Pub Date : 2023-06-05DOI: 10.7146/math.scand.a-136533
Sergio Licanic
Given a smooth irreducible curve $S$ with torsion normal bundle on a projective surface $X$, we provide a criterion for the non-emptiness of the moduli of slope stable vector bundles with prescribed Chern classes. The criterion is given in terms of the topology of the pair $(X,S)$.
{"title":"Constructing stable vector bundles from curves with torsion normal bundle","authors":"Sergio Licanic","doi":"10.7146/math.scand.a-136533","DOIUrl":"https://doi.org/10.7146/math.scand.a-136533","url":null,"abstract":"Given a smooth irreducible curve $S$ with torsion normal bundle on a projective surface $X$, we provide a criterion for the non-emptiness of the moduli of slope stable vector bundles with prescribed Chern classes. The criterion is given in terms of the topology of the pair $(X,S)$.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41609429","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 : 2023-06-05DOI: 10.7146/math.scand.a-137125
I. Peeva
We introduce the study of binomial edge ideals over an exterior algebra.
我们介绍了外代数上二项式边理想的研究。
{"title":"Binomial edge ideals over an exterior algebra","authors":"I. Peeva","doi":"10.7146/math.scand.a-137125","DOIUrl":"https://doi.org/10.7146/math.scand.a-137125","url":null,"abstract":"We introduce the study of binomial edge ideals over an exterior algebra.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43447085","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 : 2023-06-05DOI: 10.7146/math.scand.a-136539
Y. Mizuta, T. Shimomura
Our aim in this paper is to establish vanishing Morrey integrability for Riesz potentials of functions in Morrey-Orlicz spaces. We discuss the size of the exceptional sets by using a capacity and Hausdorff measure. We also give Trudinger-type exponential Morrey integrability for Riesz potentials of functions in Morrey-Orlicz spaces.
{"title":"Vanishing Morrey integrability for Riesz potentials in Morrey-Orlicz spaces","authors":"Y. Mizuta, T. Shimomura","doi":"10.7146/math.scand.a-136539","DOIUrl":"https://doi.org/10.7146/math.scand.a-136539","url":null,"abstract":"Our aim in this paper is to establish vanishing Morrey integrability for Riesz potentials of functions in Morrey-Orlicz spaces. We discuss the size of the exceptional sets by using a capacity and Hausdorff measure. We also give Trudinger-type exponential Morrey integrability for Riesz potentials of functions in Morrey-Orlicz spaces.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43563776","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 : 2023-06-05DOI: 10.7146/math.scand.a-136662
Olli Martio
The concept of capacity is an indispensable tool for analysis and path families and their moduli play a fundamental role in a metric space $X$. It is shown that the $AM_p(Gamma )$- and $M_p(Gamma )$-modulus create the capacities, $mathrm {Cap}_p^{AM}(E,G)$ and $mathrm {Cap}_p^{M}(E,G)$, respectively, where Γ is the path family connecting an arbitrary set $E subset G$ to the complement of a bounded open set $G$. The capacities use Lipschitz functions and their upper gradients. For $p > 1$ the capacities coincide but differ for $p=1$. For $p geq 1$ it is shown that the $mathrm {Cap}_p^{AM}(E,G)$-capacity equals to the classical variational Dirichlet capacity of the condenser $(E,G)$ and the $mathrm {Cap}_p^{M}(E,G)$-capacity to the $M_p(Gamma )$-modulus.
{"title":"Capacities from moduli in metric measure spaces","authors":"Olli Martio","doi":"10.7146/math.scand.a-136662","DOIUrl":"https://doi.org/10.7146/math.scand.a-136662","url":null,"abstract":"The concept of capacity is an indispensable tool for analysis and path families and their moduli play a fundamental role in a metric space $X$. It is shown that the $AM_p(Gamma )$- and $M_p(Gamma )$-modulus create the capacities, $mathrm {Cap}_p^{AM}(E,G)$ and $mathrm {Cap}_p^{M}(E,G)$, respectively, where Γ is the path family connecting an arbitrary set $E subset G$ to the complement of a bounded open set $G$. The capacities use Lipschitz functions and their upper gradients. For $p > 1$ the capacities coincide but differ for $p=1$. For $p geq 1$ it is shown that the $mathrm {Cap}_p^{AM}(E,G)$-capacity equals to the classical variational Dirichlet capacity of the condenser $(E,G)$ and the $mathrm {Cap}_p^{M}(E,G)$-capacity to the $M_p(Gamma )$-modulus.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135657342","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 : 2023-02-20DOI: 10.7146/math.scand.a-134098
A. G. Khan, T. Das
In this paper, we introduce topologically stable points, persistent points, persistent property, persistent measures and almost persistent measures for first countable Hausdorff group actions of compact metric spaces. We prove that the set of all persistent points is measurable and it is closed if the action is equicontinuous. We also prove that the set of all persistent measures is a convex set and every almost persistent measure is a persistent measure. Finally, we prove that every equicontinuous pointwise topologically stable first countable Hausdorff group action of a compact metric space is persistent. In particular, every equicontinuous pointwise topologically stable flow is persistent.
{"title":"Topologically stable and persistent points of group actions","authors":"A. G. Khan, T. Das","doi":"10.7146/math.scand.a-134098","DOIUrl":"https://doi.org/10.7146/math.scand.a-134098","url":null,"abstract":"In this paper, we introduce topologically stable points, persistent points, persistent property, persistent measures and almost persistent measures for first countable Hausdorff group actions of compact metric spaces. We prove that the set of all persistent points is measurable and it is closed if the action is equicontinuous. We also prove that the set of all persistent measures is a convex set and every almost persistent measure is a persistent measure. Finally, we prove that every equicontinuous pointwise topologically stable first countable Hausdorff group action of a compact metric space is persistent. In particular, every equicontinuous pointwise topologically stable flow is persistent.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41935957","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 : 2023-02-20DOI: 10.7146/math.scand.a-134298
S. Koumandos, Henrik L. Pedersen
A class of functions called generalized Bernstein functions is studied. The fundamental properties of this class are given and its relation to generalized Stieltjes functions via the Laplace transform is investigated. The subclass of generalized Thorin-Bernstein functions is characterized in different ways. Examples of generalized Bernstein functions include incomplete gamma functions, Lerch's transcendent and some hypergeometric functions.
{"title":"Generalized Bernstein functions","authors":"S. Koumandos, Henrik L. Pedersen","doi":"10.7146/math.scand.a-134298","DOIUrl":"https://doi.org/10.7146/math.scand.a-134298","url":null,"abstract":"A class of functions called generalized Bernstein functions is studied. The fundamental properties of this class are given and its relation to generalized Stieltjes functions via the Laplace transform is investigated. The subclass of generalized Thorin-Bernstein functions is characterized in different ways. Examples of generalized Bernstein functions include incomplete gamma functions, Lerch's transcendent and some hypergeometric functions.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46301616","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 : 2023-02-20DOI: 10.7146/math.scand.a-134104
S. A. Seyed Fakhari
Assume that $G$ is a graph with edge ideal $I(G)$ and let $I(G)^{(s)}$ denote the $s$-th symbolic power of $I(G)$. It is proved that for every integer $sgeq 1$, $$ mathrm{reg} (I(G)^{(s+1)})leq max bigl {mathrm{reg} (I(G))$$ $$+2s, mathrm{reg} bigl (I(G)^{(s+1)}+I(G)^sbigr )bigr }. $$ As a consequence, we conclude that $mathrm{reg} (I(G)^{(2)})leq mathrm{reg} (I(G))+2$, and $mathrm{reg} (I(G)^{(3)})leq mathrm{reg} (I(G))+4$. Moreover, it is shown that if for some integer $kgeq 1$, the graph $G$ has no odd cycle of length at most $2k-1$, then $mathrm{reg} (I(G)^{(s)})leq 2s+mathrm{reg} (I(G))-2$, for every integer $sleq k+1$. Finally, it is proven that $mathrm{reg} (I(G)^{(s)})=2s$, for $sin {2, 3, 4}$, provided that the complementary graph $overline {G}$ is chordal.
{"title":"On the regularity of small symbolic powers of edge ideals of graphs","authors":"S. A. Seyed Fakhari","doi":"10.7146/math.scand.a-134104","DOIUrl":"https://doi.org/10.7146/math.scand.a-134104","url":null,"abstract":"Assume that $G$ is a graph with edge ideal $I(G)$ and let $I(G)^{(s)}$ denote the $s$-th symbolic power of $I(G)$. It is proved that for every integer $sgeq 1$, $$ mathrm{reg} (I(G)^{(s+1)})leq max bigl {mathrm{reg} (I(G))$$ $$+2s, mathrm{reg} bigl (I(G)^{(s+1)}+I(G)^sbigr )bigr }. $$ As a consequence, we conclude that $mathrm{reg} (I(G)^{(2)})leq mathrm{reg} (I(G))+2$, and $mathrm{reg} (I(G)^{(3)})leq mathrm{reg} (I(G))+4$. Moreover, it is shown that if for some integer $kgeq 1$, the graph $G$ has no odd cycle of length at most $2k-1$, then $mathrm{reg} (I(G)^{(s)})leq 2s+mathrm{reg} (I(G))-2$, for every integer $sleq k+1$. Finally, it is proven that $mathrm{reg} (I(G)^{(s)})=2s$, for $sin {2, 3, 4}$, provided that the complementary graph $overline {G}$ is chordal.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43424021","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 : 2022-12-21DOI: 10.7146/math.scand.a-136693
Max Holst Mikkelsen, Jens Kaad
In this note we present explicit formulae for the Haar state on the Vaksman-Soibelman quantum spheres. Our formulae correct various statements appearing in the literature and our proof is straightforward relying simply on properties of the modular automorphism group for the Haar state.
{"title":"The Haar state on the Vaksman-Soibelman quantum spheres","authors":"Max Holst Mikkelsen, Jens Kaad","doi":"10.7146/math.scand.a-136693","DOIUrl":"https://doi.org/10.7146/math.scand.a-136693","url":null,"abstract":"In this note we present explicit formulae for the Haar state on the Vaksman-Soibelman quantum spheres. Our formulae correct various statements appearing in the literature and our proof is straightforward relying simply on properties of the modular automorphism group for the Haar state.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43862923","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 : 2022-12-04DOI: 10.7146/math.scand.a-132282
Vinícius Morelli Cortes
Let $X, Y$ be Banach spaces, τ an infinite cardinal and $1 leq p < infty $. We extend a result by E. Oja by showing that if $X$ has a boundedly complete unconditional basis and either $X widehat{otimes}_{g_p} Y$ or $X widehat{otimes}_{varepsilon _p} Y$ contains a complemented copy of $c_0(tau )$, then $Y$ contains a complemented copy of $c_0(tau )$. We show also that if α is a uniform crossnorm, $X widehat{otimes}_alpha Y$ contains a (complemented) copy of $c_0(tau )$ and the cofinality of τ is strictly greater than the density of $X$, then $Y$ also contains a (complemented) copy of $c_0(tau )$. As an application, we obtain a result concerning complemented copies of $ell _1(tau )$ in $X widehat{otimes}_alpha Y$.
设$X，Y$为Banach空间，τ为无穷基数，$1leqp
{"title":"Copies of $c_0(tau)$ in Saphar tensor products","authors":"Vinícius Morelli Cortes","doi":"10.7146/math.scand.a-132282","DOIUrl":"https://doi.org/10.7146/math.scand.a-132282","url":null,"abstract":"Let $X, Y$ be Banach spaces, τ an infinite cardinal and $1 leq p < infty $. We extend a result by E. Oja by showing that if $X$ has a boundedly complete unconditional basis and either $X widehat{otimes}_{g_p} Y$ or $X widehat{otimes}_{varepsilon _p} Y$ contains a complemented copy of $c_0(tau )$, then $Y$ contains a complemented copy of $c_0(tau )$. We show also that if α is a uniform crossnorm, $X widehat{otimes}_alpha Y$ contains a (complemented) copy of $c_0(tau )$ and the cofinality of τ is strictly greater than the density of $X$, then $Y$ also contains a (complemented) copy of $c_0(tau )$. As an application, we obtain a result concerning complemented copies of $ell _1(tau )$ in $X widehat{otimes}_alpha Y$.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46254145","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 : 2022-12-04DOI: 10.7146/math.scand.a-133418
R. Abita
In this article, we investigate the initial boundary value problem for a pseudo-parabolic equation under the influence of a linear memory term and a logarithmic nonlinear source term [ u_{t}-Delta u_{t}+int _{0}^{t}g( t-s) Delta u( x,s) mathrm {d}s-Delta u][=|u|^{p(cdot ) -2}uln (|u|), ]with a Dirichlet boundary condition. Under appropriate assumptions about the relaxation function $g$, the initial data $u_{0}$ and the function exponent $p$, we not only set the lower bounds for the blow-up time of the solution when blow-up occurs, but also by assuming that the initial energy is negative, we give a new blow-up criterion and an upper bound for the blow-up time of the solution.
{"title":"Bounds for blow-up solutions of a semilinear pseudo-parabolic equation with a memory term and logarithmic nonlinearity in variable space","authors":"R. Abita","doi":"10.7146/math.scand.a-133418","DOIUrl":"https://doi.org/10.7146/math.scand.a-133418","url":null,"abstract":"In this article, we investigate the initial boundary value problem for a pseudo-parabolic equation under the influence of a linear memory term and a logarithmic nonlinear source term [ u_{t}-Delta u_{t}+int _{0}^{t}g( t-s) Delta u( x,s) mathrm {d}s-Delta u][=|u|^{p(cdot ) -2}uln (|u|), ]with a Dirichlet boundary condition.\u0000Under appropriate assumptions about the relaxation function $g$, the initial data $u_{0}$ and the function exponent $p$, we not only set the lower bounds for the blow-up time of the solution when blow-up occurs, but also by assuming that the initial energy is negative, we give a new blow-up criterion and an upper bound for the blow-up time of the solution.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42599709","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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