Pub Date : 2023-03-30DOI: 10.31801/cfsuasmas.1029614
Roohi Bhat, M. A. Khanday
Hemoglobin $(Hb)$ possesses good properties of cooperative system and it normally executes oxygen and other essential items via erythrocytes in the body. The chemical action of $Hb$ is to combine with oxygen (O2)(O2) in the lungs to form oxyhemoglobin (HbO2)(HbO2). Binding of oxygen with a hemoglobin is one of the important cooperative mechanism and is an emerging mathematical research area with wide range of applications in biomedical engineering and medical physiology. To this end, a mathematical model is proposed to study the fractional saturation of oxygen in hemoglobin to understand the binding effect and its stability at various stages. The mathematical formulation is based on the system of ordinary differential equations together with rate equations under different association and dissociation rate constants. The five states of the cooperative systems $Hb, HbO_2, Hb(O_2)_2, Hb(O_2)_3$ and $Hb(O_2)_4$ are modelled and the Hill’s function has been used to approximate the binding effect and saturation of ligand $(O_2)$ with respect to various rate constants. Also, the Adair equation has been employed to interpret the saturation concentrations of oxygen in hemoglobin.
{"title":"A mathematical analysis of cooperativity and fractional saturation of oxygen in hemoglobin","authors":"Roohi Bhat, M. A. Khanday","doi":"10.31801/cfsuasmas.1029614","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1029614","url":null,"abstract":"Hemoglobin $(Hb)$ possesses good properties of cooperative system and it normally executes oxygen and other essential items via erythrocytes in the body. The chemical action of $Hb$ is to combine with oxygen (O2)(O2) in the lungs to form oxyhemoglobin (HbO2)(HbO2). Binding of oxygen with a hemoglobin is one of the important cooperative mechanism and is an emerging mathematical research area with wide range of applications in biomedical engineering and medical physiology. To this end, a mathematical model is proposed to study the fractional saturation of oxygen in hemoglobin to understand the binding effect and its stability at various stages. The mathematical formulation is based on the system of ordinary differential equations together with rate equations under different association and dissociation rate constants. The five states of the cooperative systems $Hb, HbO_2, Hb(O_2)_2, Hb(O_2)_3$ and $Hb(O_2)_4$ are modelled and the Hill’s function has been used to approximate the binding effect and saturation of ligand $(O_2)$ with respect to various rate constants. Also, the Adair equation has been employed to interpret the saturation concentrations of oxygen in hemoglobin.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43668375","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1052686
Gonca Kızılaslan
In this paper, we consider a generalization of a regular Tribonacci matrix for two variables and show that it can be factorized by some special matrices. We produce several new interesting identities and find an explicit formula for the inverse and k−th power. We also give a relation between the matrix and a matrix exponential of a special matrix.
{"title":"The linear algebra of a generalized Tribonacci matrix","authors":"Gonca Kızılaslan","doi":"10.31801/cfsuasmas.1052686","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1052686","url":null,"abstract":"In this paper, we consider a generalization of a regular Tribonacci matrix for two variables and show that it can be factorized by some special matrices. We produce several new interesting identities and find an explicit formula for the inverse and k−th power. We also give a relation between the matrix and a matrix exponential of a special matrix.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48786535","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1059496
Coșkun Yakar, Hazm Talab
In this paper, we investigate generalized variational comparison results aimed to study the stability properties in terms of two measures for solutions of Set Differential Equations (SDEs) involving causal operators, taking into consideration the difference in initial conditions. Next, we employ these comparison results in proving the theorems that give sufficient conditions for equi-boundedness, equi-attractiveness in the large, and Lagrange stability in terms of two measures with initial time difference for the solutions of perturbed SDEs involving causal operators in regard to their unperturbed ones.
{"title":"Lagrange stability in terms of two measures with initial time difference for set differential equations involving causal operators","authors":"Coșkun Yakar, Hazm Talab","doi":"10.31801/cfsuasmas.1059496","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1059496","url":null,"abstract":"In this paper, we investigate generalized variational comparison results aimed to study the stability properties in terms of two measures for solutions of Set Differential Equations (SDEs) involving causal operators, taking into consideration the difference in initial conditions. Next, we employ these comparison results in proving the theorems that give sufficient conditions for equi-boundedness, equi-attractiveness in the large, and Lagrange stability in terms of two measures with initial time difference for the solutions of perturbed SDEs involving causal operators in regard to their unperturbed ones.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41859536","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1121701
M. Sertbaş, Coşkun Saral
In this research, the minimal and maximal operators defined by $q$- difference expression are given in the Hilbert space $L_q^{2}( 0, + infty )$. The existence problem of a $q^{-1}$-normal extension for the minimal operator is mentioned. In addition, the sets of the minimal operator spectrum and the maximal operator spectrum are examined.
{"title":"$q$-Difference Operator on $L_q^{2}( 0, + infty )$","authors":"M. Sertbaş, Coşkun Saral","doi":"10.31801/cfsuasmas.1121701","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1121701","url":null,"abstract":"In this research, the minimal and maximal operators defined by $q$- difference expression are given in the Hilbert space $L_q^{2}( 0, + infty )$. The existence problem of a $q^{-1}$-normal extension for the minimal operator is mentioned. In addition, the sets of the minimal operator spectrum and the maximal operator spectrum are examined.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44931634","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1038245
Meryem Şenocak, E. Güner
In this article we would like to present a new type of fuzzy contractive mappings which are called $alpha-phi-mathcal{M}^{0}$ fuzzy contractive and $beta-psi-mathcal{M}^{0}$ fuzzy contractive, and then we demonstrate two theorems which ensure the existence of a fixed point for these two types of mappings. And so we combine and generalize some existing notions in the literature ([5], [7]). Proved these theorems in the extended fuzzy metric spaces are in the more general version than the existing in the literature ones.
{"title":"Fixed-point theorems in extended fuzzy metric spaces via $alpha-phi-mathcal{M}^{0}$ and $beta-psi-mathcal{M}^{0}$ fuzzy contractive mappings","authors":"Meryem Şenocak, E. Güner","doi":"10.31801/cfsuasmas.1038245","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1038245","url":null,"abstract":"In this article we would like to present a new type of fuzzy contractive mappings which are called $alpha-phi-mathcal{M}^{0}$ fuzzy contractive and $beta-psi-mathcal{M}^{0}$ fuzzy contractive, and then we demonstrate two theorems which ensure the existence of a fixed point for these two types of mappings. And so we combine and generalize some existing notions in the literature ([5], [7]). Proved these theorems in the extended fuzzy metric spaces are in the more general version than the existing in the literature ones.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41464540","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1074682
Anıl Altinkaya, M. Çalişkan
In this paper, we have described the B-Lift curve in Euclidean space as a curve obtained by combining the endpoints of the binormal vector of a unit speed curve. Subsequently, we have explored the Frenet frames of the B-Lift curves. Moreover, we have introduced the tangent, normal and binormal surfaces of the B-Lift curve and examined the geometric invariants of these surfaces. Finally, we have investigated the singularities of these surface and visualized the surfaces with MATLAB program.
{"title":"B-Lift curves and its ruled surfaces","authors":"Anıl Altinkaya, M. Çalişkan","doi":"10.31801/cfsuasmas.1074682","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1074682","url":null,"abstract":"In this paper, we have described the B-Lift curve in Euclidean space as a curve obtained by combining the endpoints of the binormal vector of a unit speed curve. Subsequently, we have explored the Frenet frames of the B-Lift curves. Moreover, we have introduced the tangent, normal and binormal surfaces of the B-Lift curve and examined the geometric invariants of these surfaces. Finally, we have investigated the singularities of these surface and visualized the surfaces with MATLAB program.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44961251","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1075157
Ferit Yalaz, Aynur KESKİN KAYMAKCI
The definitions of new type separated subsets are given in ideal topological spaces. By using these definitions, we introduce new types of connectedness. It is shown that these new types of connectedness are more general than some previously defined concepts of connectedness in ideal topological spaces. The new types of connectedness are compared with well-known connectedness in point-set topology. Then, the intermediate value theorem for ideal topological spaces is given. Also, for some special cases, it is shown that the intermediate value theorem in ideal topological spaces and the intermediate value theorem in topological spaces coincide.
{"title":"New types of connectedness and intermediate value theorem in ideal topological spaces","authors":"Ferit Yalaz, Aynur KESKİN KAYMAKCI","doi":"10.31801/cfsuasmas.1075157","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1075157","url":null,"abstract":"The definitions of new type separated subsets are given in ideal topological spaces. By using these definitions, we introduce new types of connectedness. It is shown that these new types of connectedness are more general than some previously defined concepts of connectedness in ideal topological spaces. The new types of connectedness are compared with well-known connectedness in point-set topology. Then, the intermediate value theorem for ideal topological spaces is given. Also, for some special cases, it is shown that the intermediate value theorem in ideal topological spaces and the intermediate value theorem in topological spaces coincide.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41449653","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 : 2023-03-30DOI: 10.31801/cfsuasmas.1062880
Semih Pi̇ri̇, O. Olmez, Murat Sahin
In this paper, directed strongly regular graphs (DSRGs) are constructed by using semidirect products. The orbit condition in [3] has been weakened and this gives rise to the construction of DSRGs. Moreover, a different construction is given for DSRG by using semidihedral groups.
{"title":"Constructing directed strongly regular graphs by using semidirect products and semidihedral groups","authors":"Semih Pi̇ri̇, O. Olmez, Murat Sahin","doi":"10.31801/cfsuasmas.1062880","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1062880","url":null,"abstract":"In this paper, directed strongly regular graphs (DSRGs) are constructed by using semidirect products. The orbit condition in [3] has been weakened and this gives rise to the construction of DSRGs. Moreover, a different construction is given for DSRG by using semidihedral groups.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43545904","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 : 2023-03-28DOI: 10.31801/cfsuasmas.1224326
Meryem ATEŞ, Sevda SAĞIROĞLU PEKER
In the present paper we construct a new approach structure called Fell approach structure. We define the new structure by means of lower regular function frames and prove that the Top-coreflection of this new structure is the ordinary Fell topology. We also give analogue result for the extended Fell topology and investigate some properties of Fell approach structure.
{"title":"The Fell approach structure","authors":"Meryem ATEŞ, Sevda SAĞIROĞLU PEKER","doi":"10.31801/cfsuasmas.1224326","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1224326","url":null,"abstract":"In the present paper we construct a new approach structure called Fell approach structure. We define the new structure by means of lower regular function frames and prove that the Top-coreflection of this new structure is the ordinary Fell topology. We also give analogue result for the extended Fell topology and investigate some properties of Fell approach structure.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":"278 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135777956","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 : 2023-03-28DOI: 10.31801/cfsuasmas.1252070
Gamze GUVEN
In this study, we focus on two test statistics for testing the equality of treatment means in one-way analysis of variance (ANOVA). The first one is the well known Cochran ($C_{LS}$) test statistic based on least squares (LS) estimators and the second one is robust version of it ($RC_{MML}$) based on modified maximum likelihood (MML) estimators. These two test statistics are asymptotically distributed as chi-square. However, distributions of them are unknown for small samples. Therefore, three-moment chi-square and four moment $F$ approximations to the null distributions of $C_{LS}$ and $RC_{MML}$ are derived inspired by Tiku and Wong [19]. To investigate the small and moderate sample properties of these tests based on the mentioned approximations, an extensive Monte-Carlo simulation study is performed when the underlying distribution is long-tailed symmetric (LTS). Simulation results show that four-moment $F$ approximation provides better approximation than the three-moment chi-square approximation for both $C_{LS}$ and $RC_{MML}$ tests. Therefore, the simulated Type I error rates and powers of the $C_{LS}$ and $RC_{MML}$ test statistics are calculated using four-moment $F$ approximation. According to simulation results, $RC_{MML}$ test is more powerful than the corresponding $C_{LS}$ test.
{"title":"Testing equality of means in one-way ANOVA using three and four moment approximations","authors":"Gamze GUVEN","doi":"10.31801/cfsuasmas.1252070","DOIUrl":"https://doi.org/10.31801/cfsuasmas.1252070","url":null,"abstract":"In this study, we focus on two test statistics for testing the equality of treatment means in one-way analysis of variance (ANOVA). The first one is the well known Cochran ($C_{LS}$) test statistic based on least squares (LS) estimators and the second one is robust version of it ($RC_{MML}$) based on modified maximum likelihood (MML) estimators. These two test statistics are asymptotically distributed as chi-square. However, distributions of them are unknown for small samples. Therefore, three-moment chi-square and four moment $F$ approximations to the null distributions of $C_{LS}$ and $RC_{MML}$ are derived inspired by Tiku and Wong [19]. To investigate the small and moderate sample properties of these tests based on the mentioned approximations, an extensive Monte-Carlo simulation study is performed when the underlying distribution is long-tailed symmetric (LTS). Simulation results show that four-moment $F$ approximation provides better approximation than the three-moment chi-square approximation for both $C_{LS}$ and $RC_{MML}$ tests. Therefore, the simulated Type I error rates and powers of the $C_{LS}$ and $RC_{MML}$ test statistics are calculated using four-moment $F$ approximation. According to simulation results, $RC_{MML}$ test is more powerful than the corresponding $C_{LS}$ test.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135777950","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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