MATHEMATICA SCANDINAVICA https://www.mscand.dk/ en-US mscand@math.au.dk (Arne Jensen) mscand@math.au.dk (Anne Mette Christiansen) Tue, 30 Nov 2021 00:00:00 +0100 OJS 3.2.1.4 http://blogs.law.harvard.edu/tech/rss 60 The strength for line bundles https://www.mscand.dk/article/view/128529 <p>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.</p> Edoardo Ballico, Emanuele Ventura Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/128529 Tue, 30 Nov 2021 00:00:00 +0100 Results on the normality of square-free monomial ideals and cover ideals under some graph operations https://www.mscand.dk/article/view/128963 <p>In this paper, we introduce techniques for producing normal square-free monomial ideals from old such ideals. These techniques are then used to investigate the normality of cover ideals under some graph operations. Square-free monomial ideals that come out as linear combinations of two normal ideals are shown to be not necessarily normal; under such a case we investigate the integral closedness of all powers of these ideals.</p> Ibrahim Al-Ayyoub, Mehrdad Nasernejad, Kazem Khashyarmanesh, Leslie G. Roberts, Veronica Crispin Quiñonez Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/128963 Tue, 30 Nov 2021 00:00:00 +0100 On homotopy nilpotency of the octonian plane $\mathbb{O}P^2$ https://www.mscand.dk/article/view/128541 <p>Let $\mathbb{O}P^2_{(p)}$ be the $p$-localization of the Cayley projective plane $\mathbb{O}P^2$ for a prime $p$ or $p=0$. We show that the homotopy nilpotency class $\textrm{nil} \Omega(\mathbb{O}P^2_{(p)})&lt;\infty$ for $p&gt;2$ and $\textrm{nil} \Omega (\mathbb{O}P^2_{(p)})=1$ for $p&gt;5$ or $p=0$. The homotopy nilpotency of remaining Rosenfeld projective planes are discussed as well.</p> Marek Golasi´nski Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/128541 Tue, 30 Nov 2021 00:00:00 +0100 Non-Lebesgue measurability of finite unions of Vitali selectors related to different groups https://www.mscand.dk/article/view/128969 <p>In this paper, we prove that each topological group isomorphism of the additive topological group $(\mathbb{R},+)$ of real numbers onto itself preserves the non-Lebesgue measurability of Vitali selectors of $\mathbb{R}$. Inspired by Kharazishvili's results, we further prove that each finite union of Vitali selectors related to different countable dense subgroups of $(\mathbb{R}, +)$, is not measurable in the Lebesgue sense. From here, we produce a semigroup of sets, for which elements are not measurable in the Lebesgue sense. We finally show that the produced semigroup is invariant under the action of the group of all affine transformations of $\mathbb{R}$ onto itself.</p> Venuste Nyagahakwa, Gratien Haguma Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/128969 Tue, 30 Nov 2021 00:00:00 +0100 KMS states on crossed products by abelian groups https://www.mscand.dk/article/view/128965 <p>We provide a general description of the KMS states for flows whose fixed point algebra satisfies a certain regularity condition. This is then applied to crossed products by discrete groups, and in particular to certain flows on crossed products by discrete abelian groups where the methods can be combined with spectral analysis for abelian automorphism groups.</p> Johannes Christensen, Klaus Thomsen Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/128965 Tue, 30 Nov 2021 00:00:00 +0100 Product property of global $P$-extremal functions https://www.mscand.dk/article/view/129007 <p>In this note, we establish a product property for $P$-extremal functions in the same spirit as the original product formula due to J.&nbsp;Siciak in Ann. Polon. Math., 39 (1981), 175–211. As a consequence, we obtain convexity for the sublevel sets of such extremal functions. Moreover, we also generalize the product property of $P$-extremal functions established by L.&nbsp;Bos and N.&nbsp;Levenberg in Comput. Methods Funct. Theory 18 (2018), 361–388, and later by N.&nbsp;Levenberg and M.&nbsp;Perera, in Contemporary Mathematics 743 (2020), 11–19, in which no restriction on $P$ is needed.</p> Nguyen Quang Dieu, Tang Van Long Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/129007 Tue, 30 Nov 2021 00:00:00 +0100 A note on smooth forms on analytic spaces https://www.mscand.dk/article/view/128523 <p>We prove that any smooth mapping between reduced analytic spaces induces a natural pullback operation on smooth differential forms.</p> Mats Andersson, Håkan Samuelsson Kalm Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/128523 Tue, 30 Nov 2021 00:00:00 +0100 Generalized John Gromov hyperbolic domains and extensions of maps https://www.mscand.dk/article/view/128968 <p>Let $\Omega \subset \mathbb{R}^n$ be a Gromov hyperbolic, $\varphi$-length John domain. We show that there is a uniformly continuous identification between the inner boundary of $\Omega$ and the Gromov boundary endowed with a visual metric, By using this result, we prove the boundary continuity not only for quasiconformal homeomorphisms, but also for more generally rough quasi-isometries between the domains equipped with the quasihyperbolic metrics.</p> Qingshan Zhou, Liulan Li, Antti Rasila Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/128968 Tue, 30 Nov 2021 00:00:00 +0100 The space $D$ in several variables: random variables and higher moments https://www.mscand.dk/article/view/128971 <p>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.</p> Svante Janson Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/128971 Tue, 30 Nov 2021 00:00:00 +0100 Singular integrals and sublinear operators on amalgam spaces and Hardy-amalgam spaces https://www.mscand.dk/article/view/128966 <p>In this paper, we establish the extrapolation theory for the amalgam spaces and the Hardy-amalgam spaces. By using the extrapolation theory, we obtain the mapping properties for the Calderón-Zygmund operators and its commutator, the Carleson operators and establish the Rubio de Francia inequalities for Littlewood-Paley functions of arbitrary intervals to the amalgam spaces. We also obtain the boundedness of the Calder{ó}n-Zygmund operators and the intrinsic square function on the Hardy-amalgam spaces.</p> Kwok-Pun Ho Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/128966 Tue, 30 Nov 2021 00:00:00 +0100 Analytic properties of Ohno function https://www.mscand.dk/article/view/128520 <p>Ohno's relation is a well-known relation on the field of the multiple zeta values and has an interpolation to complex function. In this paper, we call its complex function Ohno function and study it. We consider the region of absolute convergence, give some new expressions, and show new relations of the function. We also give a direct proof of the interpolation of Ohno's relation.</p> Ken Kamano, Tomokazu Onozuka Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/128520 Tue, 30 Nov 2021 00:00:00 +0100 A Schwarz lemma for hyperbolic harmonic mappings in the unit ball https://www.mscand.dk/article/view/128528 <p>Assume that $p\in [1,\infty ]$ 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 $\lVert Du(0)\rVert \le C_p\lVert \phi \rVert \le C_p\lVert \phi \rVert_{L^{p}}$. These two results generalize and extend some known results from the harmonic mapping theory (D.&nbsp;Kalaj, Complex Anal. Oper. Theory 12 (2018), 545–554, Theorem 2.1) and the hyperbolic harmonic theory (B.&nbsp;Burgeth, Manuscripta Math. 77 (1992), 283–291, Theorem 1).</p> Jiaolong Chen, David Kalaj Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/128528 Tue, 30 Nov 2021 00:00:00 +0100 Index https://www.mscand.dk/article/view/129462 <p>Index</p> Mathematica Scandinavica Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/129462 Tue, 30 Nov 2021 00:00:00 +0100 Issue covers https://www.mscand.dk/article/view/129465 <p>Issue covers</p> Mathematica Scandinavica Copyright (c) 2021 MATHEMATICA SCANDINAVICA https://www.mscand.dk/article/view/129465 Tue, 30 Nov 2021 00:00:00 +0100