{"title":"Involutivity degree of a distribution at superdensity points of its tangencies","authors":"S. Delladio","doi":"10.5817/am2021-4-195","DOIUrl":"https://doi.org/10.5817/am2021-4-195","url":null,"abstract":"","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"8 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77319943","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}
We generalize a previous result concerning the geometric realizability of model spaces as curvature homogeneous spaces, and investigate applications of this approach. We find algebraic restrictions to realize a model space as a curvature homogeneous space up to any order, and study the implications of geometrically realizing a model space as a locally symmetric space. We also present algebraic restrictions to realize a curvature model as a homothety curvature homogeneous space up to even orders, and demonstrate that for certain model spaces and realizations, homothety curvature homogeneity implies curvature homogeneity.
{"title":"Algebraic restrictions on geometric realizations of curvature models","authors":"C. Dunn, Zoë Smith","doi":"10.5817/am2021-3-175","DOIUrl":"https://doi.org/10.5817/am2021-3-175","url":null,"abstract":"We generalize a previous result concerning the geometric realizability of model spaces as curvature homogeneous spaces, and investigate applications of this approach. We find algebraic restrictions to realize a model space as a curvature homogeneous space up to any order, and study the implications of geometrically realizing a model space as a locally symmetric space. We also present algebraic restrictions to realize a curvature model as a homothety curvature homogeneous space up to even orders, and demonstrate that for certain model spaces and realizations, homothety curvature homogeneity implies curvature homogeneity.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"11 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76414163","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}
. In this paper, the authors establish sufficient conditions for the existence of solutions to implicit fractional differential inclusions with nonlocal conditions. Both of the cases of convex and nonconvex valued right hand sides are considered.
{"title":"Boundary value problems for Hadamard-Caputo implicit fractional differential inclusions with nonlocal conditions","authors":"Ahmed Zahed, S. Hamani, J. Graef","doi":"10.5817/am2021-5-285","DOIUrl":"https://doi.org/10.5817/am2021-5-285","url":null,"abstract":". In this paper, the authors establish sufficient conditions for the existence of solutions to implicit fractional differential inclusions with nonlocal conditions. Both of the cases of convex and nonconvex valued right hand sides are considered.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"59 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75964505","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}
We consider the half-linear differential equation of the form (p(t)|x′|αsgnx′)′ + q(t)|x|sgnx = 0 , t ≥ t0 , under the assumption that p(t)−1/α is integrable on [t0,∞). It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as t→∞.
{"title":"Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, II","authors":"Manabu Naito","doi":"10.5817/AM2021-1-41","DOIUrl":"https://doi.org/10.5817/AM2021-1-41","url":null,"abstract":"We consider the half-linear differential equation of the form (p(t)|x′|αsgnx′)′ + q(t)|x|sgnx = 0 , t ≥ t0 , under the assumption that p(t)−1/α is integrable on [t0,∞). It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as t→∞.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"9 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87840472","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}
The concept of generalized prime D-filters is introduced in distributive lattices. Generalized prime D-filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime D-filters is introduced in distributive lattices and properties of minimal prime D-filters are then studied with respect to congruences. Some topological properties of the space of all prime D-filters of a distributive lattice are also studied.
{"title":"Generalized prime $D$-filters of distributive lattices","authors":"A. P. P. Kumar, M. S. Rao, K. S. Babu","doi":"10.5817/am2021-3-157","DOIUrl":"https://doi.org/10.5817/am2021-3-157","url":null,"abstract":"The concept of generalized prime D-filters is introduced in distributive lattices. Generalized prime D-filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime D-filters is introduced in distributive lattices and properties of minimal prime D-filters are then studied with respect to congruences. Some topological properties of the space of all prime D-filters of a distributive lattice are also studied.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"62 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75339839","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}
In this article we study graphs with ordering of vertices, we define a generalization called a pseudoordering, and for a graph $H$ we define the $H$-Hamiltonian number of a graph $G$. We will show that this concept is a generalization of both the Hamiltonian number and the traceable number. We will prove equivalent characteristics of an isomorphism of graphs $G$ and $H$ using $H$-Hamiltonian number of $G$. Furthermore, we will show that for a fixed number of vertices, each path has a maximal upper $H$-Hamiltonian number, which is a generalization of the same claim for upper Hamiltonian numbers and upper traceable numbers. Finally we will show that for every connected graph $H$ only paths have maximal $H$-Hamiltonian number.
{"title":"An upper bound of a generalized upper Hamiltonian number of a graph","authors":"Martin Dz'urik","doi":"10.5817/am2021-5-299","DOIUrl":"https://doi.org/10.5817/am2021-5-299","url":null,"abstract":"In this article we study graphs with ordering of vertices, we define a generalization called a pseudoordering, and for a graph $H$ we define the $H$-Hamiltonian number of a graph $G$. We will show that this concept is a generalization of both the Hamiltonian number and the traceable number. We will prove equivalent characteristics of an isomorphism of graphs $G$ and $H$ using $H$-Hamiltonian number of $G$. Furthermore, we will show that for a fixed number of vertices, each path has a maximal upper $H$-Hamiltonian number, which is a generalization of the same claim for upper Hamiltonian numbers and upper traceable numbers. Finally we will show that for every connected graph $H$ only paths have maximal $H$-Hamiltonian number.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"24 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82972040","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}
in the operator order, for all 2 [0; 1] and for every selfadjoint operator A and B on a Hilbert space H whose spectra are contained in I: Notice that a function f is operator concave if f is operator convex. A real valued continuous function f on an interval I is said to be operator monotone if it is monotone with respect to the operator order, i.e., A B with Sp (A) ;Sp (B) I imply f (A) f (B) : For some fundamental results on operator convex (operator concave) and operator monotone functions, see [9] and the references therein. As examples of such functions, we note that f (t) = t is operator monotone on [0;1) if and only if 0 r 1: The function f (t) = t is operator convex on (0;1) if either 1 r 2 or 1 r 0 and is operator concave on (0;1) if 0 r 1: The logarithmic function f (t) = ln t is operator monotone and operator concave on (0;1): The entropy function f (t) = t ln t is operator concave on (0;1): The exponential function f (t) = e is neither operator convex nor operator monotone.
按运算符顺序，对于所有2 [0;1]对于希尔伯特空间H上谱包含在I中的每一个自伴随算子A和B:注意，如果函数f是算子凸，则函数f是算子凹。如果区间I上的实值连续函数f在算子阶上单调，即A B与Sp (A)单调，则称其为算子单调;Sp (B) I暗示f (A) f (B):关于算子凸(算子凹)和算子单调函数的一些基本结果，见[9]及其参考文献。作为此类功能的示例,我们注意到f (t) = t运营商单调在(0,1)当且仅当r 0 1:函数f (t) = t算子凸在(0,1)如果1 r 2或1 0和运营商凹在(0,1)如果0 r 1:对数函数f (t) = ln t运营商单调和运营商凹(0,1):熵函数f (t) = t ln t运营商凹在(0,1):指数函数f (t) = e是单调算子凸和运营商。
{"title":"Norm inequalities for the difference between weighted and integral means of operator differentiable functions","authors":"S. Dragomir","doi":"10.5817/am2020-3-183","DOIUrl":"https://doi.org/10.5817/am2020-3-183","url":null,"abstract":"in the operator order, for all 2 [0; 1] and for every selfadjoint operator A and B on a Hilbert space H whose spectra are contained in I: Notice that a function f is operator concave if f is operator convex. A real valued continuous function f on an interval I is said to be operator monotone if it is monotone with respect to the operator order, i.e., A B with Sp (A) ;Sp (B) I imply f (A) f (B) : For some fundamental results on operator convex (operator concave) and operator monotone functions, see [9] and the references therein. As examples of such functions, we note that f (t) = t is operator monotone on [0;1) if and only if 0 r 1: The function f (t) = t is operator convex on (0;1) if either 1 r 2 or 1 r 0 and is operator concave on (0;1) if 0 r 1: The logarithmic function f (t) = ln t is operator monotone and operator concave on (0;1): The entropy function f (t) = t ln t is operator concave on (0;1): The exponential function f (t) = e is neither operator convex nor operator monotone.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"27 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74587554","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}
Let $K=mathbb{Q}(theta )$ be a pure cubic field, with $theta ^3=D$, where $D$ is a cube-free integer. We will determine the reduced ideals of the order $mathcal{O}=mathbb{Z}[theta ]$ of $K$ which coincides with the maximal order of $K$ in the case where $D$ is square-free and $notequivpm1pmod9$.
{"title":"The reduced ideals of a special order in a pure cubic number field","authors":"A. Azizi, Jamal Benamara, M. C. Ismaili, M. Talbi","doi":"10.5817/am2020-3-171","DOIUrl":"https://doi.org/10.5817/am2020-3-171","url":null,"abstract":"Let $K=mathbb{Q}(theta )$ be a pure cubic field, with $theta ^3=D$, where $D$ is a cube-free integer. We will determine the reduced ideals of the order $mathcal{O}=mathbb{Z}[theta ]$ of $K$ which coincides with the maximal order of $K$ in the case where $D$ is square-free and $notequivpm1pmod9$.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"38 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79980240","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}
Let $d$ be an odd square-free integer, $mgeq 3$, $k$:$=mathbb{Q}(sqrt{d}, sqrt{-1})$, $mathbb{Q}(sqrt{-2}, sqrt{d})$ or $mathbb{Q}(sqrt{-2}, sqrt{-d})$, and $L_{m,d}:=mathbb{Q}(zeta_{2^m},sqrt{d})$. In this paper, we shall determine all the fields $L_{m, d}:=mathbb{Q}(zeta_{2^m},sqrt{d})$, with $mgeq 3$ is an integer, such that the class number of $L_{m, d}$ is odd. Furthermore, using the cyclotomic $mathbb{Z}_2$-extensions of $k$, we compute the rank of the $2$-class group of $L_{m, d}$ whenever the divisors of $d$ are congruent $3$ or $5pmod 8$.
{"title":"On the $2$-class group of some number fields with large degree","authors":"M. M. Chems-Eddin, A. Azizi, A. Zekhnini","doi":"10.5817/AM2021-1-13","DOIUrl":"https://doi.org/10.5817/AM2021-1-13","url":null,"abstract":"Let $d$ be an odd square-free integer, $mgeq 3$, $k$:$=mathbb{Q}(sqrt{d}, sqrt{-1})$, $mathbb{Q}(sqrt{-2}, sqrt{d})$ or $mathbb{Q}(sqrt{-2}, sqrt{-d})$, and $L_{m,d}:=mathbb{Q}(zeta_{2^m},sqrt{d})$. In this paper, we shall determine all the fields $L_{m, d}:=mathbb{Q}(zeta_{2^m},sqrt{d})$, with $mgeq 3$ is an integer, such that the class number of $L_{m, d}$ is odd. Furthermore, using the cyclotomic $mathbb{Z}_2$-extensions of $k$, we compute the rank of the $2$-class group of $L_{m, d}$ whenever the divisors of $d$ are congruent $3$ or $5pmod 8$.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"23 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89082098","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}
The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [3], provides a way of representing immersed surfaces in $mathbb R^3$, and equipping the set of these immersions with a "distance function" (to be precise, a pseudometric) that is easy to compute. Importantly, this distance function is invariant under reparametrizations (i.e., under self-diffeomorphisms of the domain surface) and under rigid motions of $mathbb R^3$. Thus, it induces a distance function on the shape space of immersions, i.e., the space of immersions modulo reparametrizations and rigid motions of $mathbb R^3$. In this paper, we give examples of the degeneracy of this distance function, i.e., examples of immersed surfaces (some closed and some open) that have the same SRNF, but are not the same up to reparametrization and rigid motions. We also prove that the SRNF does distinguish the shape of a standard sphere from the shape of any other immersed surface, and does distinguish between the shapes of any two embedded strictly convex surfaces.
{"title":"Closed surfaces with different shapes that are indistinguishable by the SRNF","authors":"E. Klassen, P. Michor","doi":"10.5817/am2020-2-107","DOIUrl":"https://doi.org/10.5817/am2020-2-107","url":null,"abstract":"The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [3], provides a way of representing immersed surfaces in $mathbb R^3$, and equipping the set of these immersions with a \"distance function\" (to be precise, a pseudometric) that is easy to compute. Importantly, this distance function is invariant under reparametrizations (i.e., under self-diffeomorphisms of the domain surface) and under rigid motions of $mathbb R^3$. Thus, it induces a distance function on the shape space of immersions, i.e., the space of immersions modulo reparametrizations and rigid motions of $mathbb R^3$. In this paper, we give examples of the degeneracy of this distance function, i.e., examples of immersed surfaces (some closed and some open) that have the same SRNF, but are not the same up to reparametrization and rigid motions. We also prove that the SRNF does distinguish the shape of a standard sphere from the shape of any other immersed surface, and does distinguish between the shapes of any two embedded strictly convex surfaces.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"4 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80516270","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：