bluuebunny/crossref_metadata_2025 huggingface dataset:
Generalizations of Kähler-Ricci solitons on projective bundles
Authors: Maschler Gideon , Tønnesen-Friedman Christina W.
Published: September 2016

We prove that an admissible manifold (as defined by Apostolov, Calderbank, Gauduchon and Tønnesen-Friedman), arising from a base with a local Kähler product of constant scalar curvature metrics, admits Generalized Quasi-Einstein Kähler metrics (as defined by D. Guan) in all "sufficiently small" admissible Kähler classes. We give an example where the existence of Generalized Quasi-Einstein metrics fails in some Kähler classes while not in others. We also prove an analogous existence theorem for an additional metric type, defined by the requirement that the scalar curvature is an affine combination of a Killing potential and its Laplacian.
Mapping cones of positive maps
Authors: Størmer Erling
Published: September 2016

We study mapping cones of positive maps of $B(H)$ into itself, i.e., cones which are closed under composition with completely positive maps. As applications we obtain characterizations of linear functionals with strong positivity properties with respect to so-called symmetric mapping cones, with special emphasis on separable and PPT states.
A noncommutative Gauss map
Authors: Eckhardt Caleb
Published: September 2016

The aim of this paper is to transfer the Gauss map, which is a Bernoulli shift for continued fractions, to the noncommutative setting. We feel that a natural place for such a map to act is on the AF algebra $\mathfrak A$ considered separately by F. Boca and D. Mundici. The center of $\mathfrak A$ is isomorphic to $C[0,1]$, so we first consider the action of the Gauss map on $C[0,1]$ and then extend the map to $\mathfrak A$ and show that the extension inherits many desirable properties.
A classic Morita equivalence result for Fell bundle $C^*$-algebras
Authors: Ionescu Marius , Dilliams Dana P.
Published: September 2016

We show how to extend a classic Morita Equivalence Result of Green's to the $C^*$-algebras of Fell bundles over transitive groupoids. Specifically, we show that if $p:{\mathcal B}\to G$ is a saturated Fell bundle over a transitive groupoid $G$ with stability group $H=G(u)$ at $u\in G^{(0)}$, then $C^* (G,{\mathcal B})$ is Morita equivalent to $C^*(H,{\mathcal C})$, where ${\mathcal C}={\mathcal B}_{| H}$. As an application, we show that if $p:{\mathcal B}\to G$ is a Fell bundle over a group $G$ and if there is a continuous $G$-equivariant map $\sigma:$ Prim $A\to G/H$, where $A=B(e)$ is the $C^*$-algebra of $\mathcal B$ and $H$ is a closed subgroup, then $C^*(G,{\mathcal B})$ is Morita equivalent to $C^* (H,{\mathcal C}^{I})$ where ${\mathcal C}^{I}$ is a Fell bundle over $H$ whose fibres are $A/I$-$A/I$-imprimitivity bimodules and $I=\bigcap\{ P:\sigma(P)=eH\}$. Green's result is a special case of our application to bundles over groups.
Standard ideals in weighted algebras of Korenblyum and Wiener types
Authors: Galé José E. , Wawrzynczyk Antoni
Published: September 2016

We introduce two types of Banach algebras of analytic functions on the unit disc which can be seen as weighted versions of closed primary ideals of the Korenblyum and (analytic) Wiener algebras, respectively. Such types of algebras arise in connection with convolution Banach algebras of Sobolev type, on the positive half-line, and their discrete analogues defined in terms of higher order differences. We show that all closed ideals are standard for algebras in the first class, and that closed ideals with countable hull are standard in algebras of the second class.
Custom monotonicity methods
Authors: Schechter Martin
Published: September 2016

In this paper we show how hypotheses for many problems can be significantly reduced if we employ the monotonicity method. Applications are given.
Pointwise regularity for solutions of double obstacle problems on metric spaces
Authors: Farnana Zohra
Published: September 2016

We study continuity at a given point for solutions of double obstacle problems. We obtain pointwise continuity of the solutions for discontinuous obstacles. We also show Hölder continuity for solutions of the double obstacle problems if the obstacles are Hölder continuous.
On weighted Bochner-Martinelli residue currents
Authors: Wulcan Elizabeth
Published: September 2016

We study the weighted Bochner-Martinelli residue current $R^p(f)$ associated with a sequence $f=(f_1,\dots,f_m)$ of holomorphic germs at $0\in{\mathsf C}^n$, whose common zero set equals the origin, and $p=(p_1,\ldots, p_m)\in\mathsf{N}^m$. Our main results are a description of $R^p(f)$ in terms of the Rees valuations of the ideal generated by $(f_1^{p_1},\ldots, f_m^{p_m})$ and an explicit description of $R^p(f)$ when $f$ is monomial. For a monomial sequence $f$ we show that $R^p(f)$ is independent of $p$ if and only if $f$ is a regular sequence.
Type sequences of one-dimensional local analytically irreducible rings
Authors: Barucci Valentina , Serban Ioana Cristina
Published: September 2016

We extend the notion of type sequence to rings that are not necessarily residually rational. Using this invariant we characterize different types of rings as almost Gorenstein rings and rings of maximal length.
Sequences of $\{0,1\}$-polynomials with exponents in arithmetic progression
Authors: Finch Carrie E.
Published: September 2016

This paper finds the first irreducible polynomial in the sequence $f_1(x)$, $f_2(x), \ldots$, where $f_k(x) = 1 + \sum_{i=0}^k x^{n+id}$, based on the values of $n$ and $d$. In particular, when $d$ and $n$ are distinct, the author proves that if $p$ is the smallest odd prime not dividing $d-n$, then $f_{p-2}(x)$ is irreducible, except in a few special cases. The author also completely characterizes the appearance of the first irreducible polynomial, if any, when $d=n$.
The generalized kinetic equation for symmetric particle systems
Authors: Hubal Halyna M.
Published: September 2016

The generalized kinetic equation is obtained for symmetric system of many particles interacting via a pair potential. A representation of a solution of the Cauchy problem for the BBGKY hierarchy is used in the form of an expansion over particle groups whose evolution is governed by the cumulants (semi-invariants).
From Jantzen to Andersen filtration via tilting equivalence
Authors: Kübel Johannes
Published: September 2016

The space of homomorphisms between a projective object and a Verma module in category $\mathcal O$ inherits an induced filtration from the Jantzen filtration on the Verma module. On the other hand there is the Andersen filtration on the space of homomorphisms between a Verma module and a tilting module. Arkhipov's tilting functor, a contravariant self-equivalence of a certain subcategory of $\mathcal O$, which maps projective to tilting modules induces an isomorphism of these kinds of Hom-spaces. We show that this equivalence identifies both filtrations.
The Pimsner-Voiculescu sequence for coactions of compact Lie groups
Authors: Goffeng Magnus
Published: September 2016

The Pimsner-Voiculescu sequence is generalized to a Pimsner-Voiculescu tower describing the $KK$-category equivariant with respect to coactions of a compact Lie group satisfying the Hodgkin condition. A dual Pimsner-Voiculescu tower is used to show that coactions of a compact Hodgkin-Lie group satisfy the Baum-Connes property.
A local Grothendieck duality for Cohen-Macaulay ideals
Authors: Lundqvist Johannes
Published: September 2016

We give a new proof of a recent result due to Mats Andersson and Elizabeth Wulcan, generalizing the local Grothendieck duality theorem. It can also be seen as a generalization of a previous result by Mikael Passare. Our method does not require the use of the Hironaka desingularization theorem and it provides a semi-explicit realization of the residue that is annihilated by functions from the given ideal.
Symplectic chain complex and reidemeister torsion of compact manifolds
Authors: Sözen Yaşar
Published: September 2016

Using symplectic complex, this article proves a formula for computing the Reidemeister torsion of even dimensional oriented closed connected manifolds. Moreover, it presents applications to Riemann surfaces and Grassmannians.
Minimizing roots of maps into the two-sphere
Authors: Fenille Marcio Colombo
Published: September 2016

This article is a study of the root theory for maps from two-dimensional CW-complexes into the 2-sphere. Given such a map $f:K\rightarrow S^2$ we define two integers $\zeta(f)$ and $\zeta(K,d_f)$, which are upper bounds for the minimal number of roots of $f$, denote be $\mu(f)$. The number $\zeta(f)$ is only defined when $f$ is a cellular map and $\zeta(K,d_f)$ is defined when $K$ is homotopy equivalent to the 2-sphere. When these two numbers are defined, we have the inequality $\mu(f)\leq\zeta(K,d_f)\leq\zeta(f)$, where $d_f$ is the so-called homological degree of $f$. We use these results to present two very interesting examples of maps from 2-complexes homotopy equivalent to the sphere into the sphere.
On polars of Blaschke-Minkowski homomorphisms
Authors: Chang-Jian Zhao
Published: September 2016

In this paper we establish Minkowski, Brunn-Minkowski, and Aleksandrov-Fenchel type inequalities for the volume difference of polars of Blaschke-Minkowski homomorphisms.
On the rationality of some moduli spaces related to pointed trigonal curves
Authors: Casnati G.
Published: September 2016

For each $g\ge1$, let $\mathcal{T}_{g,n}\subseteq \mathcal{M}_{g,n}$ be the locus of points corresponding to curves carrying a base-point-free $g^1_3$. Here we give a proof that $\mathcal{T}_{g,n}$ is rational if $g\ge4$ and $1\le n\le 2g+7$.
Operator system quotients of matrix algebras and their tensor products
Authors: Farenick Douglas , Paulsen Vern I.
Published: September 2016

{If} $\phi:\mathcal{S}\rightarrow\mathcal{T}$ is a completely positive (cp) linear map of operator systems and if $\mathcal{J}=\ker\phi$, then the quotient vector space $\mathcal{S}/\mathcal{J}$ may be endowed with a matricial ordering through which $\mathcal{S}/\mathcal{J}$ has the structure of an operator system. Furthermore, there is a uniquely determined cp map $\dot{\phi}:\mathcal{S}/\mathcal{J} \rightarrow\mathcal{T}$ such that $\phi=\dot{\phi}\circ q$, where $q$ is the canonical linear map of $\mathcal{S}$ onto $\mathcal{S}/\mathcal{J}$. The cp map $\phi$ is called a complete quotient map if $\dot{\phi}$ is a complete order isomorphism between the operator systems $\mathcal{S}/\mathcal{J}$ and $\mathcal{T}$. Herein we study certain quotient maps in the cases where $\mathcal{S}$ is a full matrix algebra or a full subsystem of tridiagonal matrices. Our study of operator system quotients of matrix algebras and tensor products has applications to operator algebra theory. In particular, we give a new, simple proof of Kirchberg's Theorem $\operatorname{C}^*(\mathbf{F}_\infty)\otimes_{\min}\mathcal{B}(\mathcal{H})=\operatorname{C}^*(\mathbf{F}_\infty)\otimes_{\max}\mathcal{B}(\mathcal{H})$, show that an affirmative solution to the Connes Embedding Problem is implied by various matrix-theoretic problems, and give a new characterisation of unital $\operatorname{C}^*$-algebras that have the weak expectation property.
Poincaré Series of some Hypergraph Algebras
Authors: Emtander E. , Fröberg R. , Mohammadi F. , Moradi S.
Published: September 2016

A hypergraph $H=(V,E)$, where $V=\{x_1,\ldots,x_n\}$ and $E\subseteq 2^V$ defines a hypergraph algebra $R_H=k[x_1,\ldots, x_n]/(x_{i_1}\cdots x_{i_k}; \{i_1,\ldots,i_k\}\in E)$. All our hypergraphs are $d$-uniform, i.e., $|e_i|=d$ for all $e_i\in E$. We determine the Poincaré series $P_{R_H}(t)=\sum_{i=1}^\infty\dim_k\mathrm{Tor}_i^{R_H}(k,k)t^i$ for some hypergraphs generalizing lines, cycles, and stars. We finish by calculating the graded Betti numbers and the Poincaré series of the graph algebra of the wheel graph.
On the $h$-vectors of Cohen-Macaulay Flag Complexes
Authors: Constantinescu Alexandru , Varbaro Matteo
Published: September 2016

Starting from an unpublished conjecture of Kalai and from a conjecture of Eisenbud, Green and Harris, we study several problems relating $h$-vectors of Cohen-Macaulay, flag simplicial complexes and face vectors of simplicial complexes.
On the Modulus of Continuity of Mappings Between Euclidean Spaces
Authors: Agbor Dieudonné , Boman Jan
Published: September 2016

Let $f$ be a function from $\mathbf{R}^p$ to $\mathbf{R}^q$ and let $\Lambda$ be a finite set of pairs $(\theta, \eta) \in \mathbf{R}^p \times \mathbf{R}^q$. Assume that the real-valued function $\langle\eta, f(x)\rangle$ is Lipschitz continuous in the direction $\theta$ for every $(\theta, \eta) \in \Lambda$. Necessary and sufficient conditions on $\Lambda$ are given for this assumption to imply each of the following: (1) that $f$ is Lipschitz continuous, and (2) that $f$ is continuous with modulus of continuity $\le C\epsilon |{\log \epsilon}|$.
Hankel Operators with Weighted Lipschitz Symbols in the Unit Ball
Authors: Sehba Benoît F. , Tchoundja Edgar
Published: September 2016

We characterize symbols of bounded Hankel operators between some Hardy-Orlicz spaces and usual Hardy spaces in the unit ball of $\mathbf{C}^n$.
Partitioned Binary Relations
Authors: Martin Paul , Mazorchuk Volodymyr
Published: September 2016

We define the category of partitioned binary relations and show that it contains many classical diagram categories, including categories of binary relations, maps, injective maps, partitions, (oriented) Brauer diagrams and (oriented) Temperley-Lieb diagrams. We construct a one-parameter deformation of the category of partitioned binary relations and show that it gives rise to classical one-parameter deformations of partition, Brauer and Temperley-Lieb categories. Finally, we describe a factorization of partitioned binary relations into a product of certain idempotents and pairs of usual binary relations.
Dual-depth Adapted Irreducible Formal Multizeta Values
Authors: Schneps Leila
Published: September 2016

Let $\mathfrak{ds}$ denote the double shuffle Lie algebra, equipped with the standard weight grading and depth filtration; we write $\mathfrak{ds}=\oplus_{n\ge 3} \mathfrak{ds}_n$ and denote the filtration by $\mathfrak{ds}^1\supset \mathfrak{ds}^2\supset \cdots$. The double shuffle Lie algebra is dual to the new formal multizeta space $\mathfrak{nfz}=\oplus_{n\ge 3} \mathfrak{nfz}_n$, which is equipped with the dual depth filtration $\mathfrak{nfz}^1\subset \mathfrak{nfz}^2\subset\cdots$ Via an explicit canonical isomorphism $\mathfrak{ds}\buildrel \sim\over\rightarrow\mathfrak{nfz}$, we define the "dual" in $\mathfrak{nfz}$ of an element in $\mathfrak{ds}$. For each weight $n\ge 3$ and depth $d\ge 1$, we then define the vector subspace $\mathfrak{ds}_{n,d}$ of $\mathfrak{ds}$ as the space of elements in $\mathfrak{ds}_n^d-\mathfrak{ds}_n^{d+1}$ whose duals lie in $\mathfrak{nfz}_n^d$. We prove the direct sum decomposition \[ \mathfrak{ds}=\bigoplus_{n\ge 3}\bigoplus_{d\ge 1} \mathfrak{ds}_{n,d}, \] \noindent which yields a canonical vector space isomorphism between $\mathfrak{ds}$ and its associated graded for the depth filtration, $\mathfrak{ds}_{n,d}\simeq \mathfrak{ds}_n^d/ \mathfrak{ds}_n^{d+1}$. A basis of $\mathfrak{ds}$ respecting this decomposition is dual-depth adapted, which means that it is adapted to the depth filtration on $\mathfrak{ds}$, and the basis of dual elements is adapted to the dual depth filtration on $\mathfrak{nfz}$. We use this notion to give a canonical depth 1 generator $f_n$ for $\mathfrak{ds}$ in each odd weight $n\ge 3$, namely the dual of the new formal single zeta value $\zeta(n)\in\mathfrak{nfz}_n$. At the end, we also apply the result to give canonical irreducibles for the formal multizeta algebra in weights up to 12.
Orientations on 2-vector Bundles and Determinant Gerbes
Authors: Kragh Thomas
Published: September 2016

In a paper from 2009, a half magnetic monopole was discovered by Ausoni, Dundas, and Rognes. This describes an obstruction to the existence of a continuous map $K(ku) \to B(ku^*)$ with determinant like properties. This magnetic monopole is in fact an obstruction to the existence of a map from $K(ku)$ to $K(\mathsf{Z},3)$, which is a retract of the natural map $K(\mathsf{Z},3) \to K(ku)$; and any sensible definition of determinant like should produce such a retract. In this paper we describe this obstruction precisely using monoidal categories. By a result from 2011 by Baas, Dundas, Richter and Rognes $K(ku)$ classifies 2-vector bundles. We thus define the notion of oriented 2-vector bundles, which removes the obstruction by the magnetic monopole. We use this to define an oriented K-theory of 2-vector bundles with a lift of the natural map from $K(\mathsf{Z},3)$. It is then possible to define a retraction of this map and since $K(\mathsf{Z},3)$ classifies complex gerbes we call this a determinant gerbe map.
Extension of Positive Currents with Special Properties of Monge-Ampère Operators
Authors: Abdulaali Ahmad L. al
Published: September 2016

In this paper we study the extension of currents across small obstacles. Our main results are: 1) Let $A$ be a closed complete pluripolar subset of an open subset $\Omega$ of $\mathsf{C}^n$ and $T$ be a negative current of bidimension $(p,p)$ on $\Omega\setminus A$ such that $dd^{c}T\geq-S$ on $\Omega\setminus A$ for some positive plurisubharmonic current $S$ on $\Omega$. Assume that the Hausdorff measure $\mathscr{H}_{2p}(A\cap \overline{\operatorname{Supp} T})=0$. Then $\widetilde{T}$ exists. Furthermore, the current $R= \widetilde{dd^{c}T}-{dd}^{c} \widetilde{T}$ is negative supported in $A$. 2) Let $u$ be a positive strictly $k$-convex function on an open subset $\Omega$ of $\mathsf{C}^n$ and set $A=\{z\in\Omega:u(z)=0\}$. Let $T$ be a negative current of bidimension $(p,p)$ on $\Omega\setminus A$ such that $dd^{c}T\geq -S$ on $\Omega\setminus A$ for some positive plurisubharmonic (or $dd^{c}$-negative) current $S$ on $\Omega$. If $p\geq k+1$, then $\widetilde{T}$ exists. If $p\geq k+2$, $dd^{c}S\leq 0$ and $u$ of class $\mathscr{C}^{2}$, then $\widetilde{dd^{c}T}$ exists and $\widetilde{dd^{c}T}= dd^{c}\widetilde{T}$.
Multiple Solutions for Nonlinear Dirichlet Problems with Concave Terms
Authors: Gasiński Leszek , Papageorgiou Nikolaos S.
Published: September 2016

We consider a nonlinear parametric Dirichlet problem with parameter $\lambda>0$, driven by the $p$-Laplacian and with a concave term $\lambda|u|^{q-2}u$, $1<q
0$ of the parameter such that for $\lambda\in (0,\lambda^*)$ the problem has five nontrivial smooth solutions, four of constant sign (two positive and two negative) and the fifth nodal. In the semilinear case ($p=2$), we show that there is a sixth nontrivial smooth solution, but we cannot provide information about its sign. Finally for the critical case $\lambda=\lambda^*$, we show that the nonlinear problem ($p\ne 2$) still has two nontrivial constant sign smooth solutions and the semilinear problem ($p=2$) has three nontrivial smooth solutions, two of which have constant sign.
Square Functions for Ritt Operators on Noncommutative $L^p$-Spaces
Authors: Arhancet Cédric
Published: September 2016

For any Ritt operator $T$ acting on a noncommutative $L^p$-space, we define the notion of completely bounded functional calculus $H^\infty(B_\gamma)$ where $B_\gamma$ is a Stolz domain. Moreover, we introduce the 'column square functions' \[ \|x\|_{p,T,c,\alpha}=\Bigl\|\Bigl(\sum_{k=1}^{+\infty}k^{2\alpha-1} |T^{k-1}(I-T)^{\alpha}(x)|^2\Bigr)^{\frac{1}{2}}\Bigr\|_{L^p(M)} \] and the 'row square functions' \[ \|x\|_{p,T,r,\alpha}=\Bigl\|\Bigl(\sum_{k=1}^{+\infty}k^{2\alpha-1} |(T^{k-1}(I-T)^{\alpha}(x))^*|^2\Bigr)^{\frac{1}{2}}\Bigr\|_{L^p(M)} \] for any $\alpha>0$ and any $x\in L^p(M)$. Then, we provide an example of Ritt operator which admits a completely bounded $H^\infty(B_\gamma)$ functional calculus for some $\gamma \in \mathopen{\big]}0,\frac{\pi}{2}\mathclose{\big[}$ such that the square functions $\|{\cdot}\|_{p,T,c,\alpha}$ (or $\|{\cdot}\|_{p,T,r,\alpha}$) are not equivalent to the usual norm $\|{\cdot}\|_{L^p(M)}$. Moreover, assuming $1
0$, we prove that if $\mathop{\rm Ran}\nolimits (I-T)$ is dense and $T$ admits a completely bounded $H^\infty(B_\gamma)$ functional calculus for some $\gamma \in \mathopen{\big]}0,\frac{\pi}{2}\mathclose{\big[}$ then there exists a positive constant $C$ such that for any $x \in L^p(M)$, there exists $x_1, x_2 \in L^p(M)$ satisfying $x=x_1+x_2$ and $\|x_1\|_{p,T,c,\alpha}+\|x_2\|_{p,T,r,\alpha}\leqslant C \|x\|_{L^p(M)}$. Finally, we observe that this result applies to a suitable class of selfadjoint Markov maps on noncommutative $L^p$-spaces.
Cartan-Eilenberg Gorenstein Flat Complexes
Authors: Yang Gang , Liang Li
Published: September 2016

In this paper, we study Cartan-Eilenberg Gorenstein flat complexes. We show that over coherent rings a Cartan-Eilenberg Gorenstein flat complex can be gotten by a so-called complete Cartan-Eilenberg flat resolution. We argue that over a coherent ring every complex has a Cartan-Eilenberg Gorenstein flat cover.
On $\alpha$-Short Modules
Authors: Davoudian M. , Karamzadeh O. A. S. , Shirali N.
Published: September 2016

We introduce and study the concept of $\alpha$-short modules (a $0$-short module is just a short module, i.e., for each submodule $N$ of a module $M$, either $N$ or $\frac{M}{N}$ is Noetherian). Using this concept we extend some of the basic results of short modules to $\alpha$-short modules. In particular, we show that if $M$ is an $\alpha$-short module, where $\alpha$ is a countable ordinal, then every submodule of $M$ is countably generated. We observe that if $M$ is an $\alpha$-short module then the Noetherian dimension of $M$ is either $\alpha$ or $\alpha+1$. In particular, if $R$ is a semiprime ring, then $R$ is $\alpha$-short as an $R$-module if and only if its Noetherian dimension is $\alpha$.
Parabolic Stein Manifolds
Authors: Aytuna A. , Sadullaev A.
Published: September 2016

An open Riemann surface is called parabolic in case every bounded subharmonic function on it reduces to a constant. Several authors introduced seemingly different analogs of this notion for Stein manifolds of arbitrary dimension. In the first part of this note we compile these notions of parabolicity and give some immediate relations among these different definitions. In section 3 we relate some of these notions to the linear topological type of the Fréchet space of analytic functions on the given manifold. In section 4 we look at some examples and show, for example, that the complement of the zero set of a Weierstrass polynomial possesses a continuous plurisubharmonic exhaustion function that is maximal off a compact subset.
On Fixed Divisors of Forms in Many Variables, I
Authors: Schinzel A.
Published: September 2016

Let $D_{d,r}$ be the maximal fixed divisor of a primitive form of degree $d$ in $r$ variables over $\mathsf{Z}$. A formula is given for $D_{d,2}$ and estimates for $D_{d,r}$ for $r>2$. As a consequence, a question of Nagell raised in 1919 is completely answered.
Flows on Rooted Trees and the Menous-Novelli-Thibon Idempotents
Authors: Chapoton F.
Published: September 2016

Several generating series for flows on rooted trees are introduced, as elements in the group of series associated with the Pre-Lie operad. By combinatorial arguments, one proves identities that characterise these series. One then gives a complete description of the image of these series in the group of series associated with the Dendriform operad. This allows to recover the Lie idempotents in the descent algebras recently introduced by Menous, Novelli and Thibon. Moreover, one defines new Lie idempotents and conjecture the existence of some others.
A Generalization of the Annulus Formula for the Relative Extremal Function
Authors: Lewandowski Arkadiusz
Published: September 2016

The main result of this paper is an annulus formula for the relative extremal function in the context of Stein spaces (Theorem 1.1). It has an application in the theory of extensions of holomorphic functions defined on generalized crosses in products of Stein spaces (Theorem 4.6).
Kolmogorov and Linear Widths of Balls in Sobolev Spaces on Compact Manifolds
Authors: Geller Daryl , Pesenson Isaac Z.
Published: September 2016

We determine upper asymptotic estimates of Kolmogorov and linear $n$-widths of unit balls in Sobolev norms in $L_{p}$-spaces on smooth compact Riemannian manifolds. For compact homogeneous manifolds, we establish estimates which are asymptotically exact, for the natural ranges of indices. The proofs heavily rely on our previous results such as: estimates for the near-diagonal localization of the kernels of elliptic operators, Plancherel-Polya inequalities on manifolds, cubature formulas with positive coefficients and uniform estimates on Clebsch-Gordon coefficients on general compact homogeneous manifolds.
Norm of the Bergman Projection
Authors: Kalaj David , Marković Marijan
Published: September 2016

This paper deals with the the norm of the weighted Bergman projection operator $P_{\alpha}:L^\infty(B)\rightarrow\mathscr{B}$ where $\alpha > - 1$ and $\mathscr{B}$ is the Bloch space of the unit ball $B$ of the $\mathsf{C}^n$. We consider two Bloch norms, the standard Bloch norm and invariant norm w.r.t. automorphisms of the unit ball. Our work contains as a special case the main result of the recent paper [6].
Éléments Algébriques sur le Corps des Séries Formelles Généralisées en Caractéristique Finie
Authors: Benhissi Ali
Published: September 2016

Soient $K$ un corps commutatif et $G$ un groupe abélien totalement ordonné. Nous donnons des moyens de construction d'éléments algébriques sur le corps $K((G))$ des séries fomelles généralissées à supports bien ordonnés.
Novikov Conjectures and Relative Hyperbolicity
Authors: Goldfarb Boris
Published: September 2016

We consider a class of relatively hyperbolic groups in the sense of Gromov and use an argument modeled after Carlsson-Pedersen to prove Novikov conjectures for these groups. This proof is related to [16,17] which dealt with arithmetic lattices in rank one symmetric spaces and some other arithmetic groups of higher rank. Here whe view the rank one lattices in this different larger context of relativve hyperbolicity which also inclues fundamental groups of pinched hyperbolic manifolds. Another large family of groups from this class is produced using combinatorial hyperbolization techniques.
Codimension Two Determinantal Varieties with Isolated Singularities
Authors: Ruas Maria Aparecida Soares , Pereira Miriam Da Silva
Published: September 2016

We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in $\mathsf{C}^4$, we obtain a Lê-Greuel formula expressing the Milnor number of the surface in terms of the second polar multiplicity and the Milnor number of a generic section. We also relate the Milnor number with Ebeling and Gusein-Zade index of the $1$-form given by the differential of a generic linear projection defined on the surface. To illustrate the results, in the last section we compute the Milnor number of some normal forms from Frühbis-Krüger and Neumer [7] list of simple determinantal surface singularities.
Continuous Fields with Fibres $\mathscr{O}_{\infty}$
Authors: Blanchard Etienne
Published: September 2016

We study in this article a class of unital continuous $C^*$-bundles the fibres of which are all isomorphic to the Cuntz $C^*$-algebra $\mathscr{O}_{\infty}$. This enables us to give several equivalent reformulations for the triviality of all these $C^*$-bundles.
Derivations of Murray-von Neumann Algebras
Authors: Kadison Richard V. , Liu Zhe
Published: September 2016

A Murray-von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we study derivations of Murray-von Neumann algebras and their properties. We show that the "extended derivations" of a Murray-von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray-von Neumann algebra associated with a von Neumann algebra of type ${\rm II}_1$ into that von Neumann algebra is 0. This result is an extension, in two ways, of Singer's seminal result answering a question of Kaplansky, as applied to von Neumann algebras: the algebra may be non-commutative and contain unbounded elements. In another sense, as we indicate in the introduction, all the derivation results including ours extend what Singer's result says, that the derivation is the 0-mapping, numerically in our main theorem and cohomologically in our theorem on extended derivations. The cohomology in this case is the Hochschild cohomology for associative algebras.
A Stein Criterion Via Divisors for Domains Over Stein Manifolds
Authors: Breaz Daniel , Vâjâitu Viorel
Published: September 2016

It is shown that a domain $X$ over a Stein manifold is Stein if the following two conditions are fulfilled: a) the cohomology group $H^i(X,\mathscr{O})$ vanishes for $i \geq 2$ and b) every topologically trivial holomorphic line bundle over $X$ admits a non-trivial meromorphic section. As a consequence we recover, with a different proof, a known result due to Siu stating that a domain $X$ over a Stein manifold $Y$ is Stein provided that $H^i(X,\mathscr{O})=0$ for $i \geq 1$.
Equations Related to Superderivations on Prime Superalgebras
Authors: Fošner Ajda , Fošner Maja
Published: September 2016

In this paper we investigate equations related to superderivations on prime superalgebras. We prove the following result. Let $D=D_0+D_1$ be a nonzero superderivation on a prime associative superalgebra $\mathscr{A}$ satisfying the relations $D_i(x)[D_i(x),x]_s=0$, $[D_i(x),x]_sD_i(x)=0$ for all $x\in \mathscr{A}$, $i=0,1$. Then one of the following is true: (a) $\mathscr{A}_1=0$ and $D(\mathscr{A}_0) \subseteq Z(\mathscr{A})$ or (b) $ D(\mathscr{A}_0)=0$ and $\mathscr{A}$ is commutative or (c) $D^2=0$. The research is a generalization of the results in [10] and [4] by using the theory of superalgebras.
Building Modules From the Singular Locus
Authors: Burke Jesse , Christensen Lars Winther , Takahashi Ryo
Published: September 2016

A finitely generated module over a commutative noetherian ring of finite Krull dimension can be built from the prime ideals in the singular locus by iteration of three procedures: taking extensions, direct summands, and cosyzygies. In 2003 Schoutens gave a bound on the number of iterations required to build any module, and in this note we determine the exact number. This building process yields a stratification of the module category, which we study in detail for local rings that have an isolated singularity.
Algebras on Surfaces
Authors: Stout Edgar Lee
Published: September 2016

The first part of the paper is devoted to algebras on one-dimensional varieties in $\mathsf{C}^n$ that are bounded by finite unions of mutually disjoint rectifiable simple closed curves. The relevant Shilov boundaries are considered, and certain nonapproximation phenomena are exhibited. The second part of the paper is devoted to the study of uniform algebras whose maximal ideal spaces are smooth surfaces and that admit sets of smooth generators. Such algebras are shown to consist of functions holomorphic off their Shilov boundaries.
Self-Similar Automorphisms of a Free Group of Countable Rank
Authors: Tomaszewski Witold
Published: September 2016

We investigate self-similar automorphisms of a free group $F$ of infinite countable rank, that is automorphisms for which their actions on $F$ and $F^{\prime}$ are similar. We show properties, examples and counterexamples of self-similar automorphisms and study the subgroup generated by self-similar automorphisms.
Univalence Criteria and Lipschitz-Type Spaces on Pluriharmonic Mappings
Authors: Chen Sh. , Ponnusamy S. , Wang X.
Published: September 2016

In this paper, we investigate some properties of pluriharmonic mappings defined in the unit ball. First, we discuss the relationship between the univalence of pluriharmonic mappings and linearly connected domains, and then we study Lipschitz-type spaces for pluriharmonic mappings.
A Duality of Locally Compact Groups That Does Not Involve the Haar Measure
Authors: Kuznetsova Yulia
Published: September 2016

We present a simple and intuitive framework for duality of locally compacts groups, which is not based on the Haar measure. This is a map, functorial on a non-degenerate subcategory, on the category of coinvolutive Hopf $C^*$-algebras, and a similar map on the category of coinvolutive Hopf-von Neumann algebras. In the $C^*$-version, this functor sends $C_0(G)$ to $C^*(G)$ and vice versa, for every locally compact group $G$. As opposed to preceding approaches, there is an explicit description of commutative and co-commutative algebras in the range of this map (without assumption of being isomorphic to their bidual): these algebras have the form $C_0(G)$ or $C^*(G)$ respectively, where $G$ is a locally compact group. The von Neumann version of the functor puts into duality, in the group case, the enveloping von Neumann algebras of the algebras above: $C_0(G)^{**}$ and $C^*(G)^{**}$.
Spectra of Sub-Dirac Operators on Certain Nilmanifolds
Authors: Kath Ines , Ungermann Oliver
Published: September 2016

We study sub-Dirac operators associated to left-invariant bracket-generating sub-Riemannian structures on compact quotients of nilpotent semi-direct products $G=\mathsf{R}^n\rtimes_A\mathsf{R}$. We prove that these operators admit an $L^2$-basis of eigenfunctions. Explicit examples of this type show that the spectrum of these operators can be non-discrete and that eigenvalues may have infinite multiplicity. In this case the sub-Dirac operator is neither Fredholm nor hypoelliptic.
A Complex of Modules and Its Applications to Local Cohomology and Extension Functors
Authors: Bahmanpour Kamal
Published: September 2016

Let $(R,m)$ be a commutative Noetherian complete local ring and let $M$ be a non-zero Cohen-Macaulay $R$-module of dimension $n$. It is shown that, if $\operatorname{projdim}_R(M)<\infty$, then $\operatorname{injdim}_R(D(H^n_{\mathfrak{m}}(M)))<\infty$, and if $\operatorname{injdim}_R(M)<\infty$, then $\operatorname{projdim}_R(D(H^n_{\mathfrak{m}}(M)))<\infty$, where $D(-):= \operatorname{Hom}_{R}(-,E)$ denotes the Matlis dual functor and $E := E_R(R/\mathfrak{m})$ is the injective hull of the residue field $R/\mathfrak{m}$. Also, it is shown that if $(R,\mathfrak{m})$ is a Noetherian complete local ring, $M$ is a non-zero finitely generated $R$-module and $x_1,\ldots,x_k$, $(k\geq 1)$, is an $M$-regular sequence, then \[ D(H^k_{(x_1,\ldots,x_k)}(D(H^k_{(x_1,\ldots,x_k)}(M))))\simeq M. \] In particular, $\operatorname{Ann} H^k_{(x_1,\ldots,x_k)}(M)=\operatorname{Ann} M$. Moreover, it is shown that if $R$ is a Noetherian ring, $M$ is a finitely generated $R$-module and $x_1,\ldots,x_k$ is an $M$-regular sequence, then \[ \operatorname{Ext}^{k+1}_R(R/(x_1,\ldots,x_k),M)=0. \]
The $K$-Theory of Some Reduced Inverse Semigroup $C^*$-Algebras
Authors: Norling Magnus Dahler
Published: September 2016

We use a recent result by Cuntz, Echterhoff and Li about the $K$-theory of certain reduced $C^*$-crossed products to describe the $K$-theory of $C^*_r(S)$ when $S$ is an inverse semigroup satisfying certain requirements. A result of Milan and Steinberg allows us to show that $C^*_r(S)$ is Morita equivalent to a crossed product of the type handled by Cuntz, Echterhoff and Li. We apply our result to graph inverse semigroups and the inverse semigroups of one-dimensional tilings.
Dynamics of Biholomorphic Self-Maps on Bounded Symmetric Domains
Authors: Mellon P.
Published: September 2016

Let $g$ be a fixed-point free biholomorphic self-map of a bounded symmetric domain $B$. It is known that the sequence of iterates $(g^n)$ may not always converge locally uniformly on $B$ even, for example, if $B$ is an infinite dimensional Hilbert ball. However, $g=g_a\circ T$, for a linear isometry $T$, $a=g(0)$ and a transvection $g_a$, and we show that it is possible to determine the dynamics of $g_a$. We prove that the sequence of iterates $(g_a^n)$ converges locally uniformly on $B$ if, and only if, $a$ is regular, in which case, the limit is a holomorphic map of $B$ onto a boundary component (surprisingly though, generally not the boundary component of $\frac{a}{\|a\|}$). We prove $(g_a^n)$ converges to a constant for all non-zero $a$ if, and only if, $B$ is a complex Hilbert ball. The results are new even in finite dimensions where every element is regular.
Hopf Hypersurfaces in Complex Two-Plane Grassmannians With $\mathfrak{D}$-Parallel Shape Operator
Authors: Lee Hyunjin , Pak Eunmi , Suh Young Jin
Published: September 2016

In this paper we consider a generalized condition for shape operator of a real hypersurface $M$ in complex two-plane Grassmannian $G_2(\mathsf{C}^{m+2})$, namely, $\mathfrak{D}$-parallel shape operator of $M$. Using such a notion, we prove that there does not exist a real hypersurface in complex two-plane Grassmannian $G_2(\mathsf{C}^{m+2})$ with $\mathfrak{D}$-parallel shape operator.
Extension of Derivations, and Connes- Amenability of the Enveloping Dual Banach Algebra
Authors: Choi Yemon , Samei Ebrahim , Stokke Ross
Published: September 2016

If $D:A \to X$ is a derivation from a Banach algebra to a contractive, Banach $A$-bimodule, then one can equip $X^{**}$ with an $A^{**}$-bimodule structure, such that the second transpose $D^{**}: A^{**} \to X^{**}$ is again a derivation. We prove an analogous extension result, where $A^{**}$ is replaced by $\mathsf{F}(A)$, the enveloping dual Banach algebra of $A$, and $X^{**}$ by an appropriate kind of universal, enveloping, normal dual bimodule of $X$. Using this, we obtain some new characterizations of Connes-amenability of $\mathsf{F}(A)$. In particular we show that $\mathsf{F}(A)$ is Connes-amenable if and only if $A$ admits a so-called $\operatorname{WAP}$-virtual diagonal. We show that when $A=L^1(G)$, existence of a $\operatorname{WAP}$-virtual diagonal is equivalent to the existence of a virtual diagonal in the usual sense. Our approach does not involve invariant means for $G$.
Homologie de Hochschild Et Espaces Algébriques
Authors: Banerjee Abhishek
Published: September 2016

The purpose of this article is to define the Hochschild and cyclic homologies of an algebraic space $X$. We consider two definitions of Hochschild homology of $X$ and show that these definitions coincide in the case of a separated algebraic space. Moreover, we construct a shuffle product on the Hochschild homologies of $X$. Finally, we show that one has a pairing between the Hochschild homologies and cohomologies of $X$. Résumé Le but de cet article est de définir les homologies de Hochschild et les homologies cycliques d'un espace algébrique $X$. Nous considérons deux définitions de l'homologie de Hochschild et nous montrons que ces définitions sont les mêmes en cas d'un espace algébrique séparé. De plus, nous construisons un produit shuffle sur les homologies de Hochschild de $X$. Enfin, nous montrons qu'on a un appariement entre les homologies et les cohomologies de Hochschild de $X$.
Stellar Theory for Flag Complexes
Authors: Lutz Frank H. , Nevo Eran
Published: September 2016

Refining a basic result of Alexander, we show that two flag simplicial complexes are piecewise linearly homeomorphic if and only if they can be connected by a sequence of flag complexes, each obtained from the previous one by either an edge subdivision or its inverse. For flag spheres we pose new conjectures on their combinatorial structure forced by their face numbers, analogous to the extremal examples in the upper and lower bound theorems for simplicial spheres. Furthermore, we show that our algorithm to test the conjectures searches through the entire space of flag PL spheres of any given dimension.
Von Neumann Algebra Preduals Satisfy the Linear Biholomorphic Property
Authors: Peralta Antonio M. , Stachó László L.
Published: September 2016

We prove that for every $\mathrm{JBW}^*$-triple $E$ of rank $>1$, the symmetric part of its predual reduces to zero. Consequently, the predual of every infinite dimensional von Neumann algebra $A$ satisfies the linear biholomorphic property, that is, the symmetric part of $A_*$ is zero.
Convolution in Weighted Lorentz Spaces of Type $\Gamma$
Authors: Křepela Martin
Published: September 2016

We characterize boundedness of the convolution operator between weighted Lorentz spaces $\Gamma^p(v)$ and $\Gamma^q(w)$ for the range of parameters $p,q\in[1,\infty]$, or $p\in(0,1)$ and $q\in\{1,\infty\}$, or $p=\infty$ and $q\in(0,1)$. We provide Young-type convolution inequalities of the form \[ \|f\ast g\|_{\Gamma^q(w)} \le C \|f\|_{\Gamma^p(v)}\|g\|_Y, \quad f\in\Gamma^p(v), g\in Y, \] characterizing the optimal rearrangement-invariant space $Y$ for which the inequality is satisfied.
The Internet as a medium for delivering treatment for depression. Possibilities and challenges highlighted by our experiences with MoodGYM
Authors: Kolstrup Nils
Published: September 2016

In this paper, I will present the current status of the use of the Internet as a medium for the treatment of depression. I will focus on the major challenges posed by the wide use of internet-based programmes. Recent and potential future developments of internet-based programmes for the treatment of depression will also be discussed.I am a member of a research group at UiT The Arctic University of Norway (UiT). For the past seven years, we have been working with the internet-based depression-treatment programme MoodGYM. Our motivation to perform this research was partly based on local shortage of treatment capacity. These local problems are not confined to northern Norway. The world is presently experiencing a worldwide epidemic of depression with vast personal, social, and economic costs. Health-care systems strive to cope with these challenges and investigate whether internet-based programmes can help alleviate these problems with no or limited involvement of the health-care system.
The two faces of user involvement: Everyday life and local context
Authors: Kristiansen Tine Mechlenborg , Antoft Rasmus , Primdahl Jette , Petersen Kim Hørslev
Published: September 2016

In most developed countries, healthcare systems are increasingly faced with political demands to involve users in the planning and development of their services. This article reports findings from an ethnographic fieldwork that investigated an inter-organizational project involving user representation. The project was set up to develop an educational programme for people with rheumatoid arthritis (RA). By investigating user representatives’ experiences, our aim was to bring to light more general determinants and conditions of user involvement in health services. Drawing on an analytical framework within everyday life sociology, the analysis explored the dual concept of “conditions and conditionality”, metaphorically described in this article as “the two faces of user involvement”. From one perspective, everyday life experiences – living with RA, encounters with the health system and professional identities and work life – conditioned user representatives’ participation in the project. From another perspective, the local institutional context and interactions within the project framework conditioned the way in which users are involved. The ways in which these conditions changed over time are described, in relation to the specific spatial, temporal and social developments in both the everyday lives of the user representatives and in the local project.
Tidsskrift for Forskning i Sygdom og Samfund – 10 år i et krydsfelt
Authors: Risør Torsten
Published: September 2016

Tidsskrift for Forskning i Sygdom og Samfund udkom første gang i begyndelsen af 2005, men var klar til trykning nogle måneder før, så derfor stod der “2004” på forsiden. Med det nummer du nu har i hånden fejrer tidsskriftet derfor sin 10 års fødselsdag, og som ved alle runde fødselsdage kalder det på festtaler, refleksioner og status over tiden som er gået og måske en morsom anekdote eller to om fødselaren.Men inden dette bliver ren festtale og løssluppen morskab, har vi i redaktionen også lyst til at bruge dette som en mulighed for lidt analytisk eftertanke. På den ene side ønsker vi at diskutere om tidsskriftet bevæger sig i den retning, som vi oprindelig ønskede, og om vi har opnået noget at det, som vi ville opnå. På den anden side er tidsskriftet del af større bevægelser i sundheds- og samfundsvidenskab, og det kan være nyttigt at overveje i hvilket omfang, tidsskriftet bliver et billede på disse bevægelser. Det er altså både tidsskriftet som handlende subjekt og som objekt for påvirkning udefra, som vi har lyst til at bruge lidt tid på.
Sygdommens spiserum: Har arkitekturen en overset eller glemt betydning her?
Authors: Tvedebrink Tenna Doktor Olsen , Fisker Anna Marie , Kirkegaard Poul Henning
Published: September 2016

Begrebet ’sygehus’ anvendes i dag om det offentlige rum, hvor syge undersøges og behandles. Men at være syg og indlagt på et sygehus handler ofte ikke kun om at blive rask ved hjælp af medicinsk behandling eller kirurgiske indgreb, men også om velvære og omsorg i form af sygepleje og måltider; om det ’sygdommens rum’, der skabes omkring patientens samlede helbredelse. I denne artikel vil vi argumentere for, at ’sygdommens rum’ i højere grad udbredes til også at omfatte arkitekturen – selve huset, der indrammer det hele– og vi vil, på baggrund af projektet MORE, fokusere på koblingen mellem sygdom, måltider og arkitektur. Metodisk tager vi afsæt i den tyske arkitekt Gottfried Sempers teori omkring arkitekturens grundelementer, der tilbage i midten af det 19. århundrede var med til at danne grundlaget for det, der i dag er den moderne arkitekturteoris definition af ’rummet’ som oplevet fænomen. På baggrund af Sempers teoretiske forståelsesramme og med udgangspunkt i en måltidsbeskrivelse fra renæssancehospitalet Santa Maria Nuova, vil vi give ét eksempel på, hvordan spiserummets arkitektur udgjorde en essentiel del af ’sygdommens rum’ gennem en bevidst iscenesættelse af måltidets ritualer sammen med de lægelige og religiøse handlinger. Omend scenariet forekommer teatralsk i vore dage, så mener vi, at denne historiske beskrivelse kan bidrage til nutidens forståelse af ’sygdommens rum’ og indretningen af hospitalsarkitekturen.Med denne artikel ønsker vi således at argumentere for, at spiserummets arkitektur i højere grad bør være et fokuselement i debatten om fremtidens sygehuse og ikke mindst i forskning relateret til ’sygdommens rum’.
Det hellige rum: Sjælesorgssamtaler på hospitaler
Authors: Boelsbjerg Hanne Bess
Published: September 2016

På de fleste danske hospitaler er der tilknyttet en præst og i enkelte tilfælde også en imam. Disse hospitalspræster og -imamer varetager samtaler med patienter og pårørende, samt superviserer flere steder personalet i forhold til etiske problemstillinger. Når samtalerne foregår én til én, omtales de som ’sjælesorgssamtaler’. Artiklen viser, hvordan disse samtaler medvirker til at skabe et rum for eksistentielle og religiøse overvejelser om sygdommens betydning. Der argumenteres i artiklen for, at dette rum optræder som ’et helligt rum’. Rummet adskiller sig fra den bio-medicinske kontekst i kraft af de ritualer og det sprog, der tages i brug, når patienten i samspil med sjælesørgeren søger at tillægge sygdommen betydning. Beskrivelsen af, hvad der foregår i sjælesorgsrummet er set fra sjælesørgerens perspektiv, da det empiriske materiale stammer fra 15 interviews med sjælesørgere (1). Dette suppleres med en kort deltagerobservation. Der gøres rede for de begrænsninger, som var forbundet med udførelsen af feltarbejde, hvilket indgår som en del af analysen af ’det hellige rum’. Ved at inddrage Batesons forståelse af ’det hellige’ samt Turners ritual-forståelse, udskilles de elementer, der symbolsk viser, hvilket forståelses-rum sjælesørgeren og patienten befinder sig i. Slutteligt konkluderer artiklen, at disse sjælesorgssamtaler skaber et nyt rum for patientens oplevelse af sygdom. Det karakteristiske ved rummet er, at det giver patienten mulighed for at forandre sit perspektiv på lidelsen - det er at være syg. Dette perspektiv-skifte sker ved at forbinde personens liv til noget andet og større end sig selv. Til selve livet, eller det, der i mange kulturer omtales som helligt.