmas.981876
Saeed Hashemi Sababe
In this research, we introduce the stochastic integration with respect to a cylindrical special semi-martingale, which is a specific case of general integration, with specific properties of special semi-martingales.
在这项研究中，我们引入了关于圆柱特殊半鞅的随机积分，这是一般积分的一个特例，具有特殊半鞅性质。
{"title":"Stochastic integration with respect to a cylindrical special semi martingale","authors":"Saeed Hashemi Sababe","doi":"10.31801/cfsuasmas.981876","DOIUrl":"https://doi.org/10.31801/cfsuasmas.981876","url":null,"abstract":"In this research, we introduce the stochastic integration with respect to a cylindrical special semi-martingale, which is a specific case of general integration, with specific properties of special semi-martingales.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49309767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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