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Archivum Mathematicum最新文献

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A half-space type property in the Euclidean sphere 欧几里得球的半空间型性质
IF 0.6
Archivum Mathematicum Pub Date : 2022-01-01 DOI: 10.5817/am2022-1-49
M. Velásquez
{"title":"A half-space type property in the Euclidean sphere","authors":"M. Velásquez","doi":"10.5817/am2022-1-49","DOIUrl":"https://doi.org/10.5817/am2022-1-49","url":null,"abstract":". We study the notion of strong r -stability for the context of closed hypersurfaces Σ n ( n ≥ 3) with constant ( r + 1)-th mean curvature H r +1 immersed into the Euclidean sphere S n +1 , where r ∈ { 1 ,...,n − 2 } . In this setting, under a suitable restriction on the r -th mean curvature H r , we establish that there are no r -strongly stable closed hypersurfaces immersed in a certain region of S n +1 , a region that is determined by a totally umbilical sphere of S n +1 . We also provide a rigidity result for such hypersurfaces.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82228974","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
$L_{p}$ inequalities for the growth of polynomials with restricted zeros $L_{p}$不等式对于有限制零的多项式的增长
IF 0.6
Archivum Mathematicum Pub Date : 2022-01-01 DOI: 10.5817/am2022-3-159
N. A. Rather, Suhail Gulzar, A. Bhat
{"title":"$L_{p}$ inequalities for the growth of polynomials with restricted zeros","authors":"N. A. Rather, Suhail Gulzar, A. Bhat","doi":"10.5817/am2022-3-159","DOIUrl":"https://doi.org/10.5817/am2022-3-159","url":null,"abstract":". Let P ( z ) = P n ν =0 a ν z ν be a polynomial of degree at most n which does not vanish in the disk | z | < 1, then for 1 ≤ p < ∞ and R > 1, Boas and Rahman proved In this paper, we improve the above inequality for 0 ≤ p < ∞ by involving some of the coefficients of the polynomial P ( z ). Analogous result for the class of polynomials P ( z ) having no zero in | z | > 1 is also given.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"48 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73911132","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
Initial coefficients for generalized subclasses of bi-univalent functions defined with subordination 具有隶属关系的双一元函数广义子类的初始系数
IF 0.6
Archivum Mathematicum Pub Date : 2022-01-01 DOI: 10.5817/am2022-2-105
G. Singh, G. Singh, Gurmeet Singh
{"title":"Initial coefficients for generalized subclasses of bi-univalent functions defined with subordination","authors":"G. Singh, G. Singh, Gurmeet Singh","doi":"10.5817/am2022-2-105","DOIUrl":"https://doi.org/10.5817/am2022-2-105","url":null,"abstract":". This paper is concerned with certain generalized subclasses of bi-univalent functions defined with subordination in the open unit disc E = { z : | z | < 1 } . The bounds for the initial coefficients for the functions in these classes are studied. The earlier known results follow as special cases.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"57 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72522678","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
Cyclic congruences of slim semimodular lattices and non-finite axiomatizability of some finite structures 细长半模格的循环同余与有限结构的非有限公理化性
IF 0.6
Archivum Mathematicum Pub Date : 2022-01-01 DOI: 10.5817/am2022-1-15
G. Czédli
{"title":"Cyclic congruences of slim semimodular lattices and non-finite axiomatizability of some finite structures","authors":"G. Czédli","doi":"10.5817/am2022-1-15","DOIUrl":"https://doi.org/10.5817/am2022-1-15","url":null,"abstract":". We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among finite graphs. (This fact is a consequence of a general theorem proved by L. Ham and M. Jackson, and the counterpart of this fact for all bipartite graphs in the class of all graphs is a well-known consequence of the compactness theorem.) Also, to exemplify that our method is applicable in various fields of mathematics, we prove that neither finite simple groups, nor the ordered sets of join-irreducible congruences of slim semimodular lattices can be described by finitely many axioms in the class of finite structures. Since a 2007 result of G. Grätzer and E. Knapp, slim semimodular lattices have constituted the most intensively studied part of lattice theory and they have already led to results even in group theory and geometry. In addition to the non-axiomatizability results mentioned above, we present a new property, called Decomposable Cyclic Elements Property, of the congruence lattices of slim semimodular lattices.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"122 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87740124","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: 6
Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator 具有多重泛函时滞的高阶中立型微分方程在导数算子下的振荡行为
IF 0.6
Archivum Mathematicum Pub Date : 2022-01-01 DOI: 10.5817/am2022-2-65
R. Rath, K. C. Panda, S. Rath
{"title":"Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator","authors":"R. Rath, K. C. Panda, S. Rath","doi":"10.5817/am2022-2-65","DOIUrl":"https://doi.org/10.5817/am2022-2-65","url":null,"abstract":". In this article, we obtain sufficient conditions so that every solution of neutral delay differential equation oscillates or tends to zero as t → ∞ , where, n ≥ 1 is any positive integer, p i , r i ∈ C ( n ) ([0 , ∞ ) , R ) and p i are bounded for each i = 1 , 2 ,...,k . Further, f ∈ C ([0 , ∞ ) , R ), g , h , v , u ∈ C ([0 , ∞ ) , [0 , ∞ )), G and H ∈ C ( R , R ). The functional delays r i ( t ) ≤ t , g ( t ) ≤ t and h ( t ) ≤ t and all of them approach ∞ as t → ∞ . The results hold when u ≡ 0 and f ( t ) ≡ 0. This article extends, generalizes and improves some recent results, and further answers some unanswered questions from the literature.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"17 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84764671","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
Bartz-Marlewski equation with generalized Lucas components 广义Lucas分量的Bartz-Marlewski方程
IF 0.6
Archivum Mathematicum Pub Date : 2022-01-01 DOI: 10.5817/am2022-3-189
H. Hashim
{"title":"Bartz-Marlewski equation with generalized Lucas components","authors":"H. Hashim","doi":"10.5817/am2022-3-189","DOIUrl":"https://doi.org/10.5817/am2022-3-189","url":null,"abstract":". Let { U n } = { U n ( P,Q ) } and { V n } = { V n ( P,Q ) } be the Lucas sequences of the first and second kind respectively at the parameters P ≥ 1 and Q ∈ {− 1 , 1 } . In this paper, we provide a technique for characterizing the solutions of the so-called Bartz-Marlewski equation x 2 − 3 xy + y 2 + x = 0 , where ( x,y ) = ( U i ,U j ) or ( V i ,V j ) with i , j ≥ 1. Then, the procedure of this technique is applied to completely resolve this equation with certain values of such parameters.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85304368","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
Remotely $c$-almost periodic type functions in ${mathbb{R}}^{n}$ 远程$c$- ${mathbb{R}}^{n}$中的几乎周期类型函数
IF 0.6
Archivum Mathematicum Pub Date : 2021-07-05 DOI: 10.5817/am2022-2-85
M. Kostić, Vipin Kumar
{"title":"Remotely $c$-almost periodic type functions in ${mathbb{R}}^{n}$","authors":"M. Kostić, Vipin Kumar","doi":"10.5817/am2022-2-85","DOIUrl":"https://doi.org/10.5817/am2022-2-85","url":null,"abstract":"In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely $c$-almost periodic functions in ${mathbb R}^{n},$ slowly oscillating functions in ${mathbb R}^{n},$ and further analyze the recently introduced class of quasi-asymptotically $c$-almost periodic functions in ${mathbb R}^{n}.$ We provide certain applications of our theoretical results to the abstract Volterra integro-differential equations and the ordinary differential equations.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"78 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88142681","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
Four-dimensional Einstein metrics from biconformal deformations 双共形变形的四维爱因斯坦度量
IF 0.6
Archivum Mathematicum Pub Date : 2021-05-08 DOI: 10.5817/am2021-5-255
P. Baird, J. Ventura
{"title":"Four-dimensional Einstein metrics from biconformal deformations","authors":"P. Baird, J. Ventura","doi":"10.5817/am2021-5-255","DOIUrl":"https://doi.org/10.5817/am2021-5-255","url":null,"abstract":"Biconformal deformations take place in the presence of a conformal foliation, deforming by different factors tangent to and orthogonal to the foliation. Four-manifolds endowed with a conformal foliation by surfaces present a natural context to put into effect this process. We develop the tools to calculate the transformation of the Ricci curvature under such deformations and apply our method to construct Einstein $4$-manifolds. One particular family of examples have ends that collapse asymptotically to ${mathbb R}^2$.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"99 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81070161","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
Generalized $c$-almost periodic type functions in ${mathbb{R}}^{n}$ ${mathbb{R}}^{n}$中的广义$c$-概周期型函数
IF 0.6
Archivum Mathematicum Pub Date : 2021-03-29 DOI: 10.5817/am2021-4-221
M. Kosti'c
{"title":"Generalized $c$-almost periodic type functions in ${mathbb{R}}^{n}$","authors":"M. Kosti'c","doi":"10.5817/am2021-4-221","DOIUrl":"https://doi.org/10.5817/am2021-4-221","url":null,"abstract":"Abstract. In this paper, we analyze multi-dimensional quasi-asymptotically c-almost periodic functions and their Stepanov generalizations as well as multidimensional Weyl c-almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically calmost periodic functions and reconsider the notion of semi-c-periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide certain applications of our results to the abstract Volterra integro-differential equations in Banach spaces.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"20 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75278990","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
Properties of solutions of quaternionic Riccati equations 四元数Riccati方程解的性质
IF 0.6
Archivum Mathematicum Pub Date : 2021-02-12 DOI: 10.5817/am2022-2-115
G. Grigorian
{"title":"Properties of solutions of quaternionic Riccati equations","authors":"G. Grigorian","doi":"10.5817/am2022-2-115","DOIUrl":"https://doi.org/10.5817/am2022-2-115","url":null,"abstract":". In this paper we study properties of regular solutions of quaternionic Riccati equations. The obtained results we use for study of the asymptotic behavior of solutions of two first-order linear quaternionic ordinary differential equations.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"68 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75652552","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: 5
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