MATHEMATICA SCANDINAVICA
http://www.mscand.dk/
Published by 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. Authors may submit manuscripts for publication to any member of the editorial committee.</p><p> </p>Stanley depth and symbolic powers of monomial ideals
http://www.mscand.dk/article/view/25501
<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>S. A. Seyed Fakhari
Copyright (c) 2017 MATHEMATICA SCANDINAVICA
2017-02-232017-02-23120151610.7146/math.scand.a-25501Pseudo-Skolem sequences and graph Skolem labelling
http://www.mscand.dk/article/view/25502
Pseudo-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.David A. PikeAsiyeh SanaeiNabil Shalaby
Copyright (c) 2017 MATHEMATICA SCANDINAVICA
2017-02-232017-02-231201173810.7146/math.scand.a-25502A Boas-type theorem for $\alpha$-monotone functions
http://www.mscand.dk/article/view/25503
We 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.M. DyachenkoA. MukanovE. Nursultanov
Copyright (c) 2017 MATHEMATICA SCANDINAVICA
2017-02-232017-02-231201395810.7146/math.scand.a-25503Free resolution of powers of monomial ideals and Golod rings
http://www.mscand.dk/article/view/25504
<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>N. AltafiN. NematiS. A. Seyed FakhariS. Yassemi
Copyright (c) 2017 MATHEMATICA SCANDINAVICA
2017-02-232017-02-231201596710.7146/math.scand.a-25504On the existence of certain weak Fano threefolds of Picard number two
http://www.mscand.dk/article/view/25505
This 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.Maxim ArapJoseph CutroneNicholas Marshburn
Copyright (c) 2017 MATHEMATICA SCANDINAVICA
2017-02-232017-02-231201688610.7146/math.scand.a-25505Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials
http://www.mscand.dk/article/view/25506
Harmonic 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.Jacques FarautMasato Wakayama
Copyright (c) 2017 MATHEMATICA SCANDINAVICA
2017-02-232017-02-2312018711410.7146/math.scand.a-25506Groupoid algebras as Cuntz-Pimsner algebras
http://www.mscand.dk/article/view/25507
<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>Adam RennieDavid RobertsonAidan Sims
Copyright (c) 2017 MATHEMATICA SCANDINAVICA
2017-02-232017-02-23120111512310.7146/math.scand.a-25507Application of localization to the multivariate moment problem II
http://www.mscand.dk/article/view/25508
<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>Murray Marshall
Copyright (c) 2017 MATHEMATICA SCANDINAVICA
2017-02-232017-02-23120112412810.7146/math.scand.a-25508Extensions of Euclidean operator radius inequalities
http://www.mscand.dk/article/view/25509
<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>Mohammad Sal MoslehianMostafa SattariKhalid Shebrawi
Copyright (c) 2017 MATHEMATICA SCANDINAVICA
2017-02-232017-02-23120112914410.7146/math.scand.a-25509Mild singular potentials as effective Laplacians in narrow strips
http://www.mscand.dk/article/view/25510
We 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.César R. de OliveiraAlessandra A. Verri
Copyright (c) 2017 MATHEMATICA SCANDINAVICA
2017-02-232017-02-23120114516010.7146/math.scand.a-25510Issue covers
http://www.mscand.dk/article/view/25547
Issue covers.Mathematica Scandinavica
Copyright (c) 2017 MATHEMATICA SCANDINAVICA
2017-02-232017-02-231201