bluuebunny/crossref_metadata_2025 huggingface dataset:
Item Response Theory and Computerized Adaptive Testing for Orthopaedic Outcomes Measures
Authors: Brodke Dane Jensen , Hung Man , Bozic Kevin J.
Published: September 2016

The use of patient-reported outcome measures (PROMs) to objectively and quantifiably assess patient symptomatology allows tracking of symptoms over time, measurement of the effect of healthcare interventions, and performance of cost-effectiveness analyses to assess and compare the value of treatment options. Many of the PROMs historically used had limited versatility because they were developed using classical test theory, which generates static tests that are not comparable with other measures assessing similar outcomes. Recently developed PROMs, however, were designed according to the principles of the newer item response theory (IRT), which allows for the creation of dynamic instruments deliverable in a variety of forms that are readily comparable with similar measures. IRT also enables computerized adaptive testing to decrease the burden of using PROMs by allowing rapid and complete data acquisition. IRT-based instruments are suitable for patient care and research and have been validated in a variety of populations, many of which are relevant to orthopaedic populations.
Ectopic Cushing’s syndrome due to retroperitoneal ACTH-producing paragangliomas
Authors: Chen Fan , Wang Xiangyu , Wang Yang , Meng Hui , Zhu Yaofeng , Gao Wei , Jiang Xuewen , Chen Shouzhen , Zhang Zhaocun , Zou Zhichuan , He Tianyi , Yang Yue , Zhu Kejia , Wang Yong , Liu Yaxiao , Cui Jianfeng , Shi Benkang , Yin Gang
Published: September 2016

Extra-adrenal pheochromocytomas, or paragangliomas, are rare tumours that derive from extra-adrenal chromaffin cells. Cushing’s syndrome (CS) caused by paragangliomas is extremely rare. We report a 53-year-old man with hypertension, diabetes, and symptoms of hypokalemia. Computer tomography (CT) revealed two retroperitoneal masses and bilateral adrenal hyperplasia. Together with the laboratory examinations, ectopic CS caused by multiple paragangliomas was highly suspected. The patient underwent resections of retroperitoneal tumours, left kidney, and left adrenal; postoperative histopathology confirmed two paragangliomas that were both positively stained for adrenocorticotropic hormone (ACTH). He got clinical and biochemical recoveries without any recurrent evidence at the nine-month followup.
The Construction of Collective Identity in Malaysian ESL Secondary Classrooms
Authors: Idrus Faizah , Nazri Nas Idayu Mohd
Published: September 2016

This study seeks to identify the construction of collective identity in ESL classroom among students in a secondary school in Selangor, Malaysia. Identity construction can be helpful in supporting students academically and socially, especially in the English language classrooms. Being non-native speakers, students may have the tendency to feel isolated because of the limited knowledge in English. A qualitative investigation was employed and the samples comprised of 12 secondary students from Sekolah Menengah Kebangsaan Jeram, Kuala Selangor. In-depth interviews were carried out with the respondents.The results revealed that when constructing their personal identities, individuals may want to identify themselves with the mutual interest of the groups they are part of. Identifying oneself with a group not only means wanting to be accepted, but also adhering to having mutual identities and values of the group. Therefore, the current study seems to confirm the finding of previous studies where researchers stated that the identity of an individual is defined by its majority group with whom the individuals share the physical environment and the territory they inhabit.
A Remark on the Congruence Subgroup Problem
Authors: Mennicke Jens
Published: September 2016

In the theory of congruence subgroups, one usually shows that, under suitable assumptions, the normal closure of the mth power of an elementary unipotent matrix coincides with the full con- gruence subgroup mod m. For applications, it is sometimes useful to study the subgroup generated by the mth powers of the elementary unipotent elements. We give an elementary proof for the fact that in $SL_n(Z)$ for $n > 3$, this subgroup is normal in a suitably defined congruence subgroup of $SL_n(Z)$ .
A Maximal Description for the Real Interpolation Method in the Quasi-Banach Case.
Authors: Bergh Jöran , Cobos Fernando
Published: September 2016

We give a maximal description in the sense of Aronszajn-Gagliardo for the real method in the category of quasi-Banach spaces.
Universal spectra, universal tiling sets and the spectral set conjecture
Authors: Pedersen Steen , Wang Yang
Published: September 2016

A subset $\Omega$ of $\mathbf{R}^d$ with finite positive Lebesgue measure is called a spectral set if there exists a subset $\Lambda\subset\mathbf{R}$ such that ${\mathcal E}_\Lambda :=\{e^{i2\pi \langle\lambda, x\rangle}: \lambda\in\Lambda\}$ form an orthogonal basis of $L^2(\Omega)$. The set $\Lambda$ is called a spectrum of the set $\Omega$. The Spectral Set Conjecture states that $\Omega$ is a spectral set if and only if $\Omega$ tiles $\mathbf{R}^d$ by translation. In this paper we prove the Spectral Set Conjecture for a class of sets $\Omega \subset \mathbf{R}$. Specifically we show that a spectral set possessing a spectrum that is a strongly periodic set must tile $\mathbf{R}$ by translates of a strongly periodic set depending only on the spectrum, and vice versa.
Embedding problems and equivalence of quadratic forms
Authors: Ledet Arne
Published: September 2016

If the obstruction to a Galois theoretical embedding problem with kernel of order $2$ is the product of two quaternion classes, the criterion for solvability can be reformulated as an equivalence of quadratic forms. In some cases the solutions to the embedding problem can be constructed directly from a matrix expressing this equivalence.
On weighted multidimensional embeddings for monotone functions
Authors: Barza Sorina , Persson Lars-Erik , Stepanov Vladimir D.
Published: September 2016

We characterize the inequality 7817 \left(\int_{\mathbf{R}^N_+} f^q u\right)^{1/q} \leq C \left(\int_{\mathbf{R}^N_+} f^p v \right)^{1/p},\,\,0<q ,p <\infty, 7817 for monotone functions $f\geq 0$ and nonnegative weights $u$ and $v$. The case $q < p$ is new and the case $0<p\leq q <\infty$ is extended to a modular inequality with N- functions. A remarkable fact concerning the calculation of $C$ is pointed out.
The Faraday 2-form in Einstein-Weyl geometry
Authors: Calderbank David M. J.
Published: September 2016

On a conformal manifold, a compatible torsion free connection $D$ need not be the Levi-Civita connection of a compatible Riemannian metric. The local obstruction is a real $2$-form $F^D$, the Faraday curvature. It is shown that, except in four dimensions, $F^D$ necessarily vanishes if it is divergence free. In four dimensions another differential operator may be applied to $F^D$ to show that an Einstein-Weyl $4$-manifold with selfdual Weyl curvature also has selfdual Faraday curvature and so is either Einstein or locally hypercomplex. More generally, the Bach tensor and the scalar curvature are shown to control the selfduality of $F^D$. Finally, the constancy of the sign of the scalar curvature on compact Einstein-Weyl $4$-manifolds [24] is generalised to higher dimensions. The scalar curvature need not have constant sign in dimensions two and three.
Faithful representations of crossed products by actions of $\boldsymbol N^k$
Authors: Larsen N. S. , Raeburn Iain
Published: September 2016

We study a family of semigroup crossed products arising from actions of $\boldsymbol N^k$ by endomorphisms of groups. These include the Hecke algebra arising in the Bost-Connes analysis of phase transitions in number theory, and other Hecke algebras considered by Brenken. Our main theorem is a characterisation of the faithful representations of these crossed products, and generalises a similar theorem for the Bost-Connes algebra due to Laca and Raeburn.
Kähler Yamabe minimizers on minimal ruled surfaces
Authors: Tønnesen-Friedman Christina W.
Published: September 2016

It is shown that if a minimal ruled surface $\mathrm{P}(E) \rightarrow \Sigma$ admits a Kähler Yamabe minimizer, then this metric is generalized Kähler-Einstein and the holomorphic vector bundle $E$ is quasi-stable.
Smooth Curves on Projective $K3$ Surfaces
Authors: Knutsen Andreas Leopold
Published: September 2016

In this paper we give for all $n \geq 2$, $d>0$, $g \geq 0$ necessary and sufficient conditions for the existence of a pair $(X,C)$, where $X$ is a $K3$ surface of degree $2n$ in $\mathrm{P}^{n+1}$ and $C$ is a smooth (reduced and irreducible) curve of degree $d$ and genus $g$ on $X$. The surfaces constructed have Picard group of minimal rank possible (being either $1$ or $2$), and in each case we specify a set of generators. For $n \geq 4$ we also determine when $X$ can be chosen to be an intersection of quadrics (in all other cases $X$ has to be an intersection of both quadrics and cubics). Finally, we give necessary and sufficient conditions for $\mathcal O_C (k)$ to be non-special, for any integer $k \geq 1$.
Hardy-Sobolev spaces of complex tangential derivatives of holomorphic functions in domains of finite type
Authors: Grellier Sandrine
Published: September 2016

In this paper, we prove Fefferman-Stein like characterizations of Hardy-Sobolev spaces of complex tangential derivatives of holomorphic functions in domains of finite type in $\boldsymbol C^n$. We also study the relationship between these complex tangential Hardy-Sobolev spaces and the usual ones. We also obtain partial results on domains not necessarily of finite type.
Full duality for coactions of discrete groups
Authors: Echterhoff Siegfried , Quigg John
Published: September 2016

Using the strong relation between coactions of a discrete group $G$ on $C^*$-algebras and Fell bundles over $G$ we prove a new version of Mansfield's imprimitivity theorem for coactions of discrete groups. Our imprimitivity theorem works for the universally defined full crossed products and arbitrary subgroups of $G$ as opposed to the usual theory of [16], [11] which uses the spatially defined reduced crossed products and normal subgroups of $G$. Moreover, our theorem factors through the usual one by passing to appropriate quotients. As applications we show that a Fell bundle over a discrete group is amenable in the sense of Exel [7] if and only if the double dual action is amenable in the sense that the maximal and reduced crossed products coincide. We also give a new characterization of induced coactions in terms of their dual actions.
Remarks on Determinant Line Bundles, Chern-Simons Forms and Invariants
Authors: Dupont Johan L. , Johansen Flemming Lindblad
Published: September 2016

We study generalized determinant line bundles for families of principal bundles and connections. We explore the connections of this line bundle and give conditions for the uniqueness of such. Furthermore we construct for families of bundles and connections over manifolds with boundary, a generalized Chern-Simons invariant as a section of a determinant line bundle.
Jarník and Julia; a Diophantine analysis for parabolic rational maps for Geometrically Finite Kleinian Groups with Parabolic Elements
Authors: Stratmann B. O. , Urbański M.
Published: September 2016

In this paper we derive a Diophantine analysis for Julia sets of parabolic rational maps. We generalise two theorems of Dirichlet and Jarník in number theory to the theory of iterations of these maps. On the basis of these results, we then derive a "weak multifractal analysis" of the conformal measure naturally associated with a parabolic rational map. The results in this paper contribute to a further development of Sullivan's famous dictionary translating between the theory of Kleinian groups and the theory of rational maps.
Small eigenvalues of large Hankel matrices: The indeterminate case
Authors: Berg Christian , Chen Yang , Ismail Mourad E. H.
Published: September 2016

In this paper we characterize the indeterminate case by the eigenvalues of the Hankel matrices being bounded below by a strictly positive constant. An explicit lower bound is given in terms of the orthonormal polynomials and we find expressions for this lower bound in a number of indeterminate moment problems.
On the structure of Pedersen-Poon twistor spaces
Authors: Honda Nobuhiro
Published: September 2016

We study algebro-geometric properties of certain twistor spaces over $n\boldsymbol{CP}^2$ with two dimensional torus actions, whose existence was proved by Pedersen and Poon. We show that they have a pencil whose general members are non-singular toric surface, and completely determine the structure of the reducible members of the pencil, which are also toric surfaces. In the course of our proof, we describe behaviors of the above pencil under equivariant smoothing. Relation between the weighted dual graphs of the toric surfaces in the pencil and similar invariant of the above torus action on $n\boldsymbol{CP}^2$ is also determined.
General $n$-dimensional Tauberian problems with application to the Laplace- and Stieltjes transforms
Authors: Frennemo Lennart
Published: September 2016

A general theorem on the closure of translates in certain weighted spaces in $R^n$ is proved and as a consequence a general $n$-dimensional Tauberian theorem. This is applied to the $n$-dimensional Laplace transform and to the one-dimensional Stieltjes- and Weierstrass transforms.
Relationship between polynomials with multiple roots and rational functions with common roots
Authors: Kamiyama Yasuhiko
Published: September 2016

For $F= R$ or $C$, let $\P^l_{k,n}(F){l}$ denote the space of monic polynomials $f(z)$ over $F$ of degree $k$ and such that the number of $n$-fold roots of $f(z)$ is at most $l$. Let $X^l_{k, n}(F)$ denote the space consisting of all $n$-tuples $(p_1(z),\ldots,p_n(z))$ of monic polynomials over $F$ of degree $k$ and such that there are at most $l$ roots common to all $p_i (z)$. In this paper, we prove that $P^{l}_{k,n}(F)$ and $X_{[\frac{k}{n}],n}^l(F)$ are stably homotopy equivalent. In fact, they are homotopy equivalent when $F = C$ and $(n, l) \not= (2, 0)$. We also consider the case that $n$-fold roots and common roots are not real. These results generalize previous results concerning these spaces.
Rigid $\mathcal{OL}_p$structures of non-commutative $L_p$-spaces associated with hyperfinite von Neumann algebras
Authors: Junge Marius , Ruan Zhong-Jin , Xu Quanhua
Published: September 2016

This paper is devoted to the study of rigid local operator space structures on non-commutative $L_p$-spaces. We show that for $1\le p \neq 2 < \infty$, a non-commutative $L_p$-space $L_p(\mathcal M)$ is a rigid $\mathcal{OL}_p$ space (equivalently, a rigid $\mathcal{COL}_p$ space) if and only if it is a matrix orderly rigid $\mathcal{OL}_p$ space (equivalently, a matrix orderly rigid $\mathcal{COL}_p$ space). We also show that $L_p(\mathcal M)$ has these local properties if and only if the associated von Neumann algebra $\mathcal M$ is hyperfinite. Therefore, these local operator space properties on non-commutative $L_p$-spaces characterize hyperfinite von Neumann algebras.
A note on Myrberg points and ergodicity
Authors: Falk Kurt
Published: September 2016

The main purpose of this note is to further clarify the strong relationship between ergodicity and Myrberg type dynamics in hyperbolic manifolds. This is achieved mainly via a new suggestive proof of the fact that the Myrberg limit set of a Kleinian group is of full Patterson measure if the geodesic flow on the associated hyperbolic manifold is ergodic with respect to the Patterson-Sullivan measure.
Higher order Hilbert-Schmidt Hankel forms and tensors of analytical kernels
Authors: Ferguson Sarah H. , Rochberg Richard
Published: September 2016

The symbols of $n^{\hbox{th}}$-order Hankel forms defined on the product of certain reproducing kernel Hilbert spaces $H(k_{i})$, $i=1,2$, in the Hilbert-Schmidt class are shown to coincide with the orthogonal complement in $H(k_{1})\otimes H(k_{2})$ of the ideal of polynomials which vanish up to order $n$ along the diagonal. For tensor products of weighted Bergman and Dirichlet type spaces (including the Hardy space) we introduce a higher order restriction map which allows us to identify the relative quotient of the $n^{\hbox{th}}$-order ideal modulo the $(n+1)^{\hbox{st}}$-order one as a direct sum of single variable Bergman and Dirichlet-type spaces. This generalizes the well understood $0^{\hbox{th}}$-order case.
Special homological dimensions and intersection theorem
Authors: Sharif Tirdad , Yassemi Siamak
Published: September 2016

Let $(R,m)$ be commutative Noetherian local ring. It is shown that $R$ is Cohen-Macaulay ring if there exists a Cohen-Macaulay finite (i.e. finitely generated) $R$-module with finite upper Gorenstein dimension. In addition, we show that, in the Intersection Theorem, projective dimension can be replaced by quasi-projective dimension.
On the classification of complex multi-germs of corank one and codimension one
Authors: Houston Kevin
Published: September 2016

Corank one multi-germs $f:(\mathbf{C}^n,S)\to (\mathbf{C}^p,0)$, $n<p$, of $\mathcal A_e$-codimension one are classified. The mono-germs are given in an explicit normal form and the multi-germs are described in terms of augmentations, and concatenations of mono-germs and a special bi-germ.
Spaces of fractions and positive functionals
Authors: Vasilescu F.-H.
Published: September 2016

We discuss integral representations and extensions of positive functionals in some spaces of fractions of continuous functions. As a consequence, numerical caracterizations for the solvability of power moment problems and the uniqueness of the solutions in unbounded sets are obtained.
Relationships between monotonicity and complex rotundity properties with some consequences
Authors: Hudzik Henryk , Narloch Agata
Published: September 2016

It is proved that a point $f$ of the complexification $E^C$ of a real Köthe space $E$ is a complex extreme point if and only if $|f|$ is a point of upper monotonicity in $E$. As a corollary it follows that $E$ is strictly monotone if and only if $E^C$ is complex rotund. It is also shown that $E$ is uniformly monotone if and only if $E^C$ is uniformly complex rotund. Next, the fact that $|x|\in S(E^+)$ is a ULUM-point of $E$ whenever $x$ is a $C$-LUR-point of $S(E^C)$ is proved, whence the relation that $E$ is a ULUM-space whenever $E^C$ is $C$-LUR is concluded. In the second part of this paper these general results are applied to characterize complex rotundity of properties Calderón-Lozanovskiĭ spaces, generalized Calderón-Lozanovskiĭ spaces and Orlicz-Lorentz spaces.
Construction and pure infiniteness of $C^*$-algebras associated with lambda-graph systems
Authors: Matsumoto Kengo
Published: September 2016

A $\lambda$-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. In [16] the author has introduced a $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ associated with a $\lambda$-graph system $\mathfrak{L}$ by using groupoid method as a generalization of the Cuntz-Krieger algebras. In this paper, we concretely construct the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ by using both creation operators and projections on a sub Fock Hilbert space associated with $\mathfrak{L}$. We also introduce a new irreducible condition on $\mathfrak{L}$ under which the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ becomes simple and purely infinite.
Rouché type theorems and a theorem of Adamyan, Arov and Krein
Authors: Nakazi Takahiko
Published: September 2016

We show Rouché type theorems using a theorem of Adamyan, Arov and Krein. As applications, we obtain a certain characterization of self-maps of the unit disc in terms of the location of the Denjoy-Wolf point and we study a function in the Smirnov class whose real part is positive.
Maximal operators for the holomorphic Laguerre semigroup
Authors: Sasso Emanuela
Published: September 2016

For each $p$ in $[1,\infty)$ let $\mathbf{E}_p$ denote the closure of the region of holomorphy of the Laguerre semigroup $\{M^{\alpha}_t:t>0\}$ on $L^p$ with respect to the Laguerre measure $\mu_{\alpha}$. We prove weak type and strong type estimates for the maximal operator $f\mapsto \sup\{|M^{\alpha}_z f|:z\in \mathbf{E}_p\}$. In particular, we give a new proof for the weak type $1$ estimate for the maximal operator associated to $M^{\alpha}_t$. Our starting point is the well-known relationship between the Laguerre semigroup of half-integer parameter and the Ornstein-Uhlenbeck semigroup.
Endomorphisms and automorphisms from subfactors illustrating non-commutative entropy
Authors: Svendsen Anne Louise
Published: September 2016

We present a series of examples of endomorphisms and automorphisms arising from subfactors, which illustrate some of the recent theorems in non-commutative entropy theory. Moreover it is shown that for these examples the Connes-Størmer entropy of the automorphism is maximal and coincides with the topological entropy. This follows from the theorems our examples illustrate, and is also showed directly.
Measures with unique tangent measures in metric groups
Authors: Mattila Pertti
Published: September 2016

We show that a Radon measure on a locally compact metric group with natural dilations has almost everywhere a unique tangent measure if and only if it has almost everywhere a Haar measure of a closed dilation invariant subgroup as its unique tangent measure.
On real trigonal Riemann surfaces
Authors: Costa Antonio F. , Izquierdo Milagros
Published: September 2016

A closed Riemann surface $X$ which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering will be called a trigonal morphism. A trigonal Riemann surface $X$ is called real trigonal if there is an anticonformal involution (symmetry) $\sigma$ of $X$ commuting with the trigonal morphism. If the trigonal morphism is a cyclic regular covering the Riemann surface is called real cyclic trigonal. The species of the symmetry $\sigma $ is the number of connected components of the fixed point set $\mathrm{Fix}(\sigma)$ and the orientability of the Klein surface $X/\langle\sigma\rangle$. We characterize real trigonality by means of Fuchsian and NEC groups. Using this approach we obtain all possible species for the symmetry of real cyclic trigonal and real non-cyclic trigonal Riemann surfaces.
On boundary critical points for semigroups of analytic functions
Authors: Contreras M. D. , Díaz-Madrigal S. , Pommerenke Ch.
Published: September 2016

We analyze the relationship between boundary fixed points of semigroups of analytic functions and boundary critical points of their infinitesimal generators. As a consequence, we show two new inequalities for analytic self-maps of the unit disk. The first one is about angular derivatives at fixed points of functions belonging to semigroups of analytic functions. The second one deals with angular derivatives at contact points of arbitrary analytic functions from the unit disk into itself.
Direct sums of exact covers of complexes
Authors: Iacob Alina
Published: September 2016

A ring $R$ is left noetherian if and only if the direct sum of injective envelopes of any family of left $R$-modules is the injective envelope of the direct sum of the given family of modules (or equivalently, if and only if the direct sum of any family of injective left $R$-modules is also injective). This result of Bass ([2]) led to a series of similar closure questions concerning classes of modules and classes of envelopes and covers (Chase in [4] considers the question of the closure of the class of flat modules with respect to products). Motivated by Bass' result we consider the question of direct sums of exact covers of complexes. From the close connection between minimal injective resolutions of modules and exact covers of complexes it seemed reasonable to conjecture that we get this closure over left noetherian rings. In this paper we show that this is not the case and that under various additional hypotheses on the ring that in fact the ring must have finite left global dimension for this to happen. Our results raise what we consider an interesting question about characterizing the local rings of finite global dimension in terms of a certain property of minimal projective resolutions of finitely generated modules over the local ring. We also consider the closely related question of when the direct sum of DG-injective complexes is DG-injective.
The connection between the Cegrell classes and compliant functions
Authors: Czyz} Rafal , Åhag Per
Published: September 2016

In this article the connection between the Cegrell classes and compliant functions is studied. A suitable norm is constructed which makes the compliant functions into a Banach space. As an application a characterization of the Dirichlet problem for pluriharmonic functions is achieved. Explicit examples of non-compliant functions will be constructed and a sufficient condition for compliance will be proved.
The spherical maximal function on the free two-step nilpotent Lie group
Authors: Fischer Véronique
Published: September 2016

We consider here the free two step nilpotent Lie group, provided with the homogeneous Korányi norm; we prove the $L^p$-boundedness of the maximal function corresponding to the homogeneous unit sphere, for some $p$.
Characterizations of tripotents in JB*-triples
Authors: Hügli Remo V.
Published: September 2016

The set $\mathcal{U}(A)$ of tripotents in a $\mathrm{JB}^*$-triple $A$ is characterized in various ways. Some of the characterizations use only the norm-structure of $A$. The partial order on $\mathcal{U}(A)$ as well as $\sigma$-finiteness of tripotents are described intrinsically in terms of the facial structure of the unit ball $A_1$ in $A$, i.e. without reference to the (pre-)dual of $A$. This extends similar results obtained in [6] and simplifies the metric characterization of partial isometries in $C^*$-algebras found in [1](cf. [8].
$S$-regularity and the corona factorization property
Authors: Kucerovsky D. , Ng P. W.
Published: September 2016

Stability is an important and fundamental property of $C^{*}$-algebras. Given a short exact sequence of $C^{*}$-algebras $0\longrightarrow B\longrightarrow E\longrightarrow A\longrightarrow 0$ where the ends are stable, the middle algebra may or may not be stable. We say that the first algebra, $B$, is $S$-regular if every extension of $B$ by a stable algebra $A$ has a stable extension algebra, $E$. Rördam has given a sufficient condition for $S$-regularity. We define a new condition, weaker than Rördam's, which we call the corona factorization property, and we show that the corona factorization property implies $S$-regularity. The corona factorization property originated in a study of the Kasparov $KK^1(A,B)$ group of extensions, however, we obtain our results without explicit reference to $KK$-theory. Our main result is that for a separable stable $C^{*}$-algebra $B$ the first two of the following properties (which we define later) are equivalent, and both imply the third. With additional hypotheses on the $C^{*}$-algebra, all three properties are equivalent. $B$ has the corona factorization property. Stability is a stable property for full hereditary subalgebras of $B$. $B$ is $S$-regular. We also show that extensions of separable stable $C^{*}$-algebras with the corona factorization property give extension algebras with the corona factorization property, extending the results of [9].
Connes-amenability of bidual and weighted semigroup algebras
Authors: Daws Matthew
Published: September 2016

We investigate the notion of Connes-amenability, introduced by Runde in [10], for bidual algebras and weighted semigroup algebras. We provide some simplifications to the notion of a $\sigma WC$-virtual diagonal, as introduced in [13], especially in the case of the bidual of an Arens regular Banach algebra. We apply these results to discrete, weighted, weakly cancellative semigroup algebras, showing that these behave in the same way as ${ C}^*$-algebras with regards Connes-amenability of the bidual algebra. We also show that for each one of these cancellative semigroup algebras $l^1(S,\omega)$, we have that $l^1(S,\omega)$ is Connes-amenable (with respect to the canonical predual $c_0(S)$) if and only if $l^1(S,\omega)$ is amenable, which is in turn equivalent to $S$ being an amenable group, and the weight satisfying a certain restrictive condition. This latter point was first shown by Grønnbæk in [6], but we provide a unified proof. Finally, we consider the homological notion of injectivity, and show that here, weighted semigroup algebras do not behave like ${ C}^*$-algebras.
Approximation by invertible functions of $H^{\infty}$
Authors: Nicolau Artur , Suárez Daniel
Published: September 2016

We provide an analytic proof that if $H^\infty$ is the algebra of bounded analytic functions on the unit disk, $A$ is a Banach algebra and $f: H^\infty \rightarrow A$ is a Banach algebras morphism with dense image, then $f((H^\infty)^{-1})$ is dense in $A^{-1}$.
Sums of two-dimensional spectral triples
Authors: Christensen Erik , Ivan Cristina
Published: September 2016

We study countable sums of two-dimensional modules for the continuous complex functions on a compact metric space and show that it is possible to construct a spectral triple which gives the original metric back. This spectral triple will be finitely summable for any positive parameter. We also construct a sum of two-dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in $\mathsf R$. The metric is recovered exactly, the Dixmier trace induces a multiple of the Lebesgue integral and the growth of the number of eigenvalues $N(\Lambda)$ bounded by $\Lambda$ behaves, such that $N(\Lambda)/\Lambda$ is bounded, but without limit for $\Lambda\to \infty$.
Jensen's operator inequality and its converses
Authors: Hansen Frank , Pecaric Josip , Peric Ivan
Published: September 2016

We give a general formulation of Jensen's operator inequality for unital fields of positive linear mappings, and we consider different types of converse inequalities.
Outer actions of a discrete amenable group on approximately finite dimensional factors II, the III$_{\lambda}$-case, $\lambda\neq 0$
Authors: Katayama Yoshikazu , Takesaki Masamichi
Published: September 2016

To study outer actions $\alpha$ of a group $G$ on a factor $\mathcal M$ of type $\mathrm{III}_\lambda$, $0<\lambda<1$, we study first the cohomology group of a group with the unitary group of an abelian von Neumann algebra as a coefficient group and establish a technique to reduce the coefficient group to the torus $\mathsf T$ by the Shapiro mechanism based on the groupoid approach. We then show a functorial construction of outer actions of a countable discrete amenable group on an AFD factor of type $\mathrm{III}_\lambda$, sharpening the result in [17, §4]. The periodicity of the flow of weights on a factor $\mathcal M$ of type $\mathrm{III}_\lambda$ allows us to introduce an equivariant commutative square directly related to the discrete core. But this makes it necessary to introduce an enlarged group $\mathrm{Aut}(\mathcal M)_{m}$ relative to the modulus homomorphism $m=\mod\colon \mathrm{Aut}(\mathcal M)\to \mathsf R/T'\mathsf Z$. We then discuss the reduced modified HJR-exact sequence, which allows us to describe the invariant of outer action $\alpha$ in a simpler form than the one for a general AFD factor: for example, the cohomology group $H_{m,s}^{out}(G,N,\mathsf T)$ of modular obstructions is a compact abelian group. Making use of these reductions, we prove the classification result of outer actions of $G$ on an AFD factor $\mathcal M$ of type $\mathrm{III}_{\lambda}$.
Means of unitary operators, revisited
Authors: Haagerup Uffe , Kadison Richard V. , Pedersen Gert K.
Published: September 2016

It is proved that an operator with bound not exceeding $(n-2)n^{-1}$ in a $C^*$-algebra is the mean of $n$ unitay operators in that algebra.
Dimension groups associated to $\beta$-expansions
Authors: Bates Teresa , Carlsen Toke Meier , Eilers Søren
Published: September 2016

Completing work by Shultz on one hand and by Katayama, Matsumoto, and Watatani on the other, we prove that a priori different dimension groups associated to $\beta$-expansions in fact coincide.
A global morphism from the Douady space to the cycle space
Authors: Magnússon Jón Ingólfur
Published: September 2016

We establish, for any given complex space $M$, a global morphism from the reduction of its Douady space to its cycle space. This morphism is an extension of the morphism defined in [1] from the subspace of the Douady space formed by all pure dimensional subspaces of $M$ to the cycle space of $M$. In the case where $M$ is projective this morphism is the classical morphism from the Hilbert scheme of $M$ to the Chow scheme of $M$.
On the dimension theory of von Neumann algebras
Authors: Sherman David
Published: September 2016

In this paper we study three aspects of $(\mathcal{P}(\mathcal{M})/{\sim})$, the set of Murray-von Neumann equivalence classes of projections in a von Neumann algebra $\mathcal M$. First we determine the topological structure that $(\mathcal{P}(\mathcal{M})/{\sim})$ inherits from the operator topologies on $\mathcal M$. Then we show that there is a version of the center-valued trace which extends the dimension function, even when $\mathcal M$ is not $\sigma$-finite. Finally we prove that $(\mathcal{P}(\mathcal{M})/{\sim})$ is a complete lattice, a fact which has an interesting reformulation in terms of representations.
On the size of the non-coincidence set of parabolic obstacle problems with applications to American option pricing
Authors: Arnarson Teitur , Eriksson Jonatan
Published: September 2016

The following paper is devoted to the study of the positivity set $U=\{\mathcal{L}\phi>0\}$ arising in parabolic obstacle problems. It is shown that $U$ is contained in the non-coincidence set with a positive distance between the boundaries uniformly in the spatial variable if the boundary of $U$ satisfies an interior $C^1$-Dini condition in the space variable and a Lipschitz condition in the time variable. We apply our results to American option pricing and we thus show that the positivity set is strictly contained in the continuation region, which means that the option should not be exercised in $U$ or on the boundary of $U$.
Higher minors and van Kampen's obstruction
Authors: Nevo Eran
Published: September 2016

We generalize the notion of graph minors to all (finite) simplicial complexes. For every two simplicial complexes $H$ and $K$ and every nonnegative integer $m$, we prove that if $H$ is a minor of $K$ then the non vanishing of Van Kampen's obstruction in dimension $m$ (a characteristic class indicating non embeddability in the $(m-1)$-sphere) for $H$ implies its non vanishing for $K$. As a corollary, based on results by Van Kampen and Flores, if $K$ has the $d$-skeleton of the $(2d+2)$-simplex as a minor, then $K$ is not embeddable in the $2d$-sphere. We answer affirmatively a problem asked by Dey et. al. concerning topology-preserving edge contractions, and conclude from it the validity of the generalized lower bound inequalities for a special class of triangulated spheres.
A generalized Poincaré-Lelong formula
Authors: Andersson Mats
Published: September 2016

We prove a generalization of the classical Poincaré-Lelong formula. Given a holomorphic section $f$, with zero set $Z$, of a Hermitian vector bundle $E\to X$, let $S$ be the line bundle over $X\setminus Z$ spanned by $f$ and let $Q=E/S$. Then the Chern form $c(D_Q)$ is locally integrable and closed in $X$ and there is a current $W$ such that ${dd}^cW=c(D_E)-c(D_Q)-M,$ where $M$ is a current with support on $Z$. In particular, the top Bott-Chern class is represented by a current with support on $Z$. We discuss positivity of these currents, and we also reveal a close relation with principal value and residue currents of Cauchy-Fantappiè-Leray type.
The Daugavet property for spaces of Lipschitz functions
Authors: Ivakhno Yevgen , Kadets Vladimir , Werner Dirk
Published: September 2016

For a compact metric space $K$ the space $\mathrm{Lip}(K)$ has the Daugavet property if and only if the norm of every $f \in \mathrm{Lip}(K)$ is attained locally. If $K$ is a subset of an $L_p$-space, $1<p<\infty$, this is equivalent to the convexity of $K$.
Minimal linear representations of the low-dimensional nilpotent Lie algebras
Authors: Benjumea J. C. , Núnez J. , Tenorio A. F.
Published: September 2016

The main goal of this paper is to compute a minimal matrix representation for each non-isomorphic nilpotent Lie algebra of dimension less than $6$. Indeed, for each of these algebras, we search the natural number $n\in\mathsf{N}\setminus\{1\}$ such that the linear algebra $\mathfrak{g}_n$, formed by all the $n \times n$ complex strictly upper-triangular matrices, contains a representation of this algebra. Besides, we show an algorithmic procedure which computes such a minimal representation by using the Lie algebras $\mathfrak{g}_n$. In this way, a classification of such algebras according to the dimension of their minimal matrix representations is obtained. In this way, we improve some results by Burde related to the value of the minimal dimension of the matrix representations for nilpotent Lie algebras.
$\mathsf Q$-linear functions, functions with dense graph, and everywhere surjectivity
Authors: García-Pacheco F. J. , Rambla-Barreno F. , Seoane-Sepúlveda J. B.
Published: September 2016

Let $L$, $S$ and $D$ denote, respectively, the set of $\mathsf{Q}$-linear functions, the set of everywhere surjective functions and the set of dense-graph functions on $\mathsf{R}$. In this note, we show that the sets $D\setminus(S \cup L)$, $S \setminus L$, $S \cap L$ and $D\cap L \setminus S$ are lineable. Moreover, all these sets contain (omitting zero) a vector space of the biggest possible dimension, $2^c$.
Fatou-type theorems for general approximate identities
Authors: Carlsson Marcus
Published: September 2016

For functions $f \in L^{1}(\mathsf{R}^n)$ we consider extensions to $\mathsf{R}^n \times \mathsf{R}^{+}$ given by convolving $f$ with an approximate identity. For a large class of approximate identities we obtain a Fatou-type theorem where the convergence regions are sometimes effectively larger than the non-tangential ones. We then study a more restricted class of approximate identities for which the convergence regions are shown to be optimal. Finally we will consider products of approximate identities. The results extend previous results by Sjöogren, Rönning and Brundin .
On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients
Authors: Cicognani Massimo , Hirosawa Fumihiko
Published: September 2016

We consider the loss of regularity of the solution to the backward Cauchy problem for a second order strictly hyperbolic equation on the time interval $[0,T]$ with time depending coefficients which have a singularity only at the end point $t=0$. The main purpose of this paper is to show that the loss of regularity of the solution on the Gevrey scale can be described by the order of differentiability of the coefficients on $(0,T]$, the order of singularities of each derivatives as $t\to0$ and a stabilization condition of the amplitude of oscillations described by an integral on $(0,T)$. Moreover, we prove the optimality of the conditions for $C^\infty$ coefficients on $(0,T]$ by constructing a counterexample.
Equivalence between the boundary Harnack principle and the Carleson estimate
Authors: Aikawa Hiroaki
Published: September 2016

Both the boundary Harnack principle and the Carleson estimate describe the boundary behavior of positive harmonic functions vanishing on a portion of the boundary. These notions are inextricably related and have been obtained simultaneously for domains with specific geometrical conditions. The main aim of this paper is to show that the boundary Harnack principle and the Carleson estimate are equivalent for arbitrary domains.
On spectra and Brown's spectral measures of elements in free products of matrix algebras
Authors: Fang Junsheng , Hadwin Don , Ma Xiujuan
Published: September 2016

We compute spectra and Brown measures of some non self-adjoint operators in $(M_2(\mathsf {C}), \frac{1}{2}\mathrm{Tr})*(M_2(\mathsf{C}), \frac{1}{2}\mathrm{Tr})$, the reduced free product von Neumann algebra of $M_2(\mathsf {C})$ with $M_2(\mathsf {C})$. Examples include $AB$ and $A+B$, where $A$ and $B$ are matrices in $(M_2(\mathsf {C}), \frac{1}{2}\mathrm{Tr})*1$ and $1*(M_2(\mathsf {C}), \frac{1}{2}\mathrm{Tr})$, respectively. We prove that $AB$ is an R-diagonal operator (in the sense of Nica and Speicher [12]) if and only if $\mathrm{Tr}(A)=\mathrm{Tr}(B)=0$. We show that if $X=AB$ or $X=A+B$ and $A,B$ are not scalar matrices, then the Brown measure of $X$ is not concentrated on a single point. By a theorem of Haagerup and Schultz [9], we obtain that if $X=AB$ or $X=A+B$ and $X\neq \lambda 1$, then $X$ has a nontrivial hyperinvariant subspace affiliated with $(M_2(\mathsf{C}), \frac{1}{2}\mathrm{Tr})*(M_2(\mathsf{C}), \frac{1}{2}\mathrm{Tr})$.
$L^2$-homology for compact quantum groups
Authors: Kyed David
Published: September 2016

A notion of $L^2$-homology for compact quantum groups is introduced, generalizing the classical notion for countable, discrete groups. If the compact quantum group in question has tracial Haar state, it is possible to define its $L^2$-Betti numbers and Novikov-Shubin invariants/capacities. It is proved that these $L^2$-Betti numbers vanish for the Gelfand dual of a compact Lie group and that the zeroth Novikov-Shubin invariant equals the dimension of the underlying Lie group. Finally, we relate our approach to the approach of A. Connes and D. Shlyakhtenko by proving that the $L^2$-Betti numbers of a compact quantum group, with tracial Haar state, are equal to the Connes-Shlyakhtenko $L^2$-Betti numbers of its Hopf $*$-algebra of matrix coefficients.
Quasisymmetric functions from a topological point of view
Authors: Baker Andrew , Richter Birgit
Published: September 2016

It is well-known that the homology of the classifying space of the unitary group is isomorphic to the ring of symmetric functions $\mathsf {Symm}$. We offer the cohomology of the space $\Omega \Sigma {\mathsf C} P^{\infty}$ as a topological model for the ring of quasisymmetric functions $\mathsf {QSymm}$. We exploit standard results from topology to shed light on some of the algebraic properties of $\mathsf {QSymm}$. In particular, we reprove the Ditters conjecture. We investigate a product on $\Omega \Sigma {\mathsf C} P^{\infty}$ that gives rise to an algebraic structure which generalizes the Witt vector structure in the cohomology of $BU$. The canonical Thom spectrum over $\Omega \Sigma {\mathsf C} P^{\infty}$ is highly non-commutative and we study some of its features, including the homology of its topological Hochschild homology spectrum.
Commuting semigroups of holomorphic mappings
Authors: Elin Mark , Levenshtein Marina , Reich Simeon , Shoikhet David
Published: September 2016

Let $S_{1}=\left\{F_t\right\}_{t\geq 0}$ and $S_{2}=\left\{G_t\right\}_{t\geq 0}$ be two continuous semigroups of holomorphic self-mappings of the unit disk $\Delta=\{z:|z|<1\}$ generated by $f$ and $g$, respectively. We present conditions on the behavior of $f$ (or $g$) in a neighborhood of a fixed point of $S_{1}$ (or $S_{2}$), under which the commutativity of two elements, say, $F_1$ and $G_1$ of the semigroups implies that the semigroups commute, i.e., $F_{t}\circ G_{s}=G_{s}\circ F_{t}$ for all $s,t\geq 0$. As an auxiliary result, we show that the existence of the (angular or unrestricted) $n$-th derivative of the generator $f$ of a semigroup $\left\{F_t\right\}_{t\geq 0}$ at a boundary null point of $f$ implies that the corresponding derivatives of $F_{t}$, $t\geq 0$, also exist, and we obtain formulae connecting them for $n=2,3$.
Generalized Wallace theorems
Authors: Danchev Peter V. , Keef Patrick W.
Published: September 2016

We present a number of generalizations of a classical result of Wallace regarding countable extensions of totally projective primary abelian groups.
Topology and factorization of polynomials
Authors: Shaker Hani
Published: September 2016

For any polynomial $P\in {\mathsf C} [X_1,X_2,\ldots,X_n]$, we describe a $\mathsf C$-vector space $F(P)$ of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of $F(P)$ is the number of irreducible factors of $P$. Moreover, the knowledge of $F(P)$ gives a complete factorization of the polynomial $P$ by taking gcd's. This generalizes previous results by Ruppert and Gao in the case $n=2$.
The fundamental group of the space of maps from a surface into the projective plane
Authors: Gonçalves Daciberg L. , Spreafico Mauro
Published: September 2016

In this work we compute the fundamental group of each connected component of the function space of maps from a closed surface into the projective space
vector-valued singular integrals and maximal functions on spaces of homogeneous type
Authors: Grafakos Loukas , Liu Liguang , Yang Dachun
Published: September 2016

The Fefferman-Stein vector-valued maximal function inequality is proved for spaces of homogeneous type. The approach taken here is based on the theory of vector-valued Calderón-Zygmund singular integral theory in this context, which is appropriately developed.
Distributions that are convolvable with generalized Poisson kernel of solvable extensions of homogeneous Lie groups
Authors: Damek Ewa , Dziubanski Jacek , Jaming Philippe , Pérez-Esteva Salvador
Published: September 2016

In this paper, we characterize the class of distributions on a homogeneous Lie group $\mathfrak N$ that can be extended via Poisson integration to a solvable one-dimensional extension $\mathfrak S$ of $\mathfrak N$. To do so, we introduce the $\mathcal S'$-convolution on $\mathfrak N$ and show that the set of distributions that are $\mathcal S'$-convolvable with Poisson kernels is precisely the set of suitably weighted derivatives of $L^1$-functions. Moreover, we show that the $\mathcal S'$-convolution of such a distribution with the Poisson kernel is harmonic and has the expected boundary behavior. Finally, we show that such distributions satisfy some global weak-$L^1$ estimates.
Berezin quantization on generalized flag manifolds
Authors: Cahen Benjamin
Published: September 2016

Let $M=G/H$ be a generalized flag manifold where $G$ is a compact, connected, simply-connected Lie group with Lie algebra $\mathfrak{g}$ and $H$ is the centralizer of a torus. Let $\pi$ be a unitary irreducible representation of $G$ which is holomorphically induced from a character of $H$. Using a complex parametrization of a dense open subset of $M$, we realize $\pi$ on a Hilbert space of holomorphic functions. We give explicit expressions for the differential $d\pi$ of $\pi$ and for the Berezin symbols of $\pi (g)$ ($g\in G$) and $d\pi (X)$ ($X\in \mathfrak{g}$). In particular, we recover some results of S. Berceanu and we partially generalize a result of K. H. Neeb.
Plane sets allowing bilipschitz extensions
Authors: Alestalo P. , Trotsenko D. A.
Published: September 2016

We give a geometric characterization for a plane set $A\subset {\mathsf R}^2$ to have the following linear bilipschitz extension property: For $0\le \varepsilon \le \delta$, every $(1 + \varepsilon)$-bilipschitz map $f\colon A\to {\mathsf R}^2$ has a $(1 + C\varepsilon)$-bilipschitz extension to the whole plane ${\mathsf R}^2$.