MATHEMATICA SCANDINAVICA
https://www.mscand.dk/
Mathematica Scandinavicaen-USMATHEMATICA SCANDINAVICA0025-5521<p>Submission of manuscripts implies that the work described has not been published before (except in the form of an abstract or as part of a published lecture, review or thesis), that it is not under consideration for publication elsewhere and that, if and when the manuscript is accepted for publication, the authors agree to automatic transfer of the copyright to the publisher. </p>$k$-shellable simplicial complexes and graphs
https://www.mscand.dk/article/view/102975
<p>In this paper we show that a $k$-shellable simplicial complex is the expansion of a shellable complex. We prove that the face ring of a pure $k$-shellable simplicial complex satisfies the Stanley conjecture. In this way, by applying an expansion functor to the face ring of a given pure shellable complex, we construct a large class of rings satisfying the Stanley conjecture.</p><p>Also, by presenting some characterizations of $k$-shellable graphs, we extend some results due to Castrillón-Cruz, Cruz-Estrada and Van Tuyl-Villareal.</p>Rahim Rahmati-Asghar
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2018-04-082018-04-08122216117810.7146/math.scand.a-102975Topological rigidity of quasitoric manifolds
https://www.mscand.dk/article/view/97303
<p>Quasitoric manifolds are manifolds that admit an action of the torus that is locally the same as the standard action of $T^n$ on $\mathbb{C}^n$. It is known that the quotients of such actions are nice manifolds with corners. We prove that a class of locally standard manifolds, that contains the quasitoric manifolds, is equivariantly rigid, i.e., that any manifold that is $T^n$-homotopy equivalent to a quasitoric manifold is $T^n$-homeomorphic to it.</p>Vassilis MetaftsisStratos Prassidis
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2018-04-082018-04-08122217919610.7146/math.scand.a-97303Pencils and nets on curves arising from rank $1$ sheaves on K3 surfaces
https://www.mscand.dk/article/view/97308
<p>Let $S$ be a K3 surface, $C$ a smooth curve on $S$ with $\mathcal{O} _S(C)$ ample, and $A$ a base-point free $g^2_d$ on $C$ of small degree. We use Lazarsfeld-Mukai bundles to prove that $A$ is cut out by the global sections of a rank $1$ torsion-free sheaf $\mathcal{G} $ on $S$. Furthermore, we show that $c_1(\mathcal{G} )$ with one exception is adapted to $\mathcal{O} _S(C)$ and satisfies $\operatorname{Cliff} (c_1(\mathcal{G} )_{|C})\leq \operatorname{Cliff} (A)$, thereby confirming a conjecture posed by Donagi and Morrison. We also show that the same methods can be used to give a simple proof of the conjecture in the $g^1_d$ case.</p><p>In the final section, we give an example of the mentioned exception where $h^0(C,c_1(\mathcal{G} )_{|C})$ is dependent on the curve $C$ in its linear system, thereby failing to be adapted to $\mathcal{O} _S(C)$.</p>Nils Henry Rasmussen
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2018-04-082018-04-08122219721210.7146/math.scand.a-97308Nearest points on toric varieties
https://www.mscand.dk/article/view/101478
<p>We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the $A$-discriminant in terms of Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point.</p>Martin HelmerBernd Sturmfels
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2018-04-082018-04-08122221323810.7146/math.scand.a-101478Stability of rank two Ulrich bundles on projective $K3$ surfaces
https://www.mscand.dk/article/view/101999
<p>Let $F\subseteq \mathbb{P}^{N}$ be a $K3$ surface of degree $2a$, where $a\ge 2$. In this paper we deal with Ulrich bundles on $F$ of rank $2$. We deal with their stability and we construct $K3$ surfaces endowed with families of non-special Ulrich bundles of rank $2$ for each $a\ge 2$.</p>Gianfranco CasnatiFederica Galluzzi
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2018-04-082018-04-08122223925610.7146/math.scand.a-101999Mappings preserving approximate orthogonality in Hilbert $C^*$-modules
https://www.mscand.dk/article/view/102945
<p>We introduce a notion of approximate orthogonality preserving mappings between Hilbert $C^*$-modules. We define the concept of $(\delta , \varepsilon )$-orthogonality preserving mapping and give some sufficient conditions for a linear mapping to be $(\delta , \varepsilon )$-orthogonality preserving. In particular, if $\mathscr {E}$ is a full Hilbert $\mathscr {A}$-module with $\mathbb {K}(\mathscr {H})\subseteq \mathscr {A} \subseteq \mathbb {B}(\mathscr {H})$ and $T, S\colon \mathscr {E}\to \mathscr {E}$ are two linear mappings satisfying $|\langle Sx, Sy\rangle | = \|S\|^2|\langle x, y\rangle |$ for all $x, y\in \mathscr {E}$ and $\|T - S\| \leq \theta \|S\|$, then we show that $T$ is a $(\delta , \varepsilon )$-orthogonality preserving mapping. We also prove whenever $\mathbb {K}(\mathscr {H})\subseteq \mathscr {A} \subseteq \mathbb {B}(\mathscr {H})$ and $T\colon \mathscr {E} \to \mathscr {F}$ is a nonzero $\mathscr {A}$-linear $(\delta , \varepsilon )$-orthogonality preserving mapping between $\mathscr {A}$-modules, then \[ \bigl \|\langle Tx, Ty\rangle - \|T\|^2\langle x, y\rangle \bigr \|\leq \frac {4(\varepsilon - \delta )}{(1 - \delta )(1 + \varepsilon )} \|Tx\|\|Ty\|\qquad (x, y\in \mathscr {E}). \] As a result, we present some characterizations of the orthogonality preserving mappings.</p>Mohammad Sal MoslehianAli Zamani
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2018-04-082018-04-08122225727610.7146/math.scand.a-102945Clark measures and a theorem of Ritt
https://www.mscand.dk/article/view/104444
<p>We determine when a finite Blaschke product $B$ can be written, in a non-trivial way, as a composition of two finite Blaschke products (Ritt's problem) in terms of the Clark measure for $B$. Our tools involve the numerical range of compressed shift operators and the geometry of certain polygons circumscribing the numerical range of the relevant operator. As a consequence of our results, we can determine, in terms of Clark measures, when two finite Blaschke products commute.</p>Isabelle ChalendarPamela GorkinJonathan R. PartingtonWilliam T. Ross
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2018-04-082018-04-08122227729810.7146/math.scand.a-104444The bounded approximation property of variable Lebesgue spaces and nuclearity
https://www.mscand.dk/article/view/102962
<p>In this paper we prove the bounded approximation property for variable exponent Lebesgue spaces, study the concept of nuclearity on such spaces and apply it to trace formulae such as the Grothendieck-Lidskii formula. We apply the obtained results to derive criteria for nuclearity and trace formulae for periodic operators on $\mathbb{R}^n$ in terms of global symbols.</p>Julio DelgadoMichael Ruzhansky
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2018-04-082018-04-08122229931910.7146/math.scand.a-102962Volume index
https://www.mscand.dk/article/view/105219
Volume indexMathematica Scandinavica
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2018-04-082018-04-081222320320Issue covers
https://www.mscand.dk/article/view/105220
Issure coversMathematica Scandinavica
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2018-04-082018-04-081222