Pub Date : 2020-04-13DOI: 10.7146/math.scand.a-128528
Jiaolong Chen, D. Kalaj
Assume that $pin [1,infty ]$ and $u=P_{h}[phi ]$, where $phi in L^{p}(mathbb{S}^{n-1},mathbb{R}^n)$ and $u(0) = 0$. Then we obtain the sharp inequality $lvert u(x) rvert le G_p(lvert x rvert )lVert phi rVert_{L^{p}}$ for some smooth function $G_p$ vanishing at $0$. Moreover, we obtain an explicit form of the sharp constant $C_p$ in the inequality $lVert Du(0)rVert le C_plVert phi rVert le C_plVert phi rVert_{L^{p}}$. These two results generalize and extend some known results from the harmonic mapping theory (D. Kalaj, Complex Anal. Oper. Theory 12 (2018), 545–554, Theorem 2.1) and the hyperbolic harmonic theory (B. Burgeth, Manuscripta Math. 77 (1992), 283–291, Theorem 1).
{"title":"A Schwarz lemma for hyperbolic harmonic mappings in the unit ball","authors":"Jiaolong Chen, D. Kalaj","doi":"10.7146/math.scand.a-128528","DOIUrl":"https://doi.org/10.7146/math.scand.a-128528","url":null,"abstract":"Assume that $pin [1,infty ]$ and $u=P_{h}[phi ]$, where $phi in L^{p}(mathbb{S}^{n-1},mathbb{R}^n)$ and $u(0) = 0$. Then we obtain the sharp inequality $lvert u(x) rvert le G_p(lvert x rvert )lVert phi rVert_{L^{p}}$ for some smooth function $G_p$ vanishing at $0$. Moreover, we obtain an explicit form of the sharp constant $C_p$ in the inequality $lVert Du(0)rVert le C_plVert phi rVert le C_plVert phi rVert_{L^{p}}$. These two results generalize and extend some known results from the harmonic mapping theory (D. Kalaj, Complex Anal. Oper. Theory 12 (2018), 545–554, Theorem 2.1) and the hyperbolic harmonic theory (B. Burgeth, Manuscripta Math. 77 (1992), 283–291, Theorem 1).","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45718196","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}
Pub Date : 2020-04-03DOI: 10.7146/math.scand.a-128529
E. Ballico, Emanuele Ventura
We introduce the strength for sections of a line bundle on an algebraic variety. This generalizes the strength of homogeneous polynomials that has been recently introduced to resolve Stillman's conjecture, an important problem in commutative algebra. We establish the first properties of this notion and give some tool to obtain upper bounds on the strength in this framework. Moreover, we show some results on the usual strength such as the reducibility of the set of strength two homogeneous polynomials.
{"title":"The strength for line bundles","authors":"E. Ballico, Emanuele Ventura","doi":"10.7146/math.scand.a-128529","DOIUrl":"https://doi.org/10.7146/math.scand.a-128529","url":null,"abstract":"We introduce the strength for sections of a line bundle on an algebraic variety. This generalizes the strength of homogeneous polynomials that has been recently introduced to resolve Stillman's conjecture, an important problem in commutative algebra. We establish the first properties of this notion and give some tool to obtain upper bounds on the strength in this framework. Moreover, we show some results on the usual strength such as the reducibility of the set of strength two homogeneous polynomials.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42072756","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}
Pub Date : 2020-04-01DOI: 10.7146/math.scand.a-128971
S. Janson
We study the Banach space $D([0,1]^m)$ of functions of several variables that are (in a certain sense) right-continuous with left limits, and extend several results previously known for the standard case $m=1$. We give, for example, a description of the dual space, and we show that a bounded multilinear form always is measurable with respect to the $sigma$-field generated by the point evaluations. These results are used to study random functions in the space. (I.e., random elements of the space.) In particular, we give results on existence of moments (in different senses) of such random functions, and we give an application to the Zolotarev distance between two such random functions.
{"title":"The space $D$ in several variables: random variables and higher moments","authors":"S. Janson","doi":"10.7146/math.scand.a-128971","DOIUrl":"https://doi.org/10.7146/math.scand.a-128971","url":null,"abstract":"We study the Banach space $D([0,1]^m)$ of functions of several variables that are (in a certain sense) right-continuous with left limits, and extend several results previously known for the standard case $m=1$. We give, for example, a description of the dual space, and we show that a bounded multilinear form always is measurable with respect to the $sigma$-field generated by the point evaluations. These results are used to study random functions in the space. (I.e., random elements of the space.) In particular, we give results on existence of moments (in different senses) of such random functions, and we give an application to the Zolotarev distance between two such random functions.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44516270","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}
Pub Date : 2020-03-29DOI: 10.7146/math.scand.a-115970
S. Dascalescu, C. Nastasescu, L. Nastasescu
If H is a finite-dimensional Hopf algebra acting on a finite-dimensional algebra A, we investigate the transfer of the Frobenius and symmetric properties through the algebra extensions AH⊂A⊂A#H.
{"title":"Hopf algebra actions and transfer of Frobenius and symmetric properties","authors":"S. Dascalescu, C. Nastasescu, L. Nastasescu","doi":"10.7146/math.scand.a-115970","DOIUrl":"https://doi.org/10.7146/math.scand.a-115970","url":null,"abstract":"If H is a finite-dimensional Hopf algebra acting on a finite-dimensional algebra A, we investigate the transfer of the Frobenius and symmetric properties through the algebra extensions AH⊂A⊂A#H.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"126 1","pages":"32-40"},"PeriodicalIF":0.5,"publicationDate":"2020-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49086529","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}
Pub Date : 2020-03-29DOI: 10.7146/math.scand.a-117703
C. Aquino, H. Baltazar, H. Lima
In this article, we deal with complete spacelike hypersurfaces immersed in an open region of the de Sitter space Sn+11 which is known as the steady state space Hn+1. Under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we are able to prove that they must be spacelike hyperplanes of Hn+1. Furthermore, through the analysis of the hyperbolic cylinders of Hn+1, we discuss the importance of the main hypothesis in our results. Our approach is based on a generalized maximum principle at infinity for complete Riemannian manifolds.
{"title":"New characterizations of spacelike hyperplanes in the steady state space","authors":"C. Aquino, H. Baltazar, H. Lima","doi":"10.7146/math.scand.a-117703","DOIUrl":"https://doi.org/10.7146/math.scand.a-117703","url":null,"abstract":"In this article, we deal with complete spacelike hypersurfaces immersed in an open region of the de Sitter space Sn+11 which is known as the steady state space Hn+1. Under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we are able to prove that they must be spacelike hyperplanes of Hn+1. Furthermore, through the analysis of the hyperbolic cylinders of Hn+1, we discuss the importance of the main hypothesis in our results. Our approach is based on a generalized maximum principle at infinity for complete Riemannian manifolds.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"126 1","pages":"61-72"},"PeriodicalIF":0.5,"publicationDate":"2020-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41403709","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}
Pub Date : 2020-03-29DOI: 10.7146/math.scand.a-116243
T. Caraballo, A. P. D. Silva
This paper is devoted to analysis of the stability of the economy according to an extended version of Kaldor's economic growth model. We consider the role of the government and its simultaneous monetary and fiscal policies and we study whether or not a time delay between the recognition and the implementation of its fiscal policy can affect the economic stability. Numerical simulations provide further conclusions about the long-term behavior of the four variables modeled—namely, national income, capacity of production, bonds value and money supply.
{"title":"Stability analysis of a delay differential Kaldor's model with government policies","authors":"T. Caraballo, A. P. D. Silva","doi":"10.7146/math.scand.a-116243","DOIUrl":"https://doi.org/10.7146/math.scand.a-116243","url":null,"abstract":"This paper is devoted to analysis of the stability of the economy according to an extended version of Kaldor's economic growth model. We consider the role of the government and its simultaneous monetary and fiscal policies and we study whether or not a time delay between the recognition and the implementation of its fiscal policy can affect the economic stability. Numerical simulations provide further conclusions about the long-term behavior of the four variables modeled—namely, national income, capacity of production, bonds value and money supply.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"126 1","pages":"117-141"},"PeriodicalIF":0.5,"publicationDate":"2020-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45996672","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}
Pub Date : 2020-03-12DOI: 10.7146/math.scand.a-115624
H. Najafi
In this paper, we extend the Kubo-Ando theory from operator means on C∗-algebras to a Hermitian Banach ∗-algebra A with a continuous involution. For this purpose, we show that if a and b are self-adjoint elements in A with spectra in an interval J such that a≤b, then f(a)≤f(b) for every operator monotone function f on J, where f(a) and f(b) are defined by the Riesz-Dunford integral. Moreover, we show that some convexity properties of the usual operator convex functions are preserved in the setting of Hermitian Banach ∗-algebras. In particular, Jensen's operator inequality is presented in these cases.
{"title":"Some operator inequalities for Hermitian Banach $*$-algebras","authors":"H. Najafi","doi":"10.7146/math.scand.a-115624","DOIUrl":"https://doi.org/10.7146/math.scand.a-115624","url":null,"abstract":"In this paper, we extend the Kubo-Ando theory from operator means on C∗-algebras to a Hermitian Banach ∗-algebra A with a continuous involution. For this purpose, we show that if a and b are self-adjoint elements in A with spectra in an interval J such that a≤b, then f(a)≤f(b) for every operator monotone function f on J, where f(a) and f(b) are defined by the Riesz-Dunford integral. Moreover, we show that some convexity properties of the usual operator convex functions are preserved in the setting of Hermitian Banach ∗-algebras. In particular, Jensen's operator inequality is presented in these cases.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"126 1","pages":"82-98"},"PeriodicalIF":0.5,"publicationDate":"2020-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47024143","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}
Pub Date : 2020-03-04DOI: 10.7146/math.scand.a-128523
M. Andersson, Haakan Samuelsson Kalm
We prove that any smooth mapping between reduced analytic spaces induces a natural pullback operation on smooth differential forms.
我们证明了任何简化解析空间之间的光滑映射都会在光滑微分形式上产生一个自然的回拉运算。
{"title":"A note on smooth forms on analytic spaces","authors":"M. Andersson, Haakan Samuelsson Kalm","doi":"10.7146/math.scand.a-128523","DOIUrl":"https://doi.org/10.7146/math.scand.a-128523","url":null,"abstract":"We prove that any smooth mapping between reduced analytic spaces induces a natural pullback operation on smooth differential forms.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45614211","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}
Pub Date : 2020-02-08DOI: 10.7146/math.scand.a-126041
G. Khimshiashvili, G. Panina, D. Siersma
Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type of leaves are determined. The homology groups of the spaces of polygons with fixed area and perimeter are also determined. Besides, we extend the classical isoperimetric duality to all critical points. In conclusion a few general remarks on dual extremal problems in polygon spaces and beyond are given.
{"title":"Area-perimeter duality in polygon spaces","authors":"G. Khimshiashvili, G. Panina, D. Siersma","doi":"10.7146/math.scand.a-126041","DOIUrl":"https://doi.org/10.7146/math.scand.a-126041","url":null,"abstract":"Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type of leaves are determined. The homology groups of the spaces of polygons with fixed area and perimeter are also determined. Besides, we extend the classical isoperimetric duality to all critical points. In conclusion a few general remarks on dual extremal problems in polygon spaces and beyond are given.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45043164","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}
Pub Date : 2019-11-25DOI: 10.7146/MATH.SCAND.A-122603
Lisa Nicklasson
What can be said about the subalgebras of the polynomial ring, with minimal or maximal Hilbert function? This question was discussed in a recent paper by M. Boij and A. Conca. In this paper we study the subalgebras generated in degree two with minimal Hilbert function. The problem to determine the generators of these algebras transfers into a combinatorial problem on counting maximal north-east lattice paths inside a shifted Ferrers diagram. We conjecture that the subalgebras generated in degree two with minimal Hilbert function are generated by an initial Lex or RevLex segment.
{"title":"Subalgebras generated in degree two with minimal Hilbert function","authors":"Lisa Nicklasson","doi":"10.7146/MATH.SCAND.A-122603","DOIUrl":"https://doi.org/10.7146/MATH.SCAND.A-122603","url":null,"abstract":"What can be said about the subalgebras of the polynomial ring, with minimal or maximal Hilbert function? This question was discussed in a recent paper by M. Boij and A. Conca. In this paper we study the subalgebras generated in degree two with minimal Hilbert function. The problem to determine the generators of these algebras transfers into a combinatorial problem on counting maximal north-east lattice paths inside a shifted Ferrers diagram. We conjecture that the subalgebras generated in degree two with minimal Hilbert function are generated by an initial Lex or RevLex segment.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47569963","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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