http://www.mscand.dk/issue/feedMATHEMATICA SCANDINAVICA2016-11-18T01:56:35+01:00Andrew Swannmscand@math.au.dkOpen Journal Systemshttp://www.mscand.dk/article/view/24741Reverse Lexicographic Gröbner Bases and Strongly Koszul Toric Rings2016-11-18T01:56:28+01:00Kazunori Matsudamscand@math.au.dkHidefumi Ohsugimscand@math.au.dk<p>Restuccia and Rinaldo proved that a standard graded $K$-algebra $K[x_1,\dots,x_n]/I$ is strongly Koszul if the reduced Gröbner basis of $I$ with respect to any reverse lexicographic order is quadratic. In this paper, we give a sufficient condition for a toric ring $K[A]$ to be strongly Koszul in terms of the reverse lexicographic Gröbner bases of its toric ideal $I_A$. This is a partial extension of a result given by Restuccia and Rinaldo. </p><p> In addition, we show that any strongly Koszul toric ring generated by squarefree monomials is compressed. Using this fact, we show that our sufficient condition for $K[A]$ to be strongly Koszul is both necessary and sufficient when $K[A]$ is generated by squarefree monomials.</p>2016-11-01T00:00:00+01:00Copyright (c) 2016 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/24742Smooth Rational Surfaces Of $d=11$ And $\pi=8$ In $\mathbb{P}^5$2016-11-18T01:56:29+01:00Abdul Moeed Mohammadmscand@math.au.dkWe construct a linearly normal smooth rational surface $S$ of degree $11$ and sectional genus $8$ in the projective five space. Surfaces satisfying these numerical invariants are special, in the sense that $h^1(\mathscr{O}_S(1))>0$. Our construction is done via linear systems and we describe the configuration of points blown up in the projective plane. Using the theory of adjunction mappings, we present a short list of linear systems which are the only possibilities for other families of surfaces with the prescribed numerical invariants. 2016-11-01T00:00:00+01:00Copyright (c) 2016 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/24743On the Simplicity of Multigerms2016-11-18T01:56:30+01:00R. Oset Sinhamscand@math.au.dkM. A. S. Ruasmscand@math.au.dkR. Wik Atiquemscand@math.au.dkWe prove several results regarding the simplicity of germs and multigerms obtained via the operations of augmentation, simultaneous augmentation and concatenation and generalised concatenation. We also give some results in the case where one of the branches is a non-stable primitive germ. Using our results we obtain a list which includes all simple multigerms from $\mathbb{C}^3$ to $\mathbb{C}^3$. 2016-11-01T00:00:00+01:00Copyright (c) 2016 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/24744On Open and Closed Strings2016-11-18T01:56:31+01:00Marius Thaulemscand@math.au.dkCobordism categories are highly complicated structures that can be analyzed by way of their classifying spaces. In the case of surfaces, meaning $2$-dimensional cobordisms, this has led to many important results in recent years. This paper studies the subcategory of open strings of the category of open and closed strings as introduced by Baas, Cohen and Ramírez and identifies the homotopy type of its classifying spaces. 2016-11-01T00:00:00+01:00Copyright (c) 2016 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/24745Zeros of Functions in Bergman-Type Hilbert Spaces of Dirichlet Series2016-11-18T01:56:32+01:00Ole Fredrik Brevigmscand@math.au.dkFor a real number $\alpha$ the Hilbert space $\mathscr{D}_\alpha$ consists of those Dirichlet series $\sum_{n=1}^\infty a_n/n^s$ for which $\sum_{n=1}^\infty |a_n|^2/[d(n)]^\alpha < \infty$, where $d(n)$ denotes the number of divisors of $n$. We extend a theorem of Seip on the bounded zero sequences of functions in $\mathscr{D}_\alpha$ to the case $\alpha>0$. Generalizations to other weighted spaces of Dirichlet series are also discussed, as are partial results on the zeros of functions in the Hardy spaces of Dirichlet series $\mathscr{H}^p$, for $1\leq p <2$. 2016-11-01T00:00:00+01:00Copyright (c) 2016 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/24746A Paley-Wiener Theorem for the Spherical Transform Associated with the Generalized Gelfand Pair $(U(p,q),H_{n})$, $p+q=n$2016-11-18T01:56:33+01:00Silvina Camposmscand@math.au.dk<p>In this work we prove a Paley-Wiener theorem for the spherical transform associated to the generalized Gelfand pair $(H_n\ltimes U(p,q),H_n)$, where $H_n$ is the $2n+1$-dimensional Heisenberg group. </p><p> In particular, by using the identification of the spectrum of $(U(p,q),H_n)$ with a subset $\Sigma$ of $\mathbb{R}^2$, we prove that the restrictions of the spherical transforms of functions in $C_{0}^{\infty}(H_n)$ to appropriated subsets of $\Sigma$, can be extended to holomorphic functions on $\mathbb{C}^2$. Also, we obtain a real variable characterizations of such transforms.</p>2016-11-01T00:00:00+01:00Copyright (c) 2016 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/24747Decomposability of Bimodule Maps2016-11-18T01:56:34+01:00Christian Le Merdymscand@math.au.dkLina Oliveiramscand@math.au.dkConsider a unital $C^*$-algebra $A$, a von Neumann algebra $M$, a unital sub-$C^*$-algebra $C\subset A$ and a unital $*$-homomorphism $\pi\colon C\to M$. Let $u\colon A\to M$ be a decomposable map (i.e. a linear combination of completely positive maps) which is a $C$-bimodule map with respect to $\pi$. We show that $u$ is a linear combination of $C$-bimodule completely positive maps if and only if there exists a projection $e\in \pi(C)'$ such that $u$ is valued in $\mathit{e\mkern0.5muMe}$ and $e\pi({\cdot})e$ has a completely positive extension $A\to \mathit{e\mkern0.5muMe}$. We also show that this condition is always fulfilled when $C$ has the weak expectation property. 2016-11-01T00:00:00+01:00Copyright (c) 2016 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/24748Relative Inner Amenability and Relative Property Gamma2016-11-18T01:56:35+01:00Paul Jolissaintmscand@math.au.dkLet $H$ be a proper subgroup of a discrete group $G$. We introduce a notion of relative inner amenability of $H$ in $G$, we prove some equivalent conditions and provide examples coming mainly from semidirect products, as well as counter-examples. We also discuss the corresponding relative property gamma for pairs of type II$_1$ factors $N\subset M$ and we deduce from this a characterization of discrete, icc groups which do not have property (T). 2016-11-01T00:00:00+01:00Copyright (c) 2016 MATHEMATICA SCANDINAVICA