http://www.mscand.dk/issue/feedMATHEMATICA SCANDINAVICA2017-02-25T06:24:40+01:00Andrew Swannmscand@math.au.dkOpen Journal Systemshttp://www.mscand.dk/article/view/25501Stanley depth and symbolic powers of monomial ideals2017-02-25T06:24:30+01:00S. A. Seyed Fakharifakhari@ipm.ir<p>The aim of this paper is to study the Stanley depth of symbolic powers of a squarefree monomial ideal. We prove that for every squarefree monomial ideal $I$ and every pair of integers $k, s\geq 1$, the inequalities $\mathrm{sdepth} (S/I^{(ks)}) \leq \mathrm{sdepth} (S/I^{(s)})$ and $\mathrm{sdepth}(I^{(ks)}) \leq \mathrm{sdepth} (I^{(s)})$ hold. If moreover $I$ is unmixed of height $d$, then we show that for every integer $k\geq1$, $\mathrm{sdepth}(I^{(k+d)})\leq \mathrm{sdepth}(I^{{(k)}})$ and $\mathrm{sdepth}(S/I^{(k+d)})\leq \mathrm{sdepth}(S/I^{{(k)}})$. Finally, we consider the limit behavior of the Stanley depth of symbolic powers of a squarefree monomial ideal. We also introduce a method for comparing the Stanley depth of factors of monomial ideals.</p>2017-02-23T13:38:35+01:00Copyright (c) 2017 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/25502Pseudo-Skolem sequences and graph Skolem labelling2017-02-25T06:24:31+01:00David A. Pikedapike@mun.caAsiyeh Sanaeiasanaei@mun.caNabil Shalabynshalaby@mun.caPseudo-Skolem sequences, which are similar to Skolem-type sequences in their structure and applications, are introduced. Constructions of such sequences, either directly or via the use of known Skolem-type sequences, are presented. The applicability of these sequences to Skolem labelled graphs, in particular classes of rail-siding graphs and caterpillars, are also discussed.2017-02-23T13:38:35+01:00Copyright (c) 2017 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/25503A Boas-type theorem for $\alpha$-monotone functions2017-02-25T06:24:32+01:00M. Dyachenkodyach@mail.ruA. Mukanovmukanov.askhat@gmail.comE. Nursultanover-nurs@yandex.ruWe define the class of $\alpha$-monotone functions using fractional integrals. For such functions we prove a Boas-type result on the summability of the Fourier coefficients.2017-02-23T13:38:36+01:00Copyright (c) 2017 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/25504Free resolution of powers of monomial ideals and Golod rings2017-02-25T06:24:34+01:00N. Altafinasrinar@kth.seN. Nematinavid.nemati@imj-prg.frS. A. Seyed Fakhariaminfakhari@ut.ac.irS. Yassemiyassemi@ut.ac.ir<p>Let $S = \mathbb{K}[x_1, \dots, x_n]$ be the polynomial ring over a field $\mathbb{K}$. In this paper we present a criterion for componentwise linearity of powers of monomial ideals. In particular, we prove that if a square-free monomial ideal $I$ contains no variable and some power of $I$ is componentwise linear, then $I$ satisfies the gcd condition. For a square-free monomial ideal $I$ which contains no variable, we show that $S/I$ is a Golod ring provided that for some integer $s\geq 1$, the ideal $I^s$ has linear quotients with respect to a monomial order.</p>2017-02-23T13:38:36+01:00Copyright (c) 2017 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/25505On the existence of certain weak Fano threefolds of Picard number two2017-02-25T06:24:35+01:00Maxim Arapmarap@math.jhu.eduJoseph Cutronejoseph.cutrone@goucher.eduNicholas Marshburnmarshbur@math.jhu.eduThis article settles the question of existence of smooth weak Fano threefolds of Picard number two with small anti-canonical map and previously classified numerical invariants obtained by blowing up certain curves on smooth Fano threefolds of Picard number $1$ with the exception of $12$ numerical cases.2017-02-23T13:38:37+01:00Copyright (c) 2017 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/25506Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials2017-02-25T06:24:36+01:00Jacques Farautjacques.faraut@imj-prg.frMasato Wakayamawakayama@imi.kyushu-u.ac.jpHarmonic analysis on Hermitian symmetric spaces of tube type is a natural framework for introducing multivariate Meixner-Pollaczek polynomials. Their main properties are established in this setting: orthogonality, generating and determinantal formulae, difference equations. For proving these properties we use the composition of the following transformations: Cayley transform, Laplace transform, and spherical Fourier transform associated to Hermitian symmetric spaces of tube type. In particular the difference equation for the multivariate Meixner-Pollaczek polynomials is obtained from an Euler type equation on a bounded symmetric domain.2017-02-23T13:38:38+01:00Copyright (c) 2017 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/25507Groupoid algebras as Cuntz-Pimsner algebras2017-02-25T06:24:37+01:00Adam Rennierenniea@uow.edu.auDavid Robertsondave84robertson@gmail.comAidan Simsasims@uow.edu.au<p>We show that if $G$ is a second countable locally compact Hausdorff étale groupoid carrying a suitable cocycle $c\colon G\to\mathbb{Z}$, then the reduced $C^*$-algebra of $G$ can be realised naturally as the Cuntz-Pimsner algebra of a correspondence over the reduced $C^*$-algebra of the kernel $G_0$ of $c$. If the full and reduced $C^*$-algebras of $G_0$ coincide, we deduce that the full and reduced $C^*$-algebras of $G$ coincide. We obtain a six-term exact sequence describing the $K$-theory of $C^*_r(G)$ in terms of that of $C^*_r(G_0)$.</p>2017-02-23T13:38:39+01:00Copyright (c) 2017 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/25508Application of localization to the multivariate moment problem II2017-02-25T06:24:38+01:00Murray Marshallmarshall@math.usask.ca<p>The paper is a sequel to the paper [5], Math. Scand. 115 (2014), 269--286, by the same author. A new criterion is presented for a PSD linear map $L \colon \mathbb{R}[\underline{x}] \to \mathbb{R}$ to correspond to a positive Borel measure on $\mathbb{R}^n$. The criterion is stronger than Nussbaum's criterion (Ark. Math. 6 (1965), 171--191) and is similar in nature to Schmüdgen's criterion in Marshall [5] and Schmüdgen, Ark. Math. 29 (1991), 277--284. It is also explained how the criterion allows one to understand the support of the associated measure in terms of the non-negativity of $L$ on a quadratic module of $\mathbb{R}[\underline{x}]$. This latter result extends a result of Lasserre, Trans. Amer. Math. Soc. 365 (2013), 2489--2504. The techniques employed are the same localization techniques employed already in Marshall (Cand. Math. Bull. 46 (2003), 400--418, and [5]), specifically one works in the localization of $\mathbb{R}[\underline{x}]$ at $p = \prod_{i=1}^n(1+x_i^2)$ or $p' = \prod_{i=1}^{n-1}(1+x_i^2)$.</p>2017-02-23T13:38:39+01:00Copyright (c) 2017 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/25509Extensions of Euclidean operator radius inequalities2017-02-25T06:24:39+01:00Mohammad Sal Moslehianmoslehian@um.ac.irMostafa Sattarimsattari.b@gmail.comKhalid Shebrawikhalid@bau.edu.jo<p>To extend the Euclidean operator radius, we define $w_p$ for an $n$-tuple of operators $(T_1,\dots,T_n)$ in $\mathbb{B}(\mathscr{H})$ by $w_p(T_1,\dots,T_n):= \sup_{\lVert x \rVert =1} (\sum_{i=1}^{n}\lvert \langle T_i x, x \rangle \rvert^p)^{1/p}$ for $p\geq1$. We generalize some inequalities including the Euclidean operator radius of two operators to those involving $w_p$. Further we obtain some lower and upper bounds for $w_p$. Our main result states that if $f$ and $g$ are non-negative continuous functions on $[0,\infty) $ satisfying $f(t) g(t) =t$ for all $t\in [ 0,\infty) $, then \begin{equation*} w_{p}^{rp}( A_{1}^*T_{1}B_{1}, \dots ,A_{n}^*T_{n}B_{n}) \leq \frac{n^{r-1}}{2} \Bigl\lVert \sum_{i=1}^n [ B_{i}^*f^{2}( \lvert T_{i}\rvert ) B_{i}] ^{rp} + [ A_{i}^*g^{2}( \lvert T_{i}^* \rvert ) A_{i}]^{rp} \Bigr\rVert, \end{equation*} for all $p\geq 1$, $r\geq 1$ and operators in $\mathbb{B}(\mathscr{H})$.</p>2017-02-23T13:38:39+01:00Copyright (c) 2017 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/25510Mild singular potentials as effective Laplacians in narrow strips2017-02-25T06:24:40+01:00César R. de Oliveiraoliveira@dm.ufscar.brAlessandra A. Verrialessandraverri@dm.ufscar.brWe propose to obtain information on one-dimensional Schrödinger operators on bounded intervals by approaching them as effective operators of the Laplacian in thin planar strips. Here we develop this idea to get spectral knowledge of some mild singular potentials with Dirichlet boundary conditions. Special preparations, including a result on perturbations of quadratic forms, are included as well.2017-02-23T13:38:40+01:00Copyright (c) 2017 MATHEMATICA SCANDINAVICAhttp://www.mscand.dk/article/view/25547Issue covers2017-02-23T13:38:41+01:00Mathematica Scandinavicamscand@math.au.dkIssue covers.2017-02-23T13:38:41+01:00Copyright (c) 2017 MATHEMATICA SCANDINAVICA