bluuebunny/crossref_metadata_2025 huggingface dataset:
Modules with respect to cyclic purity
Authors: Mao Lixin
Published: September 2016

An exact sequence $0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0$ of left $R$-modules is called cyclically pure if for every right ideal $I$ of $R$, the sequence $0\rightarrow (R/I)\otimes A \rightarrow (R/I)\otimes B \rightarrow (R/I)\otimes C \rightarrow 0$ is exact. In this paper, we study some special modules with respect to cyclic purity, such as $CP$-projective, $CP$-injective and $CP$-flat modules.
Extensions of the classical Cesaro operator on Hardy spaces
Authors: Curbera Guillermo P. , Ricker Werner J.
Published: September 2016

For each $1\le p<\infty$, the classical Cesàro operator $\mathcal C$ from the Hardy space $H^p$ to itself has the property that there exist analytic functions $f\notin H^p$ with ${\mathcal C}(f)\in H^p$. This article deals with the identification and properties of the (Banach) space $[{\mathcal C}, H^p]$ consisting of all analytic functions that $\mathcal C$ maps into $H^p$. It is shown that $[{\mathcal C}, H^p]$ contains classical Banach spaces of analytic functions $X$, genuinely bigger that $H^p$, such that $\mathcal C$ has a continuous $H^p$-valued extension to $X$. An important feature is that $[{\mathcal C}, H^p]$ is the largest amongst all such spaces $X$.
On the Cox ring of $\mathbf{P}^2$ blown up in points on a line
Authors: Ottem John Christian
Published: September 2016

We show that the blow-up of $\mathbf{P}^2$ in $n$ points on a line has finitely generated Cox ring. We give explicit generators for the ring and calculate its defining ideal of relations.
Certain subclasses of analytic functions associated with fractional $q$-calculus operators
Authors: Purohit Sunil Dutt , Raina Ravinder Krishna
Published: September 2016

We first define the $q$-analogue operators of fractional calculus which are then used in defining certain classes of functions analytic in the open disk. The results investigated for these classes of functions include the coefficient inequalities and some distortion theorems. The results provide extensions of various known results in the $q$-theory of analytic functions. Special cases of our results are pointed out briefly.
Quasi-multipliers of Hilbert and Banach $C^*$-bimodules
Authors: Pavlov Alexander , Pennig Ulrich , Schick Thomas
Published: September 2016

Quasi-multipliers for a Hilbert $C^*$-bimodule $V$ were introduced by L. G. Brown, J. A. Mingo, and N.-T. Shen [3] as a certain subset of the Banach bidual module $V^{**}$. We give another (equivalent) definition of quasi-multipliers for Hilbert $C^*$-bimodules using the centralizer approach and then show that quasi-multipliers are, in fact, universal (maximal) objects of a certain category. We also introduce quasi-multipliers for bimodules in Kasparov's sense and even for Banach bimodules over $C^*$-algebras, provided these $C^*$-algebras act non-degenerately. A topological picture of quasi-multipliers via the quasi-strict topology is given. Finally, we describe quasi-multipliers in two main situations: for the standard Hilbert bimodule $l_2(A)$ and for bimodules of sections of Hilbert $C^*$-bimodule bundles over locally compact spaces.
Fourier transforms of spherical distributions on compact symmetric spaces
Authors: Ólafsson Gestur , Schlichtkrull Henrik
Published: September 2016

In our previous articles [27] and [28] we studied Fourier series on a symmetric space $M=U/K$ of the compact type. In particular, we proved a Paley-Wiener type theorem for the smooth functions on $M$, which have sufficiently small support and are $K$-invariant, respectively $K$-finite. In this article we extend these results to $K$-invariant distributions on $M$. We show that the Fourier transform of a distribution, which is supported in a sufficiently small ball around the base point, extends to a holomorphic function of exponential type. We describe the image of the Fourier transform in the space of holomorphic functions. Finally, we characterize the singular support of a distribution in terms of its Fourier transform, and we use the Paley-Wiener theorem to characterize the distributions of small support, which are in the range of a given invariant differential operator. The extension from symmetric spaces of compact type to all compact symmetric spaces is sketched in an appendix.
Approximation by invertible elements and the generalized $E$-stable rank for $A({\boldsymbol D})_{\mathsf R}$ and $C({\boldsymbol D})_{\mathrm{sym}}$
Authors: Mortini Raymond , Rupp Rudolf
Published: September 2016

We determine the generalized $E$-stable ranks for the real algebra, $C(\boldsymbol{D})_{\mathrm{sym}}$, of all complex valued continuous functions on the closed unit disk, symmetric to the real axis, and its subalgebra $A(\boldsymbol{D})_{\mathsf R}$ of holomorphic functions. A characterization of those invertible functions in $C(E)$ is given that can be uniformly approximated on $E$ by invertibles in $A(\boldsymbol {D})_{\mathsf R}$. Finally, we compute the Bass and topological stable rank of $C(K)_{\mathrm{sym}}$ for real symmetric compact planar sets $K$.
Topological equivalence of finitely determined real analytic plane-to-plane map germs
Authors: Skutlaberg Olav
Published: September 2016

Generic smooth map germs $({\mathsf R}^2,0)\to ({\mathsf R}^2,0)$ are topologically equivalent to cones of mappings $S^1\to S^1$. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determined real analytic map germs $({\mathsf R}^2,0)\to ({\mathsf R}^2,0)$.
Matrices of unitary moments
Authors: Dykema Ken , Juschenko Kate
Published: September 2016

We investigate certain matrices composed of mixed, second-order moments of unitaries. The unitaries are taken from $C^*$-algebras with moments taken with respect to traces, or, alternatively, from matrix algebras with the usual trace. These sets are of interest in light of a theorem of E. Kirchberg about Connes' embedding problem.
On certain martingale inequalities for maximal functions and mean oscillations
Authors: Kikuchi Masato , Kinoshita Yasuhiro
Published: September 2016

Let $X$ be a Banach function space over a nonatomic probability space. For a uniformly integrable martingale $f=(f_n)$ with respect to a filtration ${\mathcal F}=({\mathcal F}_n)$, let $Mf =\sup_n |f_n|$ and $\theta_{\mathcal F}f=\sup_n E[|f_{\infty}- f_{n-1}| \mid{\mathcal F}_n]$. We give a necessary and sufficient condition on $X$ for the inequality $\parallel \theta_{\mathcal F}f \parallel_X \leq C\parallel Mf\parallel_X$ to hold.
Bounded approximation properties in terms of $C[0,1]$
Authors: Lima Åsvald , Lima Vegard , Oja Eve
Published: September 2016

Let $X$ be a Banach space and let $\mathcal I$ be the Banach operator ideal of integral operators. We prove that $X$ has the $\lambda$-bounded approximation property ($\lambda$-BAP) if and only if for every operator $T\in \mathcal I(X,C[0,1]^*)$ there exists a net $(S_\alpha)$ of finite-rank operators on $X$ such that $S_\alpha\to I_X$ pointwise and 26767 \limsup_\alpha\|TS_\alpha\|_{\mathcal I}\leq\lambda\|T\|_{\mathcal I}. 26767 We also prove that replacing $\mathcal I$ by the ideal $\mathcal N$ of nuclear operators yields a condition which is equivalent to the weak $\lambda$-BAP.
Continuous homomorphisms and rings of injective dimension one
Authors: Chang Shou-Te , Huang I-Chiau
Published: September 2016

Let $S$ be an $R$-algebra and $\mathfrak a$ be an ideal of $S$. We define the continuous hom functor from $R$-mod to $S$-mod with respect to the $\mathfrak a$-adic topology on $S$. We show that the continuous hom functor preserves injective modules iff the ideal-adic property and ideal-continuity property are satisfied for $S$ and $\mathfrak a$. Furthermore, if $S$ is $\mathfrak a$-finite over $R$, we show that the continuous hom functor also preserves essential extensions. Hence, the continuous hom functor can be used to construct injective modules and injective hulls over $S$ using what we know about $R$. Using the continuous hom functor we can characterize rings of injective dimension one using symmetry for a special class of formal power series subrings. In the Noetherian case, this enables us to construct one-dimensional local Gorenstein domains. In the non-Noetherian case, we can apply the continuous hom functor to a generalized form of the $D+M$ construction. We may construct a class of domains of injective dimension one and a series of almost maximal valuation rings of any complete DVR.
Involutions whose fixed set has three or four components: a small codimension phenomenon
Authors: Barbaresco Evelin M. , Desideri Patricia E. , Pergher Pedro L. Q.
Published: September 2016

Let $T:M \to M$ be a smooth involution on a closed smooth manifold and $F = \bigcup_{j=0}^n F^j$ the fixed point set of $T$, where $F^j$ denotes the union of those components of $F$ having dimension $j$ and thus $n$ is the dimension of the component of $F$ of largest dimension. In this paper we prove the following result, which characterizes a small codimension phenomenon: suppose that $n \ge 4$ is even and $F$ has one of the following forms: 1) $F=F^n \cup F^3 \cup F^2 \cup \{{\operatorname {point}}\}$; 2) $F=F^n \cup F^3 \cup F^2 $; 3) $F=F^n \cup F^3 \cup \{{\operatorname{point}}\}$; or 4) $F=F^n \cup F^3$. Also, suppose that the normal bundles of $F^n$, $F^3$ and $F^2$ in $M$ do not bound. If $k$ denote the codimension of $F^n$, then $k \le 4$. Further, we construct involutions showing that this bound is best possible in the cases 2) and 4), and in the cases 1) and 3) when $n$ is of the form $n=4t$, with $t \ge 1$.
Radial growth of harmonic functions in the unit ball
Authors: Eikrem Kjersti Solberg , Malinnikova Eugenia
Published: September 2016

Let $\Psi_v$ be the class of harmonic functions in the unit disk or unit ball in ${\mathsf R}^m$ which admit a radial majorant $v(r)$. We prove that a function in $\Psi_v$ may grow or decay as fast as $v$ only along a set of radii of measure zero. For the case when $v$ fulfills a doubling condition, we give precise estimates of these exceptional sets in terms of Hausdorff measures.
Tensor products of positive maps of matrix algebras
Authors: Størmer Erling
Published: September 2016

We give conditions for when tensor products of positive maps between matrix algebras are positive maps. Necessary and sufficient conditions are given.
On the existence of connected components of dimension one in the branch locus of moduli spaces of riemann surfaces
Authors: Costa Antonio F. , Izquierdo Milagros
Published: September 2016

Let $g$ be an integer $\geq3$ and let $B_{g}=\{X\in\mathcal{M}_{g}: \mathrm{Aut}(X)\neq Id\}$ be the branch locus of $M_{g}$, where $M_{g}$ denotes the moduli space of compact Riemann surfaces of genus $g$. The structure of $B_{g}$ is of substantial interest because $B_{g}$ corresponds to the singularities of the action of the modular group on the Teichmüller space of surfaces of genus $g$ (see [14]). Kulkarni ([15], see also [13]) proved the existence of isolated points in the branch loci of the moduli spaces of Riemann surfaces. In this work we study the isolated connected components of dimension 1 in such loci. These isolated components of dimension one appear if the genus is $g=p-1$ with $p$ prime $\geq11$. We use uniformization by Fuchsian groups and the equisymmetric stratification of the branch loci.
A taylor-like expansion of a commutator with a function of self-adjoint, pairwise commuting operators
Authors: Rasmussen Morten Grud
Published: September 2016

Let $A$ be a $\nu$-vector of self-adjoint, pairwise commuting operators and $B$ a bounded operator of class $C^{n_0}(A)$. We prove a Taylor-like expansion of the commutator $[B,f(A)]$ for a large class of functions $f\colon\mathbf{R}^\nu\to\mathbf{R}$, generalising the one-dimensional result where $A$ is just a self-adjoint operator. This is done using almost analytic extensions and the higher-dimensional Helffer-Sjöstrand formula.
The sectorial projection defined from logarithms
Authors: Grubb Gerd
Published: September 2016

For a classical elliptic pseudodifferential operator $P$ of order $>0$ on a closed manifold $X$, such that the eigenvalues of the principal symbol $p_m(x,\xi)$ have arguments in $]\theta ,\varphi [$ and $]\varphi ,\theta +2\pi [$ ($\theta <\varphi <\theta +2\pi$), the sectorial projection $\Pi_{\theta,\varphi}(P)$ is defined essentially as the integral of the resolvent along $ e^{i\varphi}\overline{\mathrm R}_{+}\cup e^{i\theta}\overline{\mathrm R}_{+}$. In a recent paper, Booss-Bavnbek, Chen, Lesch and Zhu have pointed out that there is a flaw in several published proofs that $\Pi_{\theta,\varphi}(P)$ is a $\psi$do of order 0; namely that $p_m(x,\xi)$ cannot in general be modified to allow integration of $(p_m(x,\xi )-\lambda)^{-1}$ along $ e^{i\varphi}\overline{\mathrm R}_{+}\cup e^{i\theta}\overline{\mathrm R}_{+}$ simultaneously for all $\xi$. We show that the structure of $\Pi_{\theta,\varphi}(P)$ as a $\psi$do of order 0 can be deduced from the formula $\Pi_{\theta,\varphi}(P)=\frac {i}{2\pi}(\log_{\theta} P - \log_{\varphi} P)$ proved in an earlier work (coauthored with Gaarde). In the analysis of $\log_{\theta} P$ one need only modify $p_m(x,\xi)$ in a neighborhood of $e^{i\theta}\overline{\mathrm R}_{+}$ this is known to be possible from Seeley's 1967 work on complex powers.
Almost statistical convergence in amenable semigroups
Authors: Nuray Fatih , Rhoades B.E.
Published: September 2016

The purpose of this study is to extend the notion of almost statistical convergence to functions defined on discrete countable amenable semigroups.
Nontrivially Noetherian $C^*$-algebras
Authors: Hines Taylor , Walsberg Erik
Published: September 2016

We say that a $C^*$-algebra is Noetherian if it satisfies the ascending chain condition for two-sided closed ideals. A nontrivially Noetherian $C^*$-algebra is one with infinitely many ideals. Here, we show that nontrivially Noetherian $C^*$-algebras exist, and that a separable $C^*$-algebra is Noetherian if and only if it contains countably many ideals and has no infinite strictly ascending chain of primitive ideals. Furthermore, we prove that every Noetherian $C^*$-algebra has a finite-dimensional center. Where possible, we extend results about the ideal structure of $C^*$-algebras to Artinian $C^*$-algebras (those satisfying the descending chain condition for closed ideals).
Convex characterization of linearly convex domains
Authors: Nikolov Nikolai , Thomas Pascal J.
Published: September 2016

We prove that a $C^{1,1}$-smooth bounded domain $D$ in $\mathbf{C}^n$ is linearly convex if and only if the convex hull of any two discs in $D$ with common center lies in $D$.
On area stationary surfaces in the space of oriented geodesics of hyperbolic 3-space
Authors: Georgiou Nikos
Published: September 2016

We study area-stationary surfaces in the space $\mathbf{L}(\mathbf{H}^3)$ of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. We prove that every holomorphic curve in $\mathbf{L}(\mathbf{H}^3)$ is an area-stationary surface. We then classify Lagrangian area-stationary surfaces $\Sigma$ in $\mathbf{L}(\mathbf{H}^3)$ and prove that the family of parallel surfaces in $\mathbf{H}^3$ orthogonal to the geodesics $\gamma\in \Sigma$ form a family of equidistant tubes around a geodesic. Finally we find an example of a two parameter family of rotationally symmetric area-stationary surfaces that are neither Lagrangian nor holomorphic.
On the Vanishing of Homology with Modules of Finite Length
Authors: Bergh Petter Andreas
Published: September 2016

We study the vanishing of homology and cohomology of a module of finite complete intersection dimension over a local ring. Given such a module of complexity $c$, we show that if $c$ (co)homology groups with a module of finite length vanish, then all higher (co)homology groups vanish.
Pre-jordan Algebras
Authors: Hou Dongping , Ni Xiang , Bai Chengming
Published: September 2016

The purpose of this paper is to introduce and study a notion of pre-Jordan algebra. Pre-Jordan algebras are regarded as the underlying algebraic structures of the Jordan algebras with a nondegenerate symplectic form. They are the algebraic structures behind the Jordan Yang-Baxter equation and Rota-Baxter operators in terms of $\mathcal{O}$-operators of Jordan algebras introduced in this paper. Pre-Jordan algebras are analogues for Jordan algebras of pre-Lie algebras and fit into a bigger framework with a close relationship with dendriform algebras. The anticommutator of a pre-Jordan algebra is a Jordan algebra and the left multiplication operators give a representation of the Jordan algebra, which is the beauty of such a structure. Furthermore, we introduce a notion of $\mathcal{O}$-operator of a pre-Jordan algebra which gives an analogue of the classical Yang-Baxter equation in a pre-Jordan algebra.
Transfinite Tree Quivers and their Representations
Authors: Enochs E. , Estrada S. , Özdemir S.
Published: September 2016

The idea of "vertex at the infinity" naturally appears when studying indecomposable injective representations of tree quivers. In this paper we formalize this behavior and find the structure of all the indecomposable injective representations of a tree quiver of size an arbitrary cardinal $\kappa$. As a consequence the structure of injective representations of noetherian $\kappa$-trees is completely determined. In the second part we will consider the problem whether arbitrary trees are source injective representation quivers or not.
Geometry of Vector Bundle Extensions and Applications to a Generalised Theta Divisor
Authors: Hitching George H.
Published: September 2016

Let $E$ and $F$ be vector bundles over a complex projective smooth curve $X$, and suppose that $0 \to E \to W \to F \to 0$ is a nontrivial extension. Let $G \subseteq F$ be a subbundle and $D$ an effective divisor on $X$. We give a criterion for the subsheaf $G(-D) \subset F$ to lift to $W$, in terms of the geometry of a scroll in the extension space ${\mathbf{P}} H^{1}(X, \mathrm{Hom}(F, E))$. We use this criterion to describe the tangent cone to the generalised theta divisor on the moduli space of semistable bundles of rank $r$ and slope $g-1$ over $X$, at a stable point. This gives a generalisation of a case of the Riemann-Kempf singularity theorem for line bundles over $X$. In the same vein, we generalise the geometric Riemann-Roch theorem to vector bundles of slope $g-1$ and arbitrary rank.
Existence and Concentration of Solutions for a Class of Elliptic Problems with Discontinuous Nonlinearity in $\mathbf{R}^{N}$
Authors: Alves Claudianor O. , Nascimento Rúbia G.
Published: September 2016

Using variational methods we establish existence and concentration of positive solutions for a class of elliptic problems in $\mathbf{R}^{N}$, whose nonlinearity is discontinuous.
How to Recognize Polynomials in Higher Order Sobolev Spaces
Authors: Bojarski Bogdan , Ihnatsyeva Lizaveta , JUHA KINNUNEN JUHA KINNUNEN
Published: September 2016

This paper extends characterizations of Sobolev spaces by Bourgain, Brézis, and Mironescu to the higher order case. As a byproduct, we obtain an integral condition for the Taylor remainder term, which implies that the function is a polynomial. Similar questions are also considered in the context of Whitney jets.
A Spectral Sequence for the Hochschild Cohomology of a Coconnective DGA
Authors: Shamir Shoham
Published: September 2016

A spectral sequence for the computation of the Hochschild cohomology of a coconnective dga over a field is presented. This spectral sequence has a similar flavour to the spectral sequence presented in [7] for the computation of the loop homology of a closed orientable manifold. Using this spectral sequence we identify a class of spaces for which the Hochschild cohomology of their mod-$p$ cochain algebra is Noetherian. This implies, among other things, that for such a space the derived category of mod-$p$ chains on its loop-space carries a theory of support varieties.
Index Classes for Vector Fields and their Relation to Certain Characteristic Classes
Authors: Hamlet Oskar
Published: September 2016

While studying vector fields on manifolds with boundary there are three important indexes to consider. We construct three cohomology classes to compute these. We relate these classes to other classes, the relative Euler class as defined by Sharafutdinov and the secondary Chern-Euler class as defined by Sha. Our results also yield a new proof of the Poincaré-Hopf index theorem.
On Bounded Weak and Strong Solutions of Non Linear Differential Equations with and without Delay in Banach Spaces
Authors: Gomaa Adel Mahmoud
Published: September 2016

Assume that $E$ is a Banach space, $B_{r}=\{x\in E:\Vert x\Vert \le r\}$ and $C([-d,0],B_{r})$ is the Banach space of continuous functions from $[-d,0]$ into $B_{r}$. Consider $f:\mathbf{R}^+\times E\to E$; $f^{d}:[0,T]\times C([-d,0],B_{r})\to E$; for each $t\in [0,T]$ the mapping $\theta_{t}\in C([-d,0],B_{r})$ is defined by $\theta_{t}x(s)= x(t+s)$, $s\in [-d,0]$ and let $A(t)$ be a linear operator from $E$ into itself. In this paper we give existence theorems for bounded weak and strong solutions of the nonlinear differential equation 26767 \dot{x}(t)=A(t)x+f(t,x),\qquad t\in \mathbf{R}^+, 26767 and we prove that, with certain conditions, the differential equation with delay 26767 \dot{x}(t)=L(t)x(t)+f^{d}(t,\theta_{t}x),\qquad \text{if}\quad t\in [0,T] \qquad\qquad(\mathrm{Q}) 26767 has at least one weak solution where $L(t)$ is a linear operator from $E$ into $E$. Moreover, under suitable assumptions, the problem $(\mathrm{Q})$ has a solution. Furthermore under a generalization of the compactness assumptions, we show that $(\mathrm{Q})$ has a solution too.
Discrete Hardy Spaces Related to Powers of the Poisson Kernel
Authors: Vasilis Jonatan
Published: September 2016

Discrete Hardy spaces $H^{1}_{\alpha}(\partial{T})$, related to powers $\alpha \ge 1/2$ of the Poisson kernels on boundaries $\partial{T}$ of regular rooted trees, are studied. The spaces for $\alpha > 1/2$ coincide with the ordinary atomic Hardy space on $\partial{T}$, which in turn is strictly smaller than $H^{1}_{1/2}(\partial{T})$. The Orlicz space $L\log\log L(\partial{T})$ characterizes the positive and increasing functions in $H^{1}_{1/2}(\partial{T})$, but there is no such characterization for general positive functions.
Dimension of the Boundary in Different Metrics
Authors: Klén Riku , Suomala Ville
Published: September 2016

We consider metrics on Euclidean domains $\Omega\subset\mathbf{R}^n$ that are induced by continuous densities $\rho\colon\Omega\rightarrow(0,\infty)$ and study the Hausdorff and packing dimensions of the boundary of $\Omega$ with respect to these metrics.
On Artinianness of Formal Local Cohomology, Colocalization and Coassociated Primes
Authors: Eghbali Majid
Published: September 2016

This paper at first concerns some criteria on Artinianness and vanishing of formal local cohomology modules. Then we consider the cosupport and the set of coassociated primes of these modules more precisely.
Generating Rational Loop Groups with Noncompact Reality Conditions
Authors: Goertsches Oliver
Published: September 2016

We find generators for the full rational loop group of ${\rm GL}(n,\mathsf{C})$ as well as for the subgroup consisting of loops that satisfy the reality condition with respect to the noncompact real form ${\rm GL}(n,\mathsf{R})$. We calculate the dressing action of some of those generators on the positive loop group, and apply this to the ZS-AKNS flows and the $n$-dimensional system associated to ${\rm GL}(n,\mathsf{R})/{\rm O}(n)$.
Numerical Radius Inequalities for Several Operators
Authors: Hirzallah Omar , Kittaneh Fuad
Published: September 2016

Let $A$, $B$, $X$, and $A_{1},\dots,A_{2n}$ be bounded linear operators on a complex Hilbert space. It is shown that \[ w\Bigl(\sum_{k=1}^{2n-1}A_{k+1}^{\ast}XA_{k}+A_{1}^{\ast}XA_{2n}\Bigr) \leq 2\Bigl( \sum_{k=1}^{n}\Vert A_{2k-1}\Vert^{2}\Bigr)^{1/2}\Bigl(\sum_{k=1}^{n}\left\Vert A_{2k}\right\Vert^{2}\Bigr)^{1/2}w(X) \] and \[ w(AB\pm BA)\leq 2\sqrt{2}\,\Vert B\Vert \sqrt{w^{2}(A)-\frac{\vert \Vert {\operatorname{Re} A}\Vert^{2}-\Vert {\operatorname{Im} A}\Vert^{2}\vert}{2}}, \] where $w(\cdot)$ and $\left\Vert \cdot \right\Vert$ are the numerical radius and the usual operator norm, respectively. These inequalities generalize and refine some earlier results of Fong and Holbrook. Some applications of our results are given.
Optimal Embeddings of Calderón Spaces in Hölder-Zygmund Spaces
Authors: Bashir Zia , Cobos Fernando , Karadzhov Georgi E.
Published: September 2016

We prove optimal embeddings of Calderón spaces built-up over function spaces defined in $\mathbf{R}^n$ with the Lebesgue measure into generalized Hölder-Zygmund spaces in the super-critical and critical cases.
Logarithmic Convexity of Area Integral Means for Analytic Functions
Authors: Wang Chunjie , Zhu Kehe
Published: September 2016

We show that the $L^2$ integral mean on $r\mathsf{D}$ of an analytic function in the unit disk $\mathsf{D}$ with respect to the weighted area measure $(1-|z|^2)^\alpha\,dA(z)$, where $-3\le\alpha\le0$, is a logarithmically convex function of $r$ on $(0,1)$. We also show that the range $[-3,0]$ for $\alpha$ is best possible.
Sharp Weighted Bounds for Fractional Integral Operators in a Space of Homogeneous Type
Authors: Kairema Anna
Published: September 2016

We consider a version of M. Riesz fractional integral operator on a space of homogeneous type and show an analogue of the well-known Hardy-Littlewood-Sobolev theorem in this context. In our main result, we investigate the dependence of the operator norm on weighted spaces on the weight constant, and find the relationship between these two quantities. It it shown that the estimate obtained is sharp in any given space of homogeneous type with infinitely many points. Our result generalizes the recent Euclidean result by Lacey, Moen, Pérez and Torres [21].
Irrationality Measures of Numbers Related to Some $q$-Basic Hypergeometric Series
Authors: Väänänen Keijo
Published: September 2016

We obtain rather good irrationality measures for numbers related to some $q$-basic hypergeometric series. The method uses Padé approximations combined with the iteration of the appropriate functional equation.
A Short Return to Simple Ah-Algebras with Real Rank Zero
Authors: Lin Huaxin
Published: September 2016

Let $A$ be a unital simple AH-algebra with stable rank one and real rank zero such that $kx=0$ for all $x\in\operatorname{ker}\rho_A$, the subgroup of infinitesmal elements in $K_0(A)$, and for the same integer $k\ge 1$. We show that $A$ has tracial rank zero and is isomorphic to a unital simple AH-algebra with no dimension growth.
Primeness and Primitivity Conditions for Twisted Group $C^*$-Algebras
Authors: Omland Tron Ånen
Published: September 2016

For a multiplier (2-cocycle) $\sigma$ on a discrete group $G$ we give conditions for which the twisted group $C^*$-algebra associated with the pair $(G,\sigma)$ is prime or primitive. We also discuss how these conditions behave on direct products and free products of groups.
Regularity of Tensor Products Of $k$-Algebras
Authors: Bouchiba S. , Kabbaj S.
Published: September 2016

This paper tackles a problem on the possible transfer of regularity to tensor products of algebras over a field $k$. The main result establishes necessary and sufficient conditions for a Noetherian tensor product of two extension fields of $k$ to inherit regularity in various settings of separability. Thereby, we provide some applications as well as several original examples to illustrate or delimit the scope of the established results.
A Holomorphic Characterization of Operator Algebras
Authors: Neal Matthew , Russo Bernard
Published: September 2016

A necessary and sufficient condition for an operator space to support a multiplication making it completely isometric and isomorphic to a unital operator algebra is proved. The condition involves only the holomorphic structure of the Banach spaces underlying the operator space.
Application of Localization to the Multivariate Moment Problem
Authors: Marshall Murray
Published: September 2016

It is explained how the localization technique introduced by the author in [19] leads to a useful reformulation of the multivariate moment problem in terms of extension of positive semidefinite linear functionals to positive semidefinite linear functionals on the localization of $\mathsf{R}[\underline{x}]$ at $p = \prod_{i=1}^n(1+x_i^2)$ or $p' = \prod_{i=1}^{n-1}(1+x_i^2)$. It is explained how this reformulation can be exploited to prove new results concerning existence and uniqueness of the measure $\mu$ and density of $\mathsf{C}[\underline{x}]$ in $\mathscr{L}^s(\mu)$ and, at the same time, to give new proofs of old results of Fuglede [11], Nussbaum [21], Petersen [22] and Schmüdgen [27], results which were proved previously using the theory of strongly commuting self-adjoint operators on Hilbert space.
Sharp Lipschitz Constants for the Distance Ratio Metric
Authors: Simić Slavko , Vuorinen Matti , Wang Gendi
Published: September 2016

We study expansion/contraction properties of some common classes of mappings of the Euclidean space $\mathsf{R}^n$, $n\ge 2$, with respect to the distance ratio metric. The first main case is the behavior of Möbius transformations of the unit ball in $\mathsf{R}^n$ onto itself. In the second main case we study the polynomials of the unit disk onto a subdomain of the complex plane. In both cases sharp Lipschitz constants are obtained.
Construction de Variétés de Groupes Exceptionnels Non $k$-Rationnelles
Authors: Gille Philippe
Published: September 2016

Our goal is to construct non $k$-rational varieties of exceptional groups. The relevant invariant is the defect of weak approximation.
Correlation of Paths Between Distinct Vertices in a Randomly Oriented Graph
Authors: Leander Madeleine , Linusson Svante
Published: September 2016

We prove that in a random tournament the events $\{s\rightarrow a\}$ (meaning that there is a directed path from $s$ to $a$) and $\{t\rightarrow b\}$ are positively correlated, for distinct vertices $a,s,b,t \in K_n$. It is also proven that the correlation between the events $\{s\rightarrow a\}$ and $\{t\rightarrow b\}$ in the random graphs $G(n,p)$ and $G(n,m)$ with random orientation is positive for every fixed $p>0$ and sufficiently large $n$ (with $m=\bigl\lfloor p \binom{n}{2}\bigr\rfloor$). We conjecture it to be positive for all $p$ and all $n$. An exact recursion for $\mathsf{P}(\{s\rightarrow a\} \cap \{t\rightarrow b\})$ in $G(n,p)$ is given.
Some Remarks on Close-to-Convex and Strongly Convex Functions
Authors: Trąbka-Więcław Mamoru Nunokawa, Janusz Sokół, Katarzyna
Published: September 2016

We consider questions of the following kind: When does boundedness of $|{\arg \{1+zp'(z)/p(z)\}}|$, for a given analytic function $p$, imply boundedness of $|{\arg\{p(z)\}}|$? The paper determines the order of strong close-to-convexity in the class of strongly convex functions. Also, we consider conditions that are sufficient for a function to be a Bazilevič function.
The Combinatorics of Hyperbolized Manifolds
Authors: Edmonds Allan L. , Klee Steven
Published: September 2016

A topological version of a longstanding conjecture of H. Hopf, originally proposed by W. Thurston, states that the sign of the Euler characteristic of a closed aspherical manifold of dimension $d=2m$ depends only on the parity of $m$. Gromov defined several hyperbolization functors which produce an aspherical manifold from a given simplicial or cubical manifold. We investigate the combinatorics of several of these hyperbolizations and verify the Euler Characteristic Sign Conjecture for each of them. In addition, we explore further combinatorial properties of these hyperbolizations as they relate to several well-studied generating functions.
Nonseparable Uhf Algebras Ii: Classification
Authors: Farah Ilijas , Katsura Takeshi
Published: September 2016

For every uncountable cardinal $\kappa$ there are $2^\kappa$ nonisomorphic simple AF algebras of density character $\kappa$ and $2^\kappa$ nonisomorphic hyperfinite ${\rm II}_1$ factors of density character $\kappa$. These estimates are maximal possible. All C*-algebras that we construct have the same Elliott invariant and Cuntz semigroup as the CAR algebra.
Using Edge-Induced and Vertex-Induced Subhypergraph Polynomials
Authors: Tadesse Yohannes
Published: September 2016

For a hypergraph $\mathscr{H}$, we consider the edge-induced and vertex-induced subhypergraph polynomials and study their relation. We use this relation to prove that both polynomials are reconstructible, and to prove a theorem relating the Hilbert series of the Stanley-Reisner ring of the independent complex of $\mathscr{H}$ and the edge-induced subhypergraph polynomial. We also consider reconstruction of some algebraic invariants of $\mathscr{H}$.
On the Singular Loci and the Images of Proper Holomorphic Maps From Pseudoellipsoids
Authors: Giannotti Cristina , Spiro Andrea
Published: September 2016

We prove a generalisation of Rudin's theorem on proper holomorphic maps from the unit ball to the case of proper holomorphic maps from pseudoellipsoids.
A Reflection Approach to the Broken Ray Transform
Authors: Ilmavirta Joonas
Published: September 2016

We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity results for the broken ray transform using corresponding earlier results for the geodesic ray transform. Examples of manifolds where the broken ray transform is injective include Euclidean cones and parts of the spheres $S^n$. In addition, we introduce the periodic broken ray transform and use the reflection argument to produce examples of manifolds where it is injective. We also give counterexamples to both periodic and nonperiodic cases. The broken ray transform arises in Calderón's problem with partial data, and we give implications of our results for this application.
The Convergence of Some Products in the Adams Spectral Sequence
Authors: Wang Yuyu , Wang Jianbo
Published: September 2016

In this paper, we will use the family of homotopy elements $\zeta_n\in\pi_*S$, represented by $h_0b_n\in \operatorname{Ext}_A^{3,p^{n+1} q+q}(\mathsf{Z}_p, \mathsf{Z}_p)$ in the Adams spectral sequence, to detect a $\zeta_n$-related family $\gamma_{s+3}\beta_2\zeta_{n-1}$ in $\pi_*S$. Our main methods are the Adams spectral sequence and the May spectral sequence, here prime $p\geq 7$, $n>3$, $q=2(p-1)$.
Unimodular Equivalence of Order and Chain Polytopes
Authors: Hibi Takayuki , Li Nan
Published: September 2016

Order polytope and chain polytope are two polytopes that arise naturally from a finite partially ordered set. These polytopes have been deeply studied from viewpoints of both combinatorics and commutative algebra. Even though these polytopes possess remarkable combinatorial and algebraic resemblance, they seem to be rarely unimodularly equivalent. In the present paper, we prove the following simple and elegant result: the order polytope and chain polytope for a poset are unimodularly equivallent if and only if that poset avoid the 5-element "X" shape subposet. We also explore a few equivalent statements of the main result.
Existence of Positive Solutions for a Class of Variable Exponent Elliptic Systems
Authors: Ala S. , Afrouzi G. A.
Published: September 2016

We consider the system of differential equations \[ \begin{cases} -\Delta_{p(x)}u=\lambda^{p(x)}f(u,v)&\text{in $\Omega$,}\\ -\Delta_{q(x)}v=\mu^{q(x)}g(u,v)&\text{in $\Omega$,}\\ u=v=0&\text{on $\partial\Omega$,}\end{cases} \] where $\Omega \subset\mathsf{R}^{N}$ is a bounded domain with $C^{2}$ boundary $\partial \Omega,1<p(x),q(x)\in C^{1}(\bar{\Omega})$ are functions. $\Delta_{p(x)}u=\mathop{\rm div}\nolimits(|\nabla u|^{p(x)-2}\nabla u)$ is called $p(x)$-Laplacian. We discuss the existence of a positive solution via sub-super solutions.
$K$-Continuity Is Equivalent To $K$-Exactness
Authors: Uuye Otgonbayar
Published: September 2016

Let $A$ be a $C^{*}$-algebra. It is well known that the functor $B \mapsto A \otimes B$ of taking the minimal tensor product with $A$ preserves inductive limits if and only if it is exact. $C^{*}$-algebras with this property play an important role in the structure and finite-dimensional approximation theory of $C^{*}$-algebras. We consider a $K$-theoretic analogue of this result and show that the functor $B \mapsto K_{0}(A \otimes B)$ preserves inductive limits if and only if it is half-exact.
A Decomposition Theorem for Positive Maps, and the Projection Onto a Spin Factor
Authors: Størmer Erling
Published: September 2016

It is shown that each positive map between matrix algebras is the sum of a maximal decomposable map and an atomic map which is both optimal and co-optimal. The result is studied in detail for the projection onto a spin factor.
The Determinant Line Bundle for Fredholm Operators: Construction, Properties, and Classification
Authors: Zinger Aleksey
Published: September 2016

We provide a thorough construction of a system of compatible determinant line bundles over spaces of Fredholm operators, fully verify that this system satisfies a number of important properties, and include explicit formulas for all relevant isomorphisms between these line bundles. We also completely describe all possible systems of compatible determinant line bundles and compare the conventions and approaches used elsewhere in the literature.
Existence of Continuous Functions That Are One-to-One Almost Everywhere
Authors: Izzo Alexander J.
Published: September 2016

It is shown that given a metric space $X$ and a $\sigma$-finite positive regular Borel measure $\mu$ on $X$, there exists a bounded continuous real-valued function on $X$ that is one-to-one on the complement of a set of $\mu$ measure zero.
A Characterization of Totally Real Carleman Sets and an Application to Products of Stratified Totally Real Sets
Authors: Magnusson Benedikt S. , Wold Erlend Fornæss
Published: September 2016

We give a characterization of stratified totally real sets that admit Carleman approximation by entire functions. As an application we show that the product of two stratified totally real Carleman sets is a Carleman set.
Sur Le Produit Tensoriel D'algèbres
Authors: Tabaâ Mohamed
Published: September 2016

Let $\sigma \colon A\rightarrow B$ and $\rho \colon A\rightarrow C$ be two homomorphisms of noetherian rings such that $B\otimes_{A}C$ is a noetherian ring. We show that if $\sigma$ is a regular (resp. complete intersection, resp. Gorenstein, resp. Cohen-Macaulay, resp. ($S_{n}$), resp. almost Cohen-Macaulay) homomorphism, so is $\sigma\otimes I_{C}$ and the converse is true if $\rho$ is faithfully flat. We deduce the transfer of the previous properties of $B$ and $C$ to $B\otimes_{A}C$, and then to the completed tensor product $B\mathbin{\hat\otimes}_{A}C$. If $B\otimes_{A}B$ is noetherian and $\sigma$ is flat, we give a necessary and sufficient condition for $B\otimes_{A}B$ to be a regular ring.
G-Gorenstein Complexes
Authors: Akhavin Maryam , Hyry Eero
Published: September 2016

We present in the context of Gorenstein homological algebra the notion of a "G-Gorenstein complex" as the counterpart of the classical notion of a Gorenstein complex. In particular, we investigate equivalences between the category of G-Gorenstein complexes of fixed dimension and the G-class of modules.
Telemedicin: Et maktperspektiv
Authors: Dyb Kari , Andreassen Hege K.
Published: September 2016

Til tross for betydelige statlige investeringer over flere år, er ikke telemedisin en etablert behandlingsform i norsk helsevesen. Lav utbredelse forklares ofte med at leger og andre helseprofesjonelle fungerer som portvakter. Etter vår mening er det behov for å heve blikket og supplere forklaringene på individnivå. I denne artikkelen presenterer vi en empirisk analyse inspirert av Bourdieus maktperspektiv. Vi har brukt intervju, observasjons og dokumentmateriale fra to empiriske case, teleslag og teledermatologi. I begge casene var legene positive til bruk av telemedisin, men løsningene ble lite brukt. Analysen får frem hvordan telemedisin er mer enn nye verktøy for klinkerne, og faktisk trigger diskusjoner om selve kjernen i helsefeltets autonomi; spørsmålet om hva som er den riktige behandling. Vi konkluderer med at mottagelsen av telemedisin i klinisk praksis må forstås i lys av pågående maktkamper i helsefeltet, mellom statlige styringsinteresser på den ene siden og profesjonell autonomi på den andre.Telemedicine; power disruptions in health careAlthough the development of telemedicine has been a priority in Norwegian public health care for over 20 years, only a limited number of applications have been established as routine services. Dominant explanations of slow diffusion points to clinicians and their role as gatekeepers. We argue there is a need to look beyond the ubiquitous accounts of individual influences, and include power structures in the analysis of telemedicine diffusion. In this paper, we present an empirical analysis inspired by Bourdieu’s conceptual framework. The data consist of interviews, observations, and public- and project documents from two case studies; telestroke and teledermatology. In both cases, the clinicians were positive and involved in the implementation of telemedicine. Nevertheless, the services were not developed into routine practice; in fact, they were rarely used. Telemedicine touches upon the core value of health care activity: how to define the best patient treatment. The paper argues telemedicine might disrupt and be disrupted by existing power struggles in the health care sector. We conclude that slow diffusion of telemedicine should be understood in light of ongoing negotiations and power struggles between state regulatory powers on the one hand and health professional autonomy on the other.
Designantropologiske undersøgelser af Patient 2.0
Authors: Andersen Tariq Osman
Published: September 2016

’Den aktive patient’ har siden begyndelsen 90’erne været genstand for øget opmærksomhed. Det er en udbredt forståelse, at telemedicin kan forbedre samarbejdet mellem sundhedsprofessionelle og kroniske patienter og derved øge livskvaliteten og de økonomiske besparelser. Nyere etnografiske studier viser dog, at ansvarsflytning er indskrevet i teknologierne, og at forventninger om ’hjemmearbejde’ kolliderer med patienters sociale situation og håb for fremtiden. Patient 2.0 er en figur, der favner sådanne forskelligrettede virkeligheder og drømme. Med udgangspunkt i aktør-netværk teoriens princip om ’performativitet’ og det ontologiske skifte præsenterer jeg i denne artikel, hvordan metoder fra participatory design kan blive en ressource for antropologi og sociologi. Jeg tager fat i nyere diskurser, hvor design anses for at være en nøgle til at kunne undersøge moderne og mere dynamiske fænomener. Gennem en case fra forsknings- og udviklingsprojektet CITH viser jeg, hvordan vi gennem metode-eksperimenter og undersøgelser af patient 2.0 ender med skabe en designantropologisk modalitet, der er væsentlig forskellig fra etnografien. Jeg kalder denne modalitet for det udøvende aktør-netværk. Til sidst diskuterer jeg, hvad konsekvensen er for forskerens rolle og fremhæver nødvendigheden i hurtigt at kunne skifte mellem forskellige roller og at forhandle, interessere og mediere mellem hidtil uforbundne aktører for at skabe værdifulde effekter.Design Anthropological Inquiries into Patient 2.0:‘The active patient’ has since the early 90s attracted increased attention. It is a widespread idea that telemedicine can support collaboration between health professionals and patients with chronic diseases, thereby improving the quality of life and reducing clinical costs. Recent ethnographic studies show, however, that shifts in responsibilities are inscribed in the technologies and that expectations of ‘homework’ collides with patients’ social situation and hope for the future. Patient 2.0 is a figure that embraces such divergent realities and dreams. Based on actor-network theory’s principle of ‘performativity’ and the ontological turn happening in broader lines of social science, this article presents how methods from participatory design can be a resource for anthropological and sociological inquiry. The article departs on later discourses in which design practices are considered to be a key factor when exploring modern and more dynamic phenomena. Through a case study of Patient 2.0 on a research and development project, the CITH project, I show how we created a design anthropological modality that is significantly different from ethnography. I call this modality the performing actor-network. Finally, I discuss what the consequences are for the researcher’s role, and emphasise the need for being able to make quick shifts between different roles, negotiating interest, and mediate between previously unconnected actors to create valuable effects.
Brugerinddragelse: forhandlinger af autoritet, relation og viden
Authors: Jønsson Alexandra Ryborg , Baker Vibe Hjelholt , Jacobsen Charlotte Bredahl , Pedersen Line Hjøllund
Published: September 2016

Brugerinddragelse er på alles læber i sundhedsvæsenet.  Det står nedskrevet i hospitalernes værdiformuleringer, der bliver afholdt temadage og konferencer om patientinddragelse, der er øget politisk fokus på emnet, og både ledelse og frontpersonale nævner inddragelse som en afgørende kompetence i arbejdet med patienter. Men hvad ligger der egentlig i et så bredtfavnende begreb og hvorfor denne pludselige popularitet?
Komplekse liv. Patientinddragelse som vej til et bedre hverdagsliv for multisyge?
Authors: Ørtenblad Lisbeth , Jønsson Alexandre Ryborg , Meillier Lucette
Published: September 2016

Med udgangspunkt i tre cases fra et feltarbejde blandt mennesker med multisygdom beskriver forfatterne en række temaer i informanternes hverdagsliv - social identitet, nære relationer og sygdomsforståelse - som vigtige for forståelse af multisyges oplevelse af kompleksitet i sygdomsforløb. I artiklen præsenteres data, der peger i retning af, at hverdagsliv har væsentlig indflydelse på patienternes prioriteringer af behandling og egenomsorg. Der argumenteres for, at særligt multisyge patienter har brug for at blive inddraget i beslutninger om behandling og pleje, fordi kompleksiteten af deres sygdomsforløb påvirker hverdagen i betydelig grad.
Vein action: Performativity and the material body in haemodialysis
Authors: Ådahl Susanne
Published: September 2016

For patients suffering from acute kidney failure technology is the only means of survival until a kidney graft can be secured1 - a process which may take several years. In this article I focus on patients’ ongoing, situated, and embodied practices of knowing and doing as part of their caring for kidney failure. In these practices the action of blood, veins, needles, and the dialysis machine are of central import. I argue that kidney failure is »done« through a variety of cultural practices, including medical technology. It is a process of material re-shaping I term ‘vein action’. The concept of "doing" is elaborated upon by linking it to theories of neo-materialism and particularly Karen Barad’s notion of intra-activity. I investigate how flowing of blood between the patient and the dialysis machine is constituted by analyzing the material and performative qualities of these entities as part of living with kidney failure. I ask how does the materiality of the body, needle, and machine affect the doing of dialysis, and by extension the doing of kidney failure, in an everyday context? What does doing dialysis tell us about the nature of care-oriented agency?