bluuebunny/crossref_metadata_2025 huggingface dataset:
Geometry of homogeneous polynomials on non symmetric convex bodies
Authors: Muñoz-Fernández G. A. , Révész S. Gy. , Seoane-Sepúlveda J. B.
Published: September 2016

If $\Delta$ stands for the region enclosed by the triangle in ${\mathsf R}^2$ of vertices $(0,0)$, $(0,1)$ and $(1,0)$ (or simplex for short), we consider the space ${\mathcal P}(^2\Delta)$ of the 2-homogeneous polynomials on ${\mathsf R}^2$ endowed with the norm given by $\|ax^2+bxy+cy^2\|_\Delta:=\sup\{|ax^2+bxy+cy^2|:(x,y)\in\Delta\}$ for every $a,b,c\in{\mathsf R}$. We investigate some geometrical properties of this norm. We provide an explicit formula for $\|\cdot\|_\Delta$, a full description of the extreme points of the corresponding unit ball and a parametrization and a plot of its unit sphere. Using this geometrical information we also find sharp Bernstein and Markov inequalities for ${\mathcal P}(^2\Delta)$ and show that a classical inequality of Martin does not remain true for homogeneous polynomials on non symmetric convex bodies.
Log-Sine integrals involving series associated with the zeta function and polylogarithms
Authors: Choi Junesang , Cho Young Joon , Srivastava H.M.
Published: September 2016

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the Log-Sine integrals have been evaluated, in the existing literature on the subject, in many different ways. The main object of this paper is to show how nicely some general formulas analogous to the generalized Log-Sine integral $Ls_n^{(m)}\left(\frac{\pi}{3}\right)$ can be obtained by using the theory of Polylogarithms. Relevant connections of the results presented here with those obtained in earlier works are also indicated precisely.
Real interpolation of Sobolev spaces
Authors: Badr Nadine
Published: September 2016

We prove that $W^{1}_{p}$ is a real interpolation space between $W^{1}_{p_{1}}$ and $W^{1}_{p_{2}}$ for $p>q_{0}$ and $1\leq p_{1}<p<p_{2}\leq \infty$ on some classes of manifolds and general metric spaces, where $q_{0}$ depends on our hypotheses.
External analysis of boundary points of convex sets: illumination and visibility
Authors: Moreno José Pedro , Seeger Alberto
Published: September 2016

The purpose of this work is studying the geometry of the boundary $\partial K$ of a solid closed convex set $K$ in a normed space. In a recent paper of ours, such a study has been carried out with the help of supporting cones and drops. Now, illuminated sets and visible sets are the main tools of analysis.
Creating and classifying measures of linear association by optimization techniques
Authors: Pestman Wiebe R.
Published: September 2016

The idea of measures of linear association, such as Pearson's correlation coefficient, can be put in a general framework by axiomization. Groups of linear transformations on $\mathsf{R}^n$ can be exploited to create new and classify existing measures according to their invariance properties. Thus invariance under the Euclidean transformation group leads to the class of so-called geometric measures. Similarly, a measure is called algebraic if it is invariant under scalings. Pearson's coefficient is an example of an algebraic measure; it is not geometric. It is proved that, generally, a measure of linear association cannot possibly be both geometric and algebraic. A procedure is developed to convert a geometric measure into an algebraic and vice versa. Thus a kind of a duality between algebraic and geometric measures arises. In this duality measures can be reflexive or not.
Edge ideals of clique clutters of comparability graphs and the normality of monomial ideals
Authors: Dupont Luis A. , Villarreal Rafael H.
Published: September 2016

The normality of a monomial ideal is expressed in terms of lattice points of blocking polyhedra and the integer decomposition property. For edge ideals of clutters this property characterizes normality. Let $G$ be the comparability graph of a finite poset. If $\mathrm{cl}(G)$ is the clutter of maximal cliques of $G$, we prove that $\mathrm{cl}(G)$ satisfies the max-flow min-cut property and that its edge ideal is normally torsion free. Then we prove that edge ideals of complete admissible uniform clutters are normally torsion free.
Chord properties of digital straight line segments
Authors: Samieinia Shiva
Published: September 2016

We exhibit the structure of digital straight line segments in the 8-connected plane and in the Khalimsky plane by considering vertical distances and unions of two segments.
The noncommutative Choquet Boundary III
Authors: Arveson William
Published: September 2016

We classify operator systems $S\subseteq \mathcal{B}(H)$ that act on finite dimensional Hilbert spaces $H$ by making use of the noncommutative Choquet boundary. $S$ is said to be reduced when its boundary ideal is $\{0\}$. In the category of operator systems, that property functions as semisimplicity does in the category of complex Banach algebras. We construct explicit examples of reduced operator systems using sequences of "parameterizing maps" $\Gamma_k: \mathsf{C}^r\to \mathcal{B}(H_k)$, $k=1,\dots, N$. We show that every reduced operator system is isomorphic to one of these, and that two sequences give rise to isomorphic operator systems if and only if they are "unitarily equivalent" parameterizing sequences. Finally, we construct nonreduced operator systems $S$ that have a given boundary ideal $K$ and a given reduced image in $C^*(S)/K$, and show that these constructed examples exhaust the possibilities.
A Bott inverted model for equivariant unitary topological $K$-theory
Authors: Spitzweck Markus , Østvær Paul Arne
Published: September 2016

Let $\mathsf A$ be an abelian compact Lie group. We show the Bott inverted suspension spectrum of the projective space that classifies $\mathsf A$-equivariant line bundles is a model for $\mathsf A$-equivariant unitary topological $K$-theory.
Automorphism groups and Picard groups of additive full subcategories
Authors: Hiramatsu Naoya , Yoshino Yuji
Published: September 2016

We study category equivalences between additive full subcategories of module categories over commutative rings. And we are able to define the Picard group of additive full subcategories. The aim of this paper is to study the properties of the Picard groups and show that the automorphism group of an additive full subcategory is a semi-direct product of the Picard group with the group of algebra automorphisms of the ring.
Bordism invariance in KK-theory
Authors: Hilsum Michel
Published: September 2016

A bordism invariance property in bivariant K-theory for unbounded Hilbert modules is proved. Various geometric corollaries are deduced.
The unicity of best approximation in a space of compact operators
Authors: Kowynia Joanna
Published: September 2016

Chebyshev subspaces of $\mathcal{K}(c_0,c_0)$ are studied. A $k$-dimensional non-interpolating Chebyshev subspace is constructed. The unicity of best approximation in non-Chebyshev subspaces is considered.
Algebraic quantum hypergroups of discrete type
Authors: Wang Shuanhong
Published: September 2016

In this paper we will study some structures of algebraic quantum hypergroups. First, we construct more examples of algebraic quantum hypergroups of discrete type. Next, we introduce the notion of a generalized quasi-Frobenius multiplier Hopf algebra and then show that generalized quasi-Frobenius multiplier Hopf algebras are a class of algebraic quantum hypergroups of discrete type. We also give some equivalent conditions for an algebraic quantum group to be of discrete type. Finally, we study sub-algebraic quantum hypergroups of discrete type and quotients of algebraic quantum hypergroups of discrete type.
Characterizations of Riesz sets
Authors: Ülger A.
Published: September 2016

Let $G$ be a compact abelian group, $M(G)$ its measure algebra and $L^{1}(G)$ its group algebra. For a subset $E$ of the dual group $\widehat{G}$, let $M_{E}(G)=\{\mu\in M(G):\widehat{\mu}=0$ on $\widehat{G} \backslash E\}$ and $L_{E}^{1}(G)=\{a\in L^{1}(G):\widehat{a}=0$ on $\widehat{G}\backslash E\}$. The set $E$ is said to be a Riesz set if $M_{E}(G)=L_{E}^{1}(G)$. In this paper we present several characterizations of the Riesz sets in terms of Arens multiplication and in terms of the properties of the Gelfand transform $\Gamma :L_{E}^{1}(G)\rightarrow c_{0}(E)$.
$C^*$-algebras arising from Dyck systems of topological Markov chains
Authors: Matsumoto Kengo
Published: September 2016

Let $A$ be an $N \times N$ irreducible matrix with entries in $\{0,1\}$. We define the topological Markov Dyck shift $D_A$ to be a nonsofic subshift consisting of bi-infinite sequences of the $2N$ brackets $(_1,\dots,(_N,)_1,\dots,)_N$ with both standard bracket rule and Markov chain rule coming from $A$. It is regarded as a subshift defined by the canonical generators $S_1^*,\dots, S_N^*, S_1,\dots, S_N$ of the Cuntz-Krieger algebra $\mathcal{O}_A$. We construct an irreducible $\lambda$-graph system $\mathcal{L}^{{\mathrm{Ch}}(D_A)}$ that presents the subshift $D_A$ so that we have an associated simple purely infinite $C^*$-algebra $\mathcal{O}_{\mathcal{L}^{{\mathrm{Ch}}(D_A)}}$. We prove that $\mathcal{O}_{\mathcal{L}^{{\mathrm{Ch}}(D_A)}}$ is a universal unique $C^*$-algebra subject to some operator relations among $2N$ generating partial isometries.
The uniqueness problem for meromorphic functions in the unit disc sharing values and a set in an angular domain
Authors: Xu Hong-Yan , Yi Cai-Feng , Cao Ting-Bin
Published: September 2016

We investigate the uniqueness problem for meromorphic functions in the unit disc sharing four distinct values and one set in an angular domain, and obtain some relations between the Borel points and shared values of meromorphic functions in an angular domain. These results improve the theorem of Mao-Liu [10].
On the relation of Carleson's embedding and the maximal theorem in the context of Banach space geometry
Authors: Hytönen Tuomas , Kemppainen Mikko
Published: September 2016

Hytönen, McIntosh and Portal (J. Funct. Anal., 2008) proved two vector-valued generalizations of the classical Carleson embedding theorem, both of them requiring the boundedness of a new vector-valued maximal operator, and the other one also the type $p$ property of the underlying Banach space as an assumption. We show that these conditions are also necessary for the respective embedding theorems, thereby obtaining new equivalences between analytic and geometric properties of Banach spaces.
Lower bounds for the number of semidualizing complexes over a local ring
Authors: Sather-Wagstaff Sean
Published: September 2016

We investigate the set $\mathfrak(R)$ of shift-isomorphism classes of semi-dualizing $R$-complexes, ordered via the reflexivity relation, where $R$ is a commutative noetherian local ring. Specifically, we study the question of whether $\mathfrak(R)$ has cardinality $2^n$ for some $n$. We show that, if there is a chain of length $n$ in $\mathfrak(R)$ and if the reflexivity ordering on $\mathfrak (R)$ is transitive, then $\mathfrak(R)$ has cardinality at least $2^n$, and we explicitly describe some of its order-structure. We also show that, given a local ring homomorphism $\varphi\colon R\to S$ of finite flat dimension, if $R$ and $S$ admit dualizing complexes and if $\varphi$ is not Gorenstein, then the cardinality of $\mathfrak (S)$ is at least twice the cardinality of $\mathfrak (R)$.
A mini-max problem for self-adjoint Toeplitz matrices
Authors: Courtney Dennis , Sarason Donald
Published: September 2016

We study a minimum problem and associated maximum problem for finite, complex, self-adjoint Toeplitz matrices. If $A$ is such a matrix, of size $(N+1)$-by-$(N+1)$, we identify $A$ with the operator it represents on ${\mathcal P}_N$, the space of complex polynomials of degrees at most $N$, with the usual Hilbert space structure it inherits as a subspace of $L^2$ of the unit circle. The operator $A$ is the compression to ${\mathcal P}_N$ of the multiplication operator on $L^2$ induced by any function in $L^{\infty}$ whose Fourier coefficients of indices between $-N$ and $N$ match the matrix entries of $A$. Our minimum problem is to minimize the $L^{\infty}$ norm of such inducers. We show there is a unique one of minimum norm, and we describe it. The associated maximum problem asks for the maximum of the ratio of the preceding minimum to the operator norm. That problem remains largely open. We present some suggestive numerical evidence.
On the real rank of $C^\ast$-algebras of nilpotent locally compact groups
Authors: Archbold Robert J. , Kaniuth Eberhard
Published: September 2016

If $G$ is an almost connected, nilpotent, locally compact group then the real rank of the $C^\ast$-algebra $C^\ast (G)$ is given by $\operatorname {RR} (C^\ast (G)) = \operatorname {rank} (G/[G,G]) = \operatorname {rank} (G_0/[G_0,G_0])$, where $G_0$ is the connected component of the identity element. In particular, for the continuous Heisenberg group $G_3$, $\operatorname {RR} C^\ast (G_3))=2$.
Holomorphy types and the Fourier-Borel transform between spaces of entire functions of a given type and order defined on Banach spaces
Authors: Fávaro Vinícius V. , Jatobá Ariosvaldo M.
Published: September 2016

Let $E$ be a Banach space and $\Theta$ be a $\pi_{1}$-holomorphy type. The main purpose of this paper is to show that the Fourier-Borel transform is an algebraic isomorphism between the dual of the space ${\operatorname{Exp}}_{\Theta,A}^{k}(E)$ of entire functions on $E$ of order $k$ and $\Theta$-type strictly less than $A$ and the space ${\operatorname{Exp}}_{\Theta^{\prime},0,(\lambda (k) A)^{-1}}^{k^{\prime}}(E^{\prime})$ of entire functions on $E^{\prime}$ of order $k^{\prime}$ and $\Theta^{\prime}$-type less than or equal to $(\lambda(k)A)^{-1}$. The same is proved for the dual of the space ${\operatorname{Exp}}_{\Theta,A}^{k}(E)$ of entire functions on $E$ of order $k$ and $\Theta$-type less than or equal to $A$ and the space ${\operatorname{Exp}}_{\Theta^{\prime}, (\lambda(k)A)^{-1}}^{k^{\prime}}( E^{\prime})$ of entire functions on $E^{\prime}$ of order $k^{\prime}$ and $\Theta^{\prime}$-type strictly less than $(\lambda(k)A)^{-1}$. Moreover, the Fourier-Borel transform is proved to be a topological isomorphism in certain cases.
Szemerédi's theorem, frequent hypercyclicity and multiple recurrence
Authors: Costakis George , Parissis Ioannis
Published: September 2016

Let $T$ be a bounded linear operator acting on a complex Banach space $X$ and $(\lambda_n)_{n\in\mathsf{N}}$ a sequence of complex numbers. Our main result is that if $|\lambda_n|/|\lambda_{n+1}|\to 1$ and the sequence $(\lambda_n T^n)_{n\in\mathsf{N}}$ is frequently universal then $T$ is topologically multiply recurrent. To achieve such a result one has to carefully apply Szemerédi's theorem in arithmetic progressions. We show that the previous assumption on the sequence $( \lambda_n)_{n\in\mathsf{N}}$ is optimal among sequences such that $|\lambda_{n}|/|\lambda_{n+1}|$ converges in $[0,\infty]$. In the case of bilateral weighted shifts and adjoints of multiplication operators we provide characterizations of topological multiple recurrence in terms of the weight sequence and the symbol of the multiplication operator respectively.
Un théorème de l'application ouverte sur les corps valués algébriquement clos
Authors: Moret-Bailly Laurent
Published: September 2016

Let $K$ be an algebraically closed field with a nontrivial absolute value, and let $f:X\to Y$ be a morphism of $K$-schemes of finite type. We show that $f$ is universally open if and only if the induced map on $K$-rational points is open for the topologies deduced from the absolute value. Resumé Soit $K$ un corps algébriquement clos muni d'une valeur absolue non triviale, et soit $f:X\to Y$ un morphisme de $K$-schémas de type fini. On montre que $f$ est universellement ouvert si et seulement si l'application induite sur les points $K$-rationnels est ouverte pour les topologies déduites de la valeur absolue.
Quasi-diagonal flows II
Authors: Kishimoto A.
Published: September 2016

Two similar notions defined for flows, quasi-diagonality and pseudo-diagonality, are shown to be equivalent; so approximately inner flows on a quasi-diagonal $C^{*}$-algebra are quasi-diagonal (not just pseudo-diagonal). We define a notion of MF flow which is weaker than quasi-diagonality and study equivalent conditions following Blackadar and Kirchberg's results on MF algebras and we characterize the dual flow of such on the crossed product as a dual MF flow. In the same spirit we introduce a notion of NF flow and show that NF flows are MF flows on nuclear $C^{*}$-algebras, or equivalently, quasi-diagonal flows on nuclear $C^{*}$-algebras. We also introduce a notion of strong quasi-diagonality (in parallel with strong quasi-diagonality versus quasi-diagonality for $C^{*}$-algebras), whose examples contain AF flows.
Extremal $\omega$-plurisubharmonic functions as envelopes of disc functionals: generalization and applications to the local theory
Authors: Magnússon Benedikt Steinar
Published: September 2016

We generalize the Poletsky disc envelope formula for the function $\sup \{u\in \mathcal{PSH}(X,\omega); u\leq \phi\}$ on any complex manifold $X$ to the case where the real $(1,1)$-current $\omega=\omega_1-\omega_2$ is the difference of two positive closed $(1,1)$-currents and $\varphi$ is the difference of an $\omega_1$-upper semicontinuous function and a plurisubharmonic function.
Structure Constants of the Weyl Calculus
Authors: Deng Wen
Published: September 2016

We find some explicit bounds on the $\mathcal{L}(L^2)$-norm of pseudo-differential operators with symbols defined by a metric on the phase space. In particular, we prove that this norm depends only on the "structure constants" of the metric and a fixed semi-norm of the symbol. Analogous statements are made for the Fefferman-Phong inequality.
On the Theorem of Borel for Quasianalytic Classes
Authors: Bonet José , Meise Reinhold
Published: September 2016

We investigate the surjectivity of the Borel map in the quasianalytic setting for classes of ultradifferentiable functions defined in terms of the growth of the Fourier-Laplace transform. We deal with both the Roumieu $\mathcal{E}_{\{\omega\}}$ and the Beurling $\mathcal{E}_{(\omega)}$ classes for a weight function $\omega$. In particular, we show that a classical result of Carleman for the quasianalytic classes $\mathcal{E}_{\{M_p\}}$ also holds for the classes defined using weights. We also characterize when the space of quasianalytic germs at the origin coincides with the space of real analytic germs at the origin.
Morita Equivalence of Nest Algebras
Authors: Eleftherakis G. K.
Published: September 2016

Let $\mathscr{N}_1$ (resp. $\mathscr{N}_2$) be a nest, $A$ (resp. $B$) be the corresponding nest algebra, $A_0$ (resp. $B_0$) be the subalgebra of compact operators. We prove that the nests $\mathscr{N}_1, \mathscr{N}_2$ are isomorphic if and only if $A$ and $B$ are weakly-$*$ Morita equivalent if and only if $A_0$ and $ B_0$ are strongly Morita equivalent. We characterize the nest isomorphisms which implement stable isomorphism between the corresponding nest algebras.
Asymptotic Approximations of Eigen-Functions for Regular Sturm-Liouville Problems with Eigenvalue Parameter in the Boundary Condition for Integrable Potential
Authors: Coşkun Haskiz , Kabataş Ayşe
Published: September 2016

In this paper we obtain asymptotic estimates of eigenfunctions for regular Sturm-Liouville problems having the eigenparameter in the boundary condition without smoothness conditions on the potential.
Growth of Logarithmic Derivative of Meromorphic Functions
Authors: Latreuch Zinelaâbidine , Belaïdi Benharrat
Published: September 2016

In this paper, we give some estimations about the growth of logarithmic derivative of meromorphic and entire functions and their applications in the theory of differential equations. We give also some examples to explain the sharpness of our results.
On Spectral Triples on Crossed Products Arising From Equicontinuous Actions
Authors: Hawkins A. , Skalski A. , White S. , Zacharias J.
Published: September 2016

The external Kasparov product is used to construct odd and even spectral triples on crossed products of $C^*$-algebras by actions of discrete groups which are equicontinuous in a natural sense. When the group in question is $\mathsf{Z}$ this gives another viewpoint on the spectral triples introduced by Belissard, Marcolli and Reihani. We investigate the properties of this construction and apply it to produce spectral triples on the Bunce-Deddens algebra arising from the odometer action on the Cantor set and some other crossed products of AF-algebras.
Beauville Surfaces with Abelian Beauville Group
Authors: González-Diez G. , Jones G. A. , Torres-Teigell D.
Published: September 2016

A Beauville surface is a rigid surface of general type arising as a quotient of a product of curves $C_{1}$, $C_{2}$ of genera $g_{1},g_{2}\ge 2$ by the free action of a finite group $G$. In this paper we study those Beauville surfaces for which $G$ is abelian (so that $G\cong \mathsf{Z}_{n}^{2}$ with $\gcd(n,6)=1$ by a result of Catanese). For each such $n$ we are able to describe all such surfaces, give a formula for the number of their isomorphism classes and identify their possible automorphism groups. This explicit description also allows us to observe that such surfaces are all defined over $\mathsf{Q}$.
Concrete Realizations of Quotients of Operator Spaces
Authors: Rieffel Marc A.
Published: September 2016

Let $\mathscr{B}$ be a unital C*-subalgebra of a unital C*-algebra $\mathscr{A}$, so that $\mathscr{A}/\mathscr{B}$ is an abstract operator space. We show how to realize $\mathscr{A}/\mathscr{B}$ as a concrete operator space by means of a completely contractive map from $\mathscr{A}$ into the algebra of operators on a Hilbert space, of the form $A \mapsto [Z, A]$ where $Z$ is a Hermitian unitary operator. We do not use Ruan's theorem concerning concrete realization of abstract operator spaces. Along the way we obtain corresponding results for abstract operator spaces of the form $\mathscr{A}/\mathscr{V}$ where $\mathscr{V}$ is a closed subspace of $\mathscr{A}$, and then for the more special cases in which $\mathscr{V}$ is a $*$-subspace or an operator system.
Homeomorphisms of Finite Inner Distortion: Composition Operators on Zygmund-Sobolev and Lorentz-Sobolev Spaces
Authors: Farroni F. , Giova R. , Moscariello G. , Schiattarella R.
Published: September 2016

Let $p > n-1$ and $\alpha\in\mathsf{R}$ and suppose that $f:\Omega\stackrel{\rm onto\,\,}\longrightarrow\Omega^\prime$ is a homeomorphism in the Zygmund-Sobolev space ${\it WL}^{p}\log^{\alpha} L_{\mathop{\rm loc}\nolimits} (\Omega{,}\mathsf{R}^n)$. Define $r{=}\frac p {p-n+1}$. Assume that $u{\in}{\it WL}^r\log^{-\alpha(r-1)} L_{\mathop{\rm loc}\nolimits}(\Omega)$. Then $u\circ\smash{f^{-1}}\in {\rm BV}_{\mathop{\rm loc}\nolimits}(\Omega^\prime)$. We obtain a similar result whenever $f$ is a homeomorphism in the Lorentz-Sobolev space ${\it WL}^{p,q}_{\mathop{\rm loc}\nolimits} (\Omega,\mathsf{R}^n)$ with $p,q>n-1$ and $u\in {\it WL}^{r,s}_{\mathop{\rm loc}\nolimits}(\Omega)$ with $r$ as before and $s=\frac q {q-n+1}$. Moreover, if we further assume that $f$ has finite inner distortion we obtain in both cases $u\circ \smash{f^{-1}}\in W^{1,1}_{\mathop{\rm loc}\nolimits}(\Omega^\prime)$.
Cyclic Vectors in Korenblum Type Spaces
Authors: Hanine Abdelouahab
Published: September 2016

In this paper we use the technique of premeasures, introduced by Korenblum in the 1970's, to give a characterization of cyclic functions in the Korenblum type spaces $\mathscr{A}_{\Lambda}^{-\infty}$. In particular, we give a positive answer to a conjecture by Deninger [7, Conjecture 42].
Coactions on Cuntz-Pimsner Algebras
Authors: Kaliszewski S. , Quigg J. , Robertson D.
Published: September 2016

We investigate how a correspondence coaction gives rise to a coaction on the associated Cuntz-Pimsner algebra. We apply this to recover a recent result of Hao and Ng concerning Cuntz-Pimsner algebras of crossed products of correspondences by actions of amenable groups.
Cuntz-Krieger Algebras Associated with Hilbert $C^*$-Quad Modules of Commuting Matrices
Authors: Matsumoto Kengo
Published: September 2016

Let $\mathscr{O}_{\mathscr{H}^{A,B}_{\kappa}}$ be the $C^*$-algebra associated with the Hilbert $C^*$-quad module arising from commuting matrices $A,B$ with entries in $\{0,1\}$. We will show that if the associated tiling space $X_{A,B}^\kappa$ is transitive, the $C^*$-algebra $\mathscr{O}_{\mathscr{H}^{A,B}_{\kappa}}$ is simple and purely infinite. In particular, for two positive integers $N,M$, the $K$-groups of the simple purely infinite $C^*$-algebra $\mathscr{O}_{\mathscr{H}^{[N],[M]}_{\kappa}}$ are computed by using the Euclidean algorithm.
Tribonacci Numbers Close to the Sum $2^a+3^b+5^c$
Authors: Irmak Nurettin , Szalay László
Published: September 2016

We show that there are exactly 22 solutions to the inequalities \[ 0\le T_n-2^a-3^b-5^c\le10, \] where $T_n$ denotes the $n^{\it th}$ term ($n\ge0$) of the Tribonacci sequence, and $0\le a,b\le c$ are integers. All the solutions are explicitly determined.
On Vertex Decomposable Simplicial Complexes and Their Alexander Duals
Authors: Moradi Somayeh , Khosh-Ahang Fahimeh
Published: September 2016

In this paper we study the Alexander dual of a vertex decomposable simplicial complex. We define the concept of a vertex splittable ideal and show that a simplicial complex $\Delta$ is vertex decomposable if and only if $I_{\Delta^{\vee}}$ is a vertex splittable ideal. Moreover, the properties of vertex splittable ideals are studied. As the main result, it is proved that any vertex splittable ideal has a Betti splitting and the graded Betti numbers of such ideals are explained with a recursive formula. As a corollary, recursive formulas for the regularity and projective dimension of $R/I_{\Delta}$, when $\Delta$ is a vertex decomposable simplicial complex, are given. Moreover, for a vertex decomposable graph $G$, a recursive formula for the graded Betti numbers of its vertex cover ideal is presented. In special cases, this formula is explained, when $G$ is chordal or a sequentially Cohen-Macaulay bipartite graph. Finally, among the other things, it is shown that an edge ideal of a graph is vertex splittable if and only if it has linear resolution.
Real Polynomial Maps and Singular Open Books at Infinity
Authors: Santos Raimundo N. Araújo Dos , Chen Ying , Tibăr Mihai
Published: September 2016

We provide significant conditions under which we prove the existence of stable open book structures at infinity, i.e. on spheres $S^{m-1}_R$ of large enough radius $R$. We obtain new classes of real polynomial maps $\mathsf{R}^m \to \mathsf{R}^p$ which induce such structures.
Essential Spectrum and Fredholm Index for Certain Composition Operators
Authors: Yakes Christopher J.
Published: September 2016

We investigate a composition operator on $H^\infty(U)$, $U$ a subdomain of the open unit disk, for which the essential resolvent has infinitely many components, and for which the Fredholm index of the resolvent operator attains all nonnegative integer values.
The Homotopy Lifting Theorem for Semiprojective $C^*$-Algebras
Authors: Blackadar Bruce
Published: September 2016

We prove a complete analog of the Borsuk Homotopy Extension Theorem for arbitrary semiprojective $C^*$-algebras. We also obtain some other results about semiprojective $C^*$-algebras: a partial lifting theorem with specified quotient, a lifting result for homomorphisms close to a liftable homomorphism, and that sufficiently close homomorphisms from a semiprojective $C^*$-algebra are homotopic.
On Segre Numbers of Homogeneous Map Germs
Authors: Callejas-Bedregal R. , Morgado M. F. Z. , Saia M. J.
Published: September 2016

Segre numbers and Segre cycles of ideals were independently introduced by Tworzewski, by Achilles and Manaresi and by Gaffney and Gassler. They are generalization of the Lê numbers and Lê cycles, introduced by Massey. In this article we give Lê-Iomdine type formulas for these cycles and numbers of arbitrary ideals. As a consequence we give a Plücker type formula for the Segre numbers of ideals generated by weighted homogeneous functions, in terms of their weights and degree. As an application of these results, we compute, in a purely combinatorial manner, the Segre numbers of the ideal which defines the critical loci of a map germ defined by a sequence of central hyperplane arrangements in $\mathsf{C}^{n+1}$.
Construction of the Discrete Hull for the Combinatorics of a Regular Pentagonal Tiling of the Plane
Authors: Ramirez-Solano Maria
Published: September 2016

The article A "regular" pentagonal tiling of the plane by P. L. Bowers and K. Stephenson, Conform. Geom. Dyn. 1, 58-86, 1997, defines a conformal pentagonal tiling. This is a tiling of the plane with remarkable combinatorial and geometric properties. However, it doesn't have finite local complexity in any usual sense, and therefore we cannot study it with the usual tiling theory. The appeal of the tiling is that all the tiles are conformally regular pentagons. But conformal maps are not allowable under finite local complexity. On the other hand, the tiling can be described completely by its combinatorial data, which rather automatically has finite local complexity. In this paper we give a construction of the discrete hull just from the combinatorial data. The main result of this paper is that the discrete hull is a Cantor space.
On Vandermonde Varieties
Authors: Fröberg Ralf , Shapiro Boris
Published: September 2016

Motivated by the famous Skolem-Mahler-Lech theorem we initiate in this paper the study of a natural class of determinantal varieties, which we call Vandermonde varieties. They are closely related to the varieties consisting of all linear recurrence relations of a given order possessing a non-trivial solution vanishing at a given set of integers. In the regular case, i.e., when the dimension of a Vandermonde variety is the expected one, we present its free resolution, obtain its degree and the Hilbert series. Some interesting relations among Schur polynomials are derived. Many open problems and conjectures are posed.
Negotiating experience in patient involvement: Challenges of practicing storytelling in health care conversations
Authors: Terkelsen Morten Deleuran , Wittrup Inge
Published: September 2016

This paper investigates the challenges of integrating patient experiences in patient involving health care interventions. Experience occupying a central importance is often perceived to be something inherent to the patient to be communicated to the health professional during conversations. Yet drawing on empirical material from an ‘Intercultural Health Conversation’ and by departing in anthropological debates seeing experience as something socially expressed and negotiated this article demonstrates how boundaries and constraints emerge when experiences become socially expressed through the practice of storytelling in conversations in health care.
Det æstetiske indtryks betydning for sundhed, sygdom og velvære
Authors: Birkelund Regner
Published: September 2016

I artiklen belyses den betydning for sundhed og velvære, som æstetikken er blevet tillagt i forskellige historiske perioder. Der knyttes an ved det antikke Grækenland, hvor overbevisningen om æstetikkens positive indflydelse på sundhed og sygdom, manifesterede sig i de mange lægehelligdommes arkitektoniske indretning og kunstneriske udsmykning. Det belyses endvidere, hvordan markante tænkere inden for den fænomenologiske tradition har forbundet det æstetiske indtryk med sundhedsrelaterede livsfænomener som livsglæde og livsmod, tryghed og velvære. Fra det historiske og fænomenologiske perspektiv på æstetik og sundhed trækkes en linje til nyere forskning, som bekræfter de æstetiske indtryks positive betydning.
Environmental qualities and patient well-being in hospital settings
Authors: Frandsen Anne Kathrine
Published: September 2016

Within the last decades the impacts of the physical environments of hospitals on healing and health-care outcomes have been subject to ample research. The amount of documentation linking the design of physical environments to patient and staff outcomes is increasing. A Danish research project undertaken by Architecture and Design and the Danish Building Research Institute (Aalborg University) set out in 2008 to review research on the impact of the environmental qualities of health-care facilities on patients and staff. The objective of the review team was to develop a tool that would allow an overview of this research, needed by construction clients and decision-makers in Denmark responsible for large investments in future hospitals and healthcare environments in the decade to come. The present paper offers an overview of the findings of the review team. Its point of departure is the categorisation developed during the study, which facilitated the sorting and communication of the findings. In this categorisation, research findings are grouped according to their focus on specific spatial qualities – such as light and acoustics – and not according to the different diagnoses, which may be linked to such spatial qualities, like stress and depression. In other words, the application of this categorisation foregrounds the importance and the convenience of looking at spatial qualities of the physical environment, when addressing issues related to patient or staff wellbeing.
Unwanted Childlessness and NRTs in Italy: Biology and Sociality in a Political and Infra-political Struggle
Authors: Lesmo Ilaria
Published: September 2016

This article explores the way in which people with unwanted childlessness who are undergoing the New Reproductive Technologies (NRTs) interpret and experience such technologies and their own affliction after the approval of Law 40/2004 (the first Italian law ruling NRTs’ usage). The work is grounded on an ethnographic research carried out between 2005 and 2008: in that period Law 40/2004 had just been approved and the Country was facing a socio-economical crisis. This paper specifically focuses on the narratives of seven people (six women and a man) with unwanted childlessness, whose accounts were collected during the fieldwork. Those people had undergone NRTs just before or immediately after the approval of the law.The exploration of their narratives shows, in the first place, that unwanted childlessness can be considered as a socially produced disorder in a context of structural violence. In fact, the affliction proves to be the embodied answer to limiting socio-economical conditions, further sharpened by the law’s obligations. Secondly, the analysis depicts some infra-political practices performed by people with unwanted childlessness in order to react to the situation. The work particularly underlines that those people devised some strategies - both symbolic and practical ones - in order to exert their own agency.In conclusion, unwanted childlessness results to be an embodied commentary on the structural violence imposed on some people by socio-economical conditions. From that situation of violence, new representations, and new practices have arisen, aiming to oppose the constraints which burden some reproductive experiences.
Sygdom, normalitet og egenomsorg: Diabetiske fodsår og valgfrihedens logik
Authors: Andersen Signe Lindgård , Steffen Vibeke
Published: September 2016

Med udgangspunkt i tre personers sygdomsfortællinger handler denne artikel om mennesker med diabetiske fodsår ud fra et patientperspektiv med særligt fokus på de måder, hvorpå sygdom, normalitet og egenomsorg fremstår som en palet af valgmuligheder, den enkelte patient må forholde sig til og handle ud fra. Formålet er at vise, hvordan bestemte opfattelser af diabetes som en sygdom, der relativt let kan reguleres og derfor tillader diabetikeren af leve et næsten normalt liv, får konsekvenser for udvikling og behandling af fodsår. Analysen er inspireret dels af antropologiske studier af diabetespatienter, som netop har påpeget denne særlige normalitetsdiskurs, hvor dét at være en person med diabetes ikke nødvendigvis associeres med at være syg, dels af den hollandske filosof og samfundsforsker Annemarie Mols begreber om valgfrihedens logik og omsorgens logik, som sætter spørgsmålstegn ved det hensigtsmæssige i at påføre individet øget ansvar for egen sygdom. I den forbindelse ønsker vi at pege på personer med diabetiske fodsår som en gruppe af særligt sårbare patienter, der har behov for både omsorg og valgfrihed.
Forsknings kvalitative fundament. Om kvalitativ naturvidenskab og objektivt feltarbejde
Authors: Seeberg Jens
Published: September 2016

Med udgangspunkt i det forhold, at naturvidenskabelig metode ofte også er kvalitativ – baseret på formbestemmelse og afhængig af fortolkning – diskuteres nogle af de misforståelser, som af og til præger diskussioner af objektivitet og generalisérbarhed i kvalitativ analyse. Kvalitativ forskning kan bestemmes i relation til en række forskellige videnskabelige ræsonneringsstile, men det er kun få ræsonneringsstile der kan anvendes til at vurdere kvaliteten af kvalitativ forskning. Begrebet objektivitet bestemmes med inspiration fra Latour som genstandsfeltets mulighed for at yde modstand mod den analytiske ramme. Dette objektivitetsbegreb er fælles for human, social og naturvidenskab og indebærer et radikalt opgør med forestillingen om at kvalitativ metode er mere ’subjektiv’ end kvantitativ metode. Derimod er kvalitativ forskning bedre stillet til at forstå kontekstuelle forhold, herunder forskerens position i forhold til det studerede. Kontekstens rolle hvad angår analysens generelle udsigelseskraft diskuteres i lyset af en skelnen mellem deskriptiv og analytisk kvalitativ forskning, og artiklen argumenterer for, at den grundliggende forskel mellem naturvidenskab og humanvidenskab ikke kan reduceres til forkærlighed for bestemte metoder men primært beror på objektets evne til at reflektere over og reagere meningsfuldt på den menneskelige interaktion, hvori forskningsprocessen indgår. Artiklen afrundes med en diskussion af de seneste tyve års intense interesse for kvalitativ metode og de konsekvenser den har for tværfagligt samarbejde på tværs af ræsonneringsstile indenfor sundhedsforskning.
I grænselandet mellem optimering og helbredelse: Alternativ behandling som medicinsk forbedringsteknologi
Authors: Pedersen Inger Kryger
Published: September 2016

Alternative behandlingsformers stigende popularitet i vestlige lande forklares oftest med lægevidenskabens utilstrækkelige håndtering af især kroniske sygdomme, men også lægers distance og manglende empati overfor patienterne. Imidlertid tyder flere undersøgelser på, at brugere af alternativ behandlingsformer anvender det konventionelle system i endnu højere grad end folk, der ikke har erfaringer med alternativ behandling. I artiklen diskuteres med udgangspunkt i en brugerundersøgelse, hvorfor en udbredt anvendelse af alternativ behandling ikke nødvendigvis er udtryk for en afvisning af teknologiske metoder inden for biomedicinen. Der argumenteres for, at udbredelsen kan ses i perspektivet af en tendens til optimering og præstationsfremme, og at alternative behandlingsformer kan betragtes som medicinske forbedringsteknologier.
Mistede liv og nye chancer: Kropsdelenes komplekse sociale betydninger i
Authors: Jensen Anja Marie Bornø
Published: September 2016

Denne artikel udforsker gennem empiriske eksempler fra forskning i USA og Danmark de mange betydninger, der knytter sig til kroppens dele i den særlige medicinske teknologi, der omhandler organdonation og transplantation. Formålet er at nuancere den nuværende fremherskende forestilling om og fremstilling af organer som en efterspurgt mangelvare for syge patienter på ventelisterne. Artiklen belyser i stedet hvorledes kroppens organer er komplekse og flertydige symboler på liv og død, der gennem strategiske processer tillægges meningsfulde betydninger af såvel modtagere som donorpårørende. Det diskuteres ligeledes hvordan opfattelsen af kroppens organer bliver afgørende for, hvorledes efterladte pårørende håndterer sorgen over et pludseligt dødsfald, og på hvilke måder donation af organer afføder komplekse sociale relationer i denne medicinske kontekst. Endelig diskuteres det hvordan forskellige opfattelser af ejerskab af kroppens organer og deres betydning for ritualer og praksisser omkring døden kan afstedkomme kontroverser blandt både pårørende og det me­dicinske personale.
Variationer af liv i døden: Transcendenser i hverdagslivets (nye) polydoksi
Authors: Rubow Cecilie , Johannessen-Henry Christine Tind
Published: September 2016

Mennesker som har mistet nærtstående, eller som står i fare for at miste deres liv på grund af sygdom, har ofte en mangfoldighed af forestillinger om livets forhold til døden. Det fænomen at der er flere variationer af liv i døden, er omdrejningspunktet for denne artikel. Som henholdsvis antropolog og teolog [i] er vi særligt optagede af hvordan mennesker erfarer og formulerer flere former for transcendens, dvs. overskridende forhold mellem ’denne verden’ og ’den anden verden’, i et samfund præget af især kristen kosmologi, vestlig videnskab, men også en hel række andre kosmologier. Forestillinger om liv i og efter døden vil vi se som udtryk for erfaringer af menneskelig forbundethed og adskillelse i forhold til medmennesker og verden og ad den vej forsøge at eksplicitere den polydoksi, dvs. de mangeartede former for tro, som kommer til udtryk.
De store teoriers fald - Træk af sorgteori gennem tiden
Authors: Guldin Mai-britt
Published: September 2016

Sorg er et eksistentielt livsvilkår de fleste mennesker gennemlever flere gange i deres liv. I de fleste tilfælde er sorg pinefuld om end ikke udtryk for psykopatologi. Teoretikere har beskæftiget sig med fænomenet sorg gennem det seneste århundrede. Teorierne handler om beskrivelsen af sorgreaktionen, hvordan forskellige personligheder håndterer sorgen samt hvilke interventionsformer der er hensigtsmæssige. Klassisk freudiansk sorgteori har haft en gennemgribende indflydelse på forståelsen af sorg og først indenfor de seneste år, er de tidlige sorgteorier for alvor blevet revideret. Træk af sorgteori gennem tiden gennemgås og udviklingen af teorierne diskuteres i lyset af den metodemæssige udvikling området har gennemgået fra kliniske observationer til systematiske kvantitative metoder i postmodernismens tidsalder.
The medicalization of chronic pain
Authors: Conrad Peter , Muñoz Vanessa Lopes
Published: September 2016

This paper presents an initial analysis of the medicalization of chronic pain, focusing on the definitions and treatment of chronic pain in recent decades. We identify several factors that contributed to this medicalization including the emergence of the gate control theory of pain, medical advocates for pain treatment and speciality training, the development of multidisciplinary pain clinics, the emergence of professional pain associations, extended medical treatments, and governmental decisions and support. The increased attention to chronic pain as a discrete medical category and innovations in chronic pain treatment have contributed to the medicalization of chronic pain in ways that suggest there may be benefits to society and pain sufferers, in contrast to many other cases of medicalization.
The circular structure of policy failure and learning. Danish and American public health policy 1975-2005
Authors: Larsen Lars Thorup
Published: September 2016

The literature on policy learning has focused our attention on how governments ’puzzle’ over society’s great problems and foster solutions based on the experience of previous policy as well as new knowledge and ideas. While policy learning is often seen as a linear process, this article aims to show how the learning process can also be circular in the sense that the previous policy from which a given new policy departs is constructed over and over again, which should not be confused with actual past policy. The argument is backed by a comparative policy analysis of lifestyle-focused public health policy in Denmark and the United States over the past three decades. While downplaying their belief in traditional medical treatment technology, most Western nations shifted their health policy objectives in the mid-1970s in order to get into what one report termed ’the business of modifying behaviour’, i.e. to counter lifestyle diseases by getting citizens to exercise more, but eat, drink, and smoke less. Based on a study of three decades of Danish and American public health programs, the article shows how two very different health care systems experienced a similar pattern of policy failure. While both systems continually experience that citizens fail to live by what they know is healthy, public health policies always seem to able to generate strong optimism for each new policy program, because the values responsible for policy failure are associated with the medical treatment paradigm that the policies depart from, but never with prevention itself.
Mad, kontrol og subjektivitet
Authors: Kristensen Dorthe Brogård , Jacobsen Charlotte Bredahl
Published: September 2016

I bogen Liquid Life gør Zimunt Bauman den interessante observation at selv om bestseller listen i USA ændrer sig hver uge, er der altid to typer af bøger, som ufravigeligt findes på listen: kogebøger, som tilbyder lækre og forførende retter og diæt manualer, som tilbyder forskellige regimer til at opnå slanke og nydelige kroppe (2005: 89). Man skal ikke åbne mange aviser og blade i dagens Danmark førend man er klar over at mad også er et allestedsnærværende tema i den offentlige diskurs herhjemme og at mad både knytter an til en forestilling om kulinarisk nydelse som en rundbestanddel i et lykkeligt liv, og som et middel til at opnå en sund krop. I mediebilledet er kokke som Camilla Plum, Claus Meyer og Jamie Oliver vor tids stjerner, der inspirerer til at afprøve nye og inspirerende opskrifter, og hvis man bekymrer sig om, hvordan man skal kombinere de kulinariske udfoldelser med en sund krop, kan man lade sig inspirere af livsstilsprogrammer som Praxis og Livet er Fedt. Også i den offentlige forebyggelsesstrategi finder vi en allestedsnærværende diskurs om mad. For sundhedens skyld opfordres danskerne til at spise seks stykker frugt og grønt om dagen, spise fisk to gange om ugen og nøjes med 5 genstande om dagen og ½ liter saftevand om ugen. Mad-indtag skal måles, vejes og kontrolleres – af hensyn til folkesundheden. Budskaberne der kobler mad til nydelse og mad til selvkontrol er overalt. I kampagner og reklamer, i tv-programmer, aviser og ugeblade.Spørgsmålet for denne artikel er hvordan forbrugere navigerer mellem disse to så tilsyneladende kontrasterende tilgange til mad og spisning. Baggrunden er en etnografisk Baggrunden er en etnografisk undersøgelse blandt danske forbrugere om deres forbrug af fødevarer og opfattelser af sundhed. Vi var stærkt forundrede over ovenfor beskrevne dobbelttydighed i den offentlige diskurs om mad og sundhed, og lige så stærkt inspirerede af tidligere forskere, herunder særligt Gregory Bateson og Niklas Rose. Vi forventede på den baggrund at møde mennesker som var ofre for urimelige krav om selvkontrol, og som kæmpede en kamp for at navigere inden for to modsatrettede diskurser om kost. Vores forforståelse blev imidlertid gjort til skamme. For det vi primært så, var ikke mennesker som kæmpede urimelige kampe. I stedet så vi mennesker som skabte sig selv i samfundets spejl på befriende og uventede måder. Og derfor er denne artikel blevet det den er: en granskning af de forskelligartede måder 34 danskere forbinder mad, selvkontrol og subjektivitet anno 2009.