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Involutivity degree of a distribution at superdensity points of its tangencies 分布在其切线的超密度点上的对合度
IF 0.6
Archivum Mathematicum Pub Date : 2021-01-01 DOI: 10.5817/am2021-4-195
S. Delladio
{"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}
引用次数: 0
Algebraic restrictions on geometric realizations of curvature models 曲率模型几何实现的代数限制
IF 0.6
Archivum Mathematicum Pub Date : 2021-01-01 DOI: 10.5817/am2021-3-175
C. Dunn, Zoë Smith
{"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}
引用次数: 0
Boundary value problems for Hadamard-Caputo implicit fractional differential inclusions with nonlocal conditions 具有非局部条件的Hadamard-Caputo隐式分数阶微分内含的边值问题
IF 0.6
Archivum Mathematicum Pub Date : 2021-01-01 DOI: 10.5817/am2021-5-285
Ahmed Zahed, S. Hamani, J. Graef
{"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}
引用次数: 0
Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, II 关于半线性常微分方程非振动解的存在性的注解，2
IF 0.6
Archivum Mathematicum Pub Date : 2021-01-01 DOI: 10.5817/AM2021-1-41
Manabu Naito
{"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}
引用次数: 2
Generalized prime $D$-filters of distributive lattices 分配格的广义素$D$滤子
IF 0.6
Archivum Mathematicum Pub Date : 2021-01-01 DOI: 10.5817/am2021-3-157
A. P. P. Kumar, M. S. Rao, K. S. Babu
{"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}
引用次数: 1
An upper bound of a generalized upper Hamiltonian number of a graph 图的广义上哈密顿数的上界
IF 0.6
Archivum Mathematicum Pub Date : 2020-03-17 DOI: 10.5817/am2021-5-299
Martin Dz'urik
{"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}
引用次数: 1
Norm inequalities for the difference between weighted and integral means of operator differentiable functions 算子可微函数的加权均值与积分均值之差的范数不等式
IF 0.6
Archivum Mathematicum Pub Date : 2020-01-01 DOI: 10.5817/am2020-3-183
S. Dragomir
{"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}
引用次数: 0
The reduced ideals of a special order in a pure cubic number field 纯三次数域中特殊阶的约化理想
IF 0.6
Archivum Mathematicum Pub Date : 2020-01-01 DOI: 10.5817/am2020-3-171
A. Azizi, Jamal Benamara, M. C. Ismaili, M. Talbi
{"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}
引用次数: 0
On the $2$-class group of some number fields with large degree 若干大次数域的$2$-类群
IF 0.6
Archivum Mathematicum Pub Date : 2019-11-25 DOI: 10.5817/AM2021-1-13
M. M. Chems-Eddin, A. Azizi, A. Zekhnini
{"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}
引用次数: 9
Closed surfaces with different shapes that are indistinguishable by the SRNF 具有不同形状的封闭表面，SRNF无法区分
IF 0.6
Archivum Mathematicum Pub Date : 2019-10-23 DOI: 10.5817/am2020-2-107
E. Klassen, P. Michor
{"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}
引用次数: 9
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