Abstract Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation x2 − y2m = zn, x, y, z, m, n ∈ ℕ, gcd(x, y) = 1, m ≥ 2, n ≥ 3.
设n为所有正整数的集合。本文利用一些已知的关于各种丢芬图方程的结果，解决了一类三元方程x2−y2m = zn, x, y, z, m, n∈_1,gcd(x, y) = 1, m≥2,n≥3的几个特殊情况。
{"title":"A note on the ternary Diophantine equation x2 − y2m = zn","authors":"A. Bérczes, M. Le, I. Pink, G. Soydan","doi":"10.2478/auom-2021-0020","DOIUrl":"https://doi.org/10.2478/auom-2021-0020","url":null,"abstract":"Abstract Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation x2 − y2m = zn, x, y, z, m, n ∈ ℕ, gcd(x, y) = 1, m ≥ 2, n ≥ 3.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75098137","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}
Abstract In real life, variability and inaccuracy are always presentand must be calculated by either possibilistic, probabilistic, polymorphic or other uncertainty approach. This benchmark study is about to construct new types of fuzzy soft ideals i.e., (∈, ∈ ∨qk)-FSR(L)Is of ordered semigroup(OSG). Based on this inception, fuzzy soft level subsets are defined which link ordinary ideals with (∈, ∈ ∨qk)-fuzzy soft left(right) ideals. Some binary operations like ◦λ, intersection ∩λ and union of fuzzy soft sets ∪λ are given and various fundamental results of ideal theory are developed through these types of fuzzy soft ideals.
{"title":"A Benchmark Generalization of Fuzzy Soft Ideals in Ordered Semigroups","authors":"F. Khan, V. Leoreanu-Fotea, Saifullah, Amanullah","doi":"10.2478/auom-2021-0023","DOIUrl":"https://doi.org/10.2478/auom-2021-0023","url":null,"abstract":"Abstract In real life, variability and inaccuracy are always presentand must be calculated by either possibilistic, probabilistic, polymorphic or other uncertainty approach. This benchmark study is about to construct new types of fuzzy soft ideals i.e., (∈, ∈ ∨qk)-FSR(L)Is of ordered semigroup(OSG). Based on this inception, fuzzy soft level subsets are defined which link ordinary ideals with (∈, ∈ ∨qk)-fuzzy soft left(right) ideals. Some binary operations like ◦λ, intersection ∩λ and union of fuzzy soft sets ∪λ are given and various fundamental results of ideal theory are developed through these types of fuzzy soft ideals.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83556310","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}
Abstract In this paper, in the setting of Hadamard spaces, a iterative scheme is proposed for approximating a solution of the inclusion problem for a finite family of monotone operators which is a unique solution of a variational inequality. Some applications in convex minimization and fixed point theory are also presented to support the main result.
{"title":"Strong convergence to a solution of the inclusion problem for a finite family of monotone operators in Hadamard spaces","authors":"S. Ranjbar","doi":"10.2478/auom-2021-0028","DOIUrl":"https://doi.org/10.2478/auom-2021-0028","url":null,"abstract":"Abstract In this paper, in the setting of Hadamard spaces, a iterative scheme is proposed for approximating a solution of the inclusion problem for a finite family of monotone operators which is a unique solution of a variational inequality. Some applications in convex minimization and fixed point theory are also presented to support the main result.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83468844","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}
Abstract We give a stochastic order for Varma residual entropy and study several properties of it, like closure, reversed closure and preservation of this order in some stochastic models.
{"title":"Varma Quantile Entropy Order","authors":"Sorina-Cezarina Sfetcu","doi":"10.2478/auom-2021-0029","DOIUrl":"https://doi.org/10.2478/auom-2021-0029","url":null,"abstract":"Abstract We give a stochastic order for Varma residual entropy and study several properties of it, like closure, reversed closure and preservation of this order in some stochastic models.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86051184","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}
Abstract Archimedes’ well known theorem on the area of a parabolic segment says that this area is 4/3 of the area of a certain inscribed triangle. In this paper we generalize this theorem to the n-dimensional euclidean space, n ≥ 3. It appears that the ratio of the volume of an n-dimensional solid bounded by an (n − 1)-dimensional hyper-paraboloid and an (n − 1)-dimensional hyperplane and the volume of a certain inscribed cone (we analogously repeat Archimedes’ procedure) depends only on the dimension of the euclidean space and it equals to 2n/(n +1).
{"title":"A Generalization of Archimedes’ Theorem on the Area of a Parabolic Segment","authors":"A. Grigoryan, S. Ignaciuk, M. Parol","doi":"10.2478/auom-2021-0026","DOIUrl":"https://doi.org/10.2478/auom-2021-0026","url":null,"abstract":"Abstract Archimedes’ well known theorem on the area of a parabolic segment says that this area is 4/3 of the area of a certain inscribed triangle. In this paper we generalize this theorem to the n-dimensional euclidean space, n ≥ 3. It appears that the ratio of the volume of an n-dimensional solid bounded by an (n − 1)-dimensional hyper-paraboloid and an (n − 1)-dimensional hyperplane and the volume of a certain inscribed cone (we analogously repeat Archimedes’ procedure) depends only on the dimension of the euclidean space and it equals to 2n/(n +1).","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72405953","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}
E. A. Bakare, B. Onasanya, Š. Hošková-Mayerová, O. Olubosede
Abstract The aim of this paper is to analyse the potential impact of multiple current interventions in communities with limited resources in order to obtain optimal control strategies and provide a basis for future predictions of the most effective control measures against the spread of malaria. We developed a population-based model of malaria transmission dynamics to investigate the effectiveness of five different interventions. The model captured both the human and the mosquito compartments. The control interventions considered were: educational campaigns to mobilise people for diagnostic test and treatment and to sleep under bed nets; treatment through mass drug administration; indoor residual spraying(IRS) with insecticide to reduce malaria transmission; insecticide treated net (ITN) to reduce morbidity; and regular destruction of mosquito breeding sites to reduce the number of new mosquito and bites/contact at dusks and dawn. Analysis of the potential impact of the multiple control interventions were carried out and the optimal control strategies that minimized the number of infected human and mosquito and the cost of applying the various control interventions were determined.
{"title":"Analysis of Control Interventions against Malaria in communities with Limited Resources","authors":"E. A. Bakare, B. Onasanya, Š. Hošková-Mayerová, O. Olubosede","doi":"10.2478/auom-2021-0019","DOIUrl":"https://doi.org/10.2478/auom-2021-0019","url":null,"abstract":"Abstract The aim of this paper is to analyse the potential impact of multiple current interventions in communities with limited resources in order to obtain optimal control strategies and provide a basis for future predictions of the most effective control measures against the spread of malaria. We developed a population-based model of malaria transmission dynamics to investigate the effectiveness of five different interventions. The model captured both the human and the mosquito compartments. The control interventions considered were: educational campaigns to mobilise people for diagnostic test and treatment and to sleep under bed nets; treatment through mass drug administration; indoor residual spraying(IRS) with insecticide to reduce malaria transmission; insecticide treated net (ITN) to reduce morbidity; and regular destruction of mosquito breeding sites to reduce the number of new mosquito and bites/contact at dusks and dawn. Analysis of the potential impact of the multiple control interventions were carried out and the optimal control strategies that minimized the number of infected human and mosquito and the cost of applying the various control interventions were determined.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74318023","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}
Abstract We translate some graph properties of 𝔸𝔾(R) and Γ(R) to some topological properties of Zariski topology. We prove that the facts “(1) The zero ideal of R is an anti fixed-place ideal. (2) Min(R) does not have any isolated point. (3) Rad(𝔸𝔾 (R)) = 3. (4) Rad(Γ(R)) = 3. (5) Γ(R) is triangulated (6) 𝔸𝔾 (R) is triangulated.” are equivalent. Also, we show that if the zero ideal of a ring R is a fixed-place ideal, then dtt(𝔸𝔾 (R)) = |ℬ(R)| and also if in addition |Min(R)| > 2, then dt(𝔸𝔾 (R)) = |ℬ (R)|. Finally, it is shown that dt(𝔸𝔾 (R)) is finite if and only if dtt(𝔸𝔾 (R)) is finite if and only if Min(R) is finite.
{"title":"Notes on the zero-divisor graph and annihilating-ideal graph of a reduced ring","authors":"M. Badie","doi":"10.2478/auom-2021-0018","DOIUrl":"https://doi.org/10.2478/auom-2021-0018","url":null,"abstract":"Abstract We translate some graph properties of 𝔸𝔾(R) and Γ(R) to some topological properties of Zariski topology. We prove that the facts “(1) The zero ideal of R is an anti fixed-place ideal. (2) Min(R) does not have any isolated point. (3) Rad(𝔸𝔾 (R)) = 3. (4) Rad(Γ(R)) = 3. (5) Γ(R) is triangulated (6) 𝔸𝔾 (R) is triangulated.” are equivalent. Also, we show that if the zero ideal of a ring R is a fixed-place ideal, then dtt(𝔸𝔾 (R)) = |ℬ(R)| and also if in addition |Min(R)| > 2, then dt(𝔸𝔾 (R)) = |ℬ (R)|. Finally, it is shown that dt(𝔸𝔾 (R)) is finite if and only if dtt(𝔸𝔾 (R)) is finite if and only if Min(R) is finite.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86519228","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}
Abstract Matrix expressions composed by generalized inverses can generally be written as f(A−1, A−2, . . ., A−k), where A1, A2, . . ., Ak are a family of given matrices of appropriate sizes, and (·)− denotes a generalized inverse of matrix. Once such an expression is given, people are primarily interested in its uniqueness (invariance property) with respect to the choice of the generalized inverses. As such an example, this article describes a general method for deriving necessary and sufficient conditions for the matrix equality A1A−2A3A−4A5 = A to always hold for all generalized inverses A−2 and A−4 of A2 and A4 through use of the block matrix representation method and the matrix rank method, and discusses some special cases of the equality for different choices of the five matrices.
{"title":"Invariance property of a five matrix product involving two generalized inverses","authors":"Bo Jiang, Yongge Tian","doi":"10.2478/auom-2021-0006","DOIUrl":"https://doi.org/10.2478/auom-2021-0006","url":null,"abstract":"Abstract Matrix expressions composed by generalized inverses can generally be written as f(A−1, A−2, . . ., A−k), where A1, A2, . . ., Ak are a family of given matrices of appropriate sizes, and (·)− denotes a generalized inverse of matrix. Once such an expression is given, people are primarily interested in its uniqueness (invariance property) with respect to the choice of the generalized inverses. As such an example, this article describes a general method for deriving necessary and sufficient conditions for the matrix equality A1A−2A3A−4A5 = A to always hold for all generalized inverses A−2 and A−4 of A2 and A4 through use of the block matrix representation method and the matrix rank method, and discusses some special cases of the equality for different choices of the five matrices.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84880814","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}
Abstract The main goal of this study is to define a new metric space which is a generalization of complex valued metric spaces introduced by Azam et al. [1] using the set of elliptic numbers𝔼p={∈=υ+iω:υ,ω∈ℝ, i2=p<0},{mathbb{E}_p} = left{ { in = upsilon + iomega :upsilon ,omega in mathbb{R},,,{i^2} = p < 0} right}, and this space is named as an elliptic valued metric space. Some topological properties of this new space are examined. Also, some fixed point results are established in the setting of elliptic valued metric spaces by introducing new classes of mappings which the obtained results are real generalizations of the consequences of several fixed point theorems in the existing literature.
{"title":"Coincidence and Common Fixed Point Theorems via ϱ-Class Functions in Elliptic Valued Metric Spaces","authors":"M. Öztürk, I. A. Kösal, Hidayet Kösal","doi":"10.2478/auom-2021-0011","DOIUrl":"https://doi.org/10.2478/auom-2021-0011","url":null,"abstract":"Abstract The main goal of this study is to define a new metric space which is a generalization of complex valued metric spaces introduced by Azam et al. [1] using the set of elliptic numbers𝔼p={∈=υ+iω:υ,ω∈ℝ, i2=p<0},{mathbb{E}_p} = left{ { in = upsilon + iomega :upsilon ,omega in mathbb{R},,,{i^2} = p < 0} right}, and this space is named as an elliptic valued metric space. Some topological properties of this new space are examined. Also, some fixed point results are established in the setting of elliptic valued metric spaces by introducing new classes of mappings which the obtained results are real generalizations of the consequences of several fixed point theorems in the existing literature.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85842825","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}
Abstract In this paper, we consider the orbits of an affine nonexpansive mapping in Hadamard (nonpositive curvature metric) spaces and prove an ergodic theorem for the inductive mean, which extends the von Neumann linear ergodic theorem. The main result shows that the sequence given by the inductive means of iterations of an affine nonexpansive mapping with a nonempty fixed point set converges strongly to a fixed point of the mapping. A Tauberian theorem is also proved in order to ensure convergence of the iterations.
{"title":"A Mean Ergodic Theorem for Affine Nonexpansive Mappings in Nonpositive Curvature Metric Spaces","authors":"H. Khatibzadeh, Hadi Pouladi","doi":"10.2478/auom-2021-0008","DOIUrl":"https://doi.org/10.2478/auom-2021-0008","url":null,"abstract":"Abstract In this paper, we consider the orbits of an affine nonexpansive mapping in Hadamard (nonpositive curvature metric) spaces and prove an ergodic theorem for the inductive mean, which extends the von Neumann linear ergodic theorem. The main result shows that the sequence given by the inductive means of iterations of an affine nonexpansive mapping with a nonempty fixed point set converges strongly to a fixed point of the mapping. A Tauberian theorem is also proved in order to ensure convergence of the iterations.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86218471","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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