Pub Date : 2023-12-08DOI: 10.17398/2605-5686.38.2.125
Extracta Mathematicae Volumen, A. Sarikaya, ¨O. G¨olbas¸i
Let R be a prime ring of characteristic not 2 and U be a noncentral square closed Lie ideal of R. An additive mapping Hon R is called a homoderivation if H(xy) =H(x)H(y)+H(x)y+xH(y)for all x, y∈R. In this paper we investigate homoderivations satisfying certain differential identitieson square closed Lie ideals of prime rings.
设 R 是特征不为 2 的素环，U 是 R 的一个非中心方形闭列理想。在本文中，我们将研究素环的方闭列理想上满足某些微分等式的同模化。
{"title":"Results on Lie ideals of prime ringswith homoderivations","authors":"Extracta Mathematicae Volumen, A. Sarikaya, ¨O. G¨olbas¸i","doi":"10.17398/2605-5686.38.2.125","DOIUrl":"https://doi.org/10.17398/2605-5686.38.2.125","url":null,"abstract":"Let R be a prime ring of characteristic not 2 and U be a noncentral square closed Lie ideal of R. An additive mapping Hon R is called a homoderivation if H(xy) =H(x)H(y)+H(x)y+xH(y)for all x, y∈R. In this paper we investigate homoderivations satisfying certain differential identitieson square closed Lie ideals of prime rings.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":"83 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139011000","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 : 2023-12-01DOI: 10.17398/2605-5686.38.2.237
S.S. Dragomir
Let H be a Hilbert space. In this paper we show among others that, if f, g are continuous on the interval I with 0 <γ ≤ f (t)/g (t)≤ Γ for t ∈ I and if A and B are selfadjoint operators with Sp (A), Sp (B) ⊂ I, then [f1−ν(A)g ν(A)] ⊗ [f ν(B)g 1−ν(B)] ≤ (1 − ν) f(A) ⊗ g (B) + νg(A) ⊗ f(B) ≤[(γ + Γ)2/4γΓ ]R [f1−ν (A) g ν(A)] ⊗ [f ν(B) g1−ν (B)]. The above inequalities also hold for the Hadamard product “ ◦ ” instead of tensorial product “ ⊗ ”.
假设 H 是一个希尔伯特空间。在本文中，我们特别证明了，如果 f、g 在区间 I 上连续，且 t∈I 时 0 <γ ≤ f (t)/g (t)≤ Γ，并且如果 A 和 B 是 Sp (A)、Sp (B) ⊂ I 的自交算子，那么 [f1-ν(A)g ν(A)] ⊗ [f ν(B)g 1-ν(B)] ≤ Γ、则 [f1-ν(A)g ν(A)] ⊗ [f ν(B)g 1-ν(B)] ≤ (1 -ν) f(A) ⊗ g (B) + νg(A) ⊗ f(B) ≤[(γ + Γ)2/4γΓ ]R [f1-ν (A) g ν(A)] ⊗ [f ν(B) g1-ν (B)].上述不等式对于哈达玛积 " ◦ " 而不是张量积 " ⊗ " 同样成立。
{"title":"Tensorial and Hadamard product inequalities for functions of selfadjoint operators in Hilbert spaces in terms of Kantorovich ratio","authors":"S.S. Dragomir","doi":"10.17398/2605-5686.38.2.237","DOIUrl":"https://doi.org/10.17398/2605-5686.38.2.237","url":null,"abstract":"Let H be a Hilbert space. In this paper we show among others that, if f, g are continuous on the interval I with \u00000 <γ ≤ f (t)/g (t)≤ Γ for t ∈ I \u0000and if A and B are selfadjoint operators with Sp (A), Sp (B) ⊂ I, then \u0000[f1−ν(A)g ν(A)] ⊗ [f ν(B)g 1−ν(B)] ≤ (1 − ν) f(A) ⊗ g (B) + νg(A) ⊗ f(B) \u0000 ≤[(γ + Γ)2/4γΓ ]R [f1−ν (A) g ν(A)] ⊗ [f ν(B) g1−ν (B)]. \u0000The above inequalities also hold for the Hadamard product “ ◦ ” instead of tensorial product “ ⊗ ”.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":"27 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139014492","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 : 2023-12-01DOI: 10.17398/2605-5686.38.2.139
T. De Pauw, P. Bouafia
We study measurable spaces equipped with a σ-ideal of negligible sets. We find conditions under which they admit a localizable locally determined version – a kind of fiber space that locally describes their directions – defined by a universal property in an appropriate category that we introduce. These methods allow to promote each measure space (X, A , µ) to a strictly localizable version (X̂, Â, µ̂), so that the dual of L1 (X, A , µ) is L∞ (X̂, Â, µ̂). Corresponding to this duality is a generalized Radon-Nikodým theorem. We also provide a characterization of the strictly localizable version in special cases that include integral geometric measures, when the negligibles are the purely unrectifiable sets in a given dimension.
{"title":"Radon-Nikodýmification of arbitrary measure spaces","authors":"T. De Pauw, P. Bouafia","doi":"10.17398/2605-5686.38.2.139","DOIUrl":"https://doi.org/10.17398/2605-5686.38.2.139","url":null,"abstract":"We study measurable spaces equipped with a σ-ideal of negligible sets. We find conditions under which they admit a localizable locally determined version – a kind of fiber space that locally describes their directions – defined by a universal property in an appropriate category that we introduce. These methods allow to promote each measure space (X, A , µ) to a strictly localizable version (X̂, Â, µ̂), so that the dual of L1 (X, A , µ) is L∞ (X̂, Â, µ̂). Corresponding to this duality is a generalized Radon-Nikodým theorem. We also provide a characterization of the strictly localizable version in special cases that include integral geometric measures, when the negligibles are the purely unrectifiable sets in a given dimension.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139026314","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 : 2023-12-01DOI: 10.17398/2605-5686.38.2.205
Extracta Mathematicae Volumen, S. Mac´ıas, Jr S.B. Nadler
We determine several classes of continua whose hyperspaces of subcontinua are infinite dimensional and homeomorphic to cones over (usually) other continuum. In particular, we obtain many Peano continua with such a property.
{"title":"Continua whose hyperspace of subcontinua is infinite dimensional and a cone","authors":"Extracta Mathematicae Volumen, S. Mac´ıas, Jr S.B. Nadler","doi":"10.17398/2605-5686.38.2.205","DOIUrl":"https://doi.org/10.17398/2605-5686.38.2.205","url":null,"abstract":"We determine several classes of continua whose hyperspaces of subcontinua are infinite dimensional and homeomorphic to cones over (usually) other continuum. In particular, we obtain many Peano continua with such a property.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":"62 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139023458","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 : 2023-07-20DOI: 10.17398/2605-5686.38.2.235
J.B. Sancho de Salas
We deal with a natural generalization of the classical Fundamental Theorem of Affine Geometry to the case of non bijective maps. This extension geometrically characterizes semiaffine morphisms. It was obtained by W. Zick in 1981, although it is almost unknown. Our aim is to present and discuss a simplified proof of this result.
{"title":"The fundamental theorem of affine geometry","authors":"J.B. Sancho de Salas","doi":"10.17398/2605-5686.38.2.235","DOIUrl":"https://doi.org/10.17398/2605-5686.38.2.235","url":null,"abstract":"We deal with a natural generalization of the classical Fundamental Theorem of Affine Geometry to the case of non bijective maps. This extension geometrically characterizes semiaffine morphisms. It was obtained by W. Zick in 1981, although it is almost unknown. Our aim is to present and discuss a simplified proof of this result.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139357448","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 : 2023-06-01DOI: 10.17398/2605-5686.38.1.105
Extracta Mathematicae Volumen, A. Cavicchioli, F. Spaggiari
We consider some families of one relator groups arising as fundamental groups of 3-dimensional manifolds, and calculate their character varieties in SL(2, C). Then we give simple geometrical descriptions of such varieties, and determine the number of their irreducible components. Our paper relates to the work of Baker-Petersen, Qazaqzeh and Morales-Marcén on the character variety of certain classes of one relator groups, but we use different methods based on the concept of palindrome presentations of given groups.
{"title":"The character variety of one relator groups","authors":"Extracta Mathematicae Volumen, A. Cavicchioli, F. Spaggiari","doi":"10.17398/2605-5686.38.1.105","DOIUrl":"https://doi.org/10.17398/2605-5686.38.1.105","url":null,"abstract":"We consider some families of one relator groups arising as fundamental groups of 3-dimensional manifolds, and calculate their character varieties in SL(2, C). Then we give simple geometrical descriptions of such varieties, and determine the number of their irreducible components. Our paper relates to the work of Baker-Petersen, Qazaqzeh and Morales-Marcén on the character variety of certain classes of one relator groups, but we use different methods based on the concept of palindrome presentations of given groups.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43857039","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 : 2023-06-01DOI: 10.17398/2605-5686.38.1.17
M. Weigt
We consider the question as to whether a quantum system is uniquely determined by all values of all its observables. For this, we consider linearly nuclear GB*-algebras over W*-algebras as models of quantum systems.
{"title":"A note on isomorphisms of quantum systems","authors":"M. Weigt","doi":"10.17398/2605-5686.38.1.17","DOIUrl":"https://doi.org/10.17398/2605-5686.38.1.17","url":null,"abstract":"We consider the question as to whether a quantum system is uniquely determined by all values of all its observables. For this, we consider linearly nuclear GB*-algebras over W*-algebras as models of quantum systems.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42396092","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 : 2023-06-01DOI: 10.17398/2605-5686.38.1.67
Extracta Mathematicae Volumen, B. Dhara, S. Ghosh, G. Sandhu
Let R be a prime ring of characteristic not 2, L a nonzero square closed Lie ideal of R and let F : R → R, G : R → R be generalized derivations associated with derivations d : R → R, g : R → R respectively. In this paper, we study several conditions that imply that the Lie ideal is central. Moreover, it is shown that the assumption of primeness of R can not be removed.
{"title":"On Lie ideals satisfying certain differential identities in prime rings","authors":"Extracta Mathematicae Volumen, B. Dhara, S. Ghosh, G. Sandhu","doi":"10.17398/2605-5686.38.1.67","DOIUrl":"https://doi.org/10.17398/2605-5686.38.1.67","url":null,"abstract":"Let R be a prime ring of characteristic not 2, L a nonzero square closed Lie ideal of R and let F : R → R, G : R → R be generalized derivations associated with derivations d : R → R, g : R → R respectively. In this paper, we study several conditions that imply that the Lie ideal is central. Moreover, it is shown that the assumption of primeness of R can not be removed.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44820156","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 : 2023-06-01DOI: 10.17398/2605-5686.38.1.85
Extracta Mathematicae Volumen, M. MolaeiDerakhtenjani, O. RabieiMotlagh, H. Mohammadinejad
We consider a homogeneous degenerate center of order 2m + 1 and perturb it by a homogeneous polynomial of order 2m. We study the Lyapunov constants around the origin to estimate the number of limit cycles. To do it, we classify the parameters and study their effect on the number of limit cycles. Finally, we find that the perturbed degenerate center without any condition has at least two limit cycles, and the number of the bifurcated limit cycles could reach 2m + 3.
{"title":"Estimating the number of limit cycles for one step perturbed homogeneous degenerate centers","authors":"Extracta Mathematicae Volumen, M. MolaeiDerakhtenjani, O. RabieiMotlagh, H. Mohammadinejad","doi":"10.17398/2605-5686.38.1.85","DOIUrl":"https://doi.org/10.17398/2605-5686.38.1.85","url":null,"abstract":"We consider a homogeneous degenerate center of order 2m + 1 and perturb it by a homogeneous polynomial of order 2m. We study the Lyapunov constants around the origin to estimate the number of limit cycles. To do it, we classify the parameters and study their effect on the number of limit cycles. Finally, we find that the perturbed degenerate center without any condition has at least two limit cycles, and the number of the bifurcated limit cycles could reach 2m + 3.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41592780","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 : 2023-01-23DOI: 10.17398/2605-5686.38.1.51
Extracta Mathematicae Volumen, A. En-guady, A. Boua
We will extend in this paper some results about commutativity of Jordan ideals proved in [2] and [6]. However, we will consider left derivations instead of derivations, which is enough to get good results in relation to the structure of near-rings. We will also show that the conditions imposed in the paper cannot be removed.
{"title":"On Jordan ideals with left derivations in 3-prime near-rings","authors":"Extracta Mathematicae Volumen, A. En-guady, A. Boua","doi":"10.17398/2605-5686.38.1.51","DOIUrl":"https://doi.org/10.17398/2605-5686.38.1.51","url":null,"abstract":"We will extend in this paper some results about commutativity of Jordan ideals proved in [2] and [6]. However, we will consider left derivations instead of derivations, which is enough to get good results in relation to the structure of near-rings. We will also show that the conditions imposed in the paper cannot be removed.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":"158 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41276625","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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