bluuebunny/crossref_metadata_2025 huggingface dataset:
The Western snip, stitch, and tug hydrocelectomy: How I do it
Authors: Rowe Neal E. , Martin Paul , Luke Patrick P.
Published: September 2016

Introduction: Adult idiopathic hydrocele is a common benign disorder that merits surgical correction when symptomatic. The most popular techniques for repair are plication (Lord’s procedure) or excision and eversion of the tunica vaginalis (Jaboulay procedure). Established complications from these traditional repairs include hematoma, recurrence, and infection. These procedures are performed through a scrotal incision. We describe a novel technique of hydrocele repair with gubernaculum preservation through a subinguinal incision.

Methods: The novel technique is described in detail. A retrospective review was performed of those patients treated by a single surgeon with the subinguinal technique. Demographic information, indication for treatment, success rate, and details regarding complications were collected.

Results: We term the technique the “Snip, Stitch & Tug” repair. Through a small subinguinal incision, the tunica is everted posterior to the spermatic cord and testis without resection of the hydrocele sac or division of the gubernaculum. Twelve patients with postoperative followup were identified. Eleven patients (92%) treated with the novel technique were cured. There was only one complication (superficial wound infection) recorded after this technique.

Conclusions: Idiopathic hydrocele repair with gubernaculum preservation can be easily and safely performed through a small subinguinal incision.
Reflections on the Grammatical Category of before, after and since Introducing Non-finite -ing Clauses: A Corpus Approach
Authors: He Qingshun
Published: September 2016

English language learners may be confused in identifying the grammatical category of such conjunctive expressions as before, after and since introducing non-finite -ing clauses. In this article, we will conduct a corpus-based investigation of hypotactic conjunctions and conjunctive prepositions following the principle of unidirectional transfer in grammatical metaphor proposed by He and Yang (2014) within the framework of Systemic Functional Linguistics. The research concludes that hypotactic conjunctions tend to transfer to zero conjunctions and before, after and since introducing non-finite -ing clauses should be included into the grammatical category of conjunctive prepositions.
Multiple Measures of Family and Social Support as Predictors of Psychological Well-Being: An Additive Approach
Authors: Mason Hema O.
Published: September 2016

The purpose of this study was to (1) examine the direct relations of multiple sources of social support on psychological well-being and (2) to examine the utility of an additive model on these variables, in a sample of 251 participants from a Southwestern Georgia University. The sources of support included family environment, friendship, family and significant other support, father’s bonding and mother’s bonding. Measures of psychological well-being included the summed total of Ryff’s Scale of Psychological Well-Being (PWB), as well as self-confidence-an additional measure of psychological well-being. In addition to direct effects, it was hypothesized that having multiple, rather than fewer sources of support would be more beneficial to an individual. Hierarchical regression analyses were conducted to test the unique variability each variable added, as well as to determine whether the additive model predicted PWB above and beyond singular sources of support. Results revealed that the hypotheses predicting direct relationships between the social supports of interest and PWB were largely supported by the data with the exception of father bonding. Results for the additive model revealed mixed results, indicating that having numerous concurrent support lines are beneficial in certain cases. The importance of having multiple social supports from which one can rely, especially when dealing with stressors and crises are also expressed.
The occurrence of fungi on roots and stem bases of Triticum aestivum ssp. spelta L. Thell. grown under two levels of chemical protection and harmfulness of Fusarium graminearum Schwabe to seedlings of selected genotypes
Authors: Cegiełko Małgorzata , Kiecana Irena , Rachoń Leszek , Pastucha Alina , Wit Marcin , Pojmaj Mirosław
Published: September 2016

Investigations were carried out in 2007–2009 on the plots of the Felin Experimental Station belonging to the University of Life Sciences in Lublin, Poland. The studies comprised two breeding lines of spelt wheat (Triticum aestivum ssp. spelta L. Thell.) – STH 3 and STH 715. Two levels of chemical protection were applied in the cultivation with minimal and complex protection. Infection of winter spelt wheat roots and stem bases was recorded in each growing season at hard dough stage (87 in Zadok’s scale). After 3 years of the study, the mean values of disease indexes for the analyzed spelt wheat lines in the experimental treatment with minimal protection were 28.53 and 40.30 respectively for STH 3 and STH 715. In the experimental combination with complex protection, after 3 years of the study the mean values of disease indexes ranged from 25.96 (STH 3) to 26.90 (STH 715). The mycological analysis showed that Fusarium spp., especially F. culmorum, caused root rot and necrosis of stem bases of spelt wheat in the experimental combination with minimal and complex protection. Moreover, Fusarium avenaceum and Bipolaris sorokiniana caused root rot and necrosis of stem bases of spelt wheat. Investigation carried out in a growth chamber on susceptibility of seedlings of three lines of spelt wheat (LO 2/09/n/2, LO 5/09/13/3, LO 5/09/5/4) to infection with Fusarium graminearum No. 8 and F. graminearum No. 45 showed that the genotypes did not differ in their susceptibility. All of them were susceptible, as indicated by high values of the disease indexes. No interaction was found between genotypes and strains of the fungus. This indicates the differential pathogenicity of Fusarium graminearum species.
On Some Deformations of Riemann Surfaces. I
Authors: Rubinsztein Ryszard L.
Published: September 2016

We define a family of infinitesimal deformations of compact Riemann surfaces of genus $g > 2$ which generalizes the Fenchel-Nielsen deformations. Those new deformations are associated to smooth vector fields on the circle. We compute a representation of the deformations in terms of Poincaré series and determine the corresponding Eichler cohomology classes.
On Additive K-Theory with the Loday - Quillen *-Product
Authors: Kuribayashi Katsuhiko , Yamaguchi Toshihiro
Published: September 2016

The $*$-product defined by Loday and Quillen [17] on the additive $\mathbf{K}$-theory (the cyclic homology with shifted degrees) $K_*^+(A)$ for a commutative ring $A$ is naturally extended to a product ($*$-product) on the additive $\mathbf{K}$-theory $K_*^+(\Omega)$ for a differential graded algebra $(\Omega,d)$ over a commutative ring. We prove that Connes' $\mathbf{B}$-maps from the additive $\mathbf{K}$-theory $K_*^+(\Omega)$ to the negative cyclic homology $\mathrm{HC}_*^-(\Omega)$ and to the Hochschild homology $\mathrm{HH}_*(\Omega)$ are morphisms of algebras under the $*$-product on $K_*^+(\Omega)$. Applications to topology of Connes' $\mathbf{B}$-maps are also described.
Approximate formulas for canonical homotopy operators for the $\bar \partial$ complex in strictly pseudoconvex domains
Authors: Andersson Mats , Boo Jörgen
Published: September 2016

Let $D=\{ \rho <0 \}$ be a smoothly bounded strictly pseudoconvex domain in $\boldsymbol C^n$ and $\rho$ a strictly plurisubharmonic smooth defining function. We construct explicit homotopy operators for the $\bar \partial$ complex, which are approximately equal to the homotopy operators that are canonical with respect to the metric $\Omega = i\varphi(-\rho)\partial \bar \partial \log(1/-\rho)$ and weights $(-\rho)^\alpha$, where $\varphi$ is a strictly positive smooth function. We also obtain an explicit operator which is approximately equal to the canonical homotopy operator for $\bar \partial_b$ on $\partial D$. From the explicit operators we obtain regularity results for these canonical operators, including $C^\infty$ regularity and $L^p$-boundedness for the orthogonal projections onto Ker $\bar \partial$ and Ker $\bar \partial_b$. Previously it has been proved, in the ball case and $\varphi \equiv 1$, that the boundary values of the canonical operators coincide with the values of well-known explicit operators due to Henkin and Skoda et al. Previously Lieb and Range have constructed an explicit homotopy operator which is approximately equal to the canonical operator with respect to the metric $i\varphi \partial \bar \partial_\rho$.
Stable vector bundles on curves: numerical invariants of their extremal subbundles
Authors: Ballico E.
Published: September 2016

Let $X$ be a smooth projective curve of genus $g \geq 2$ and $E$ a rank $r$ vector bundle on $X$. If $1 \leq t < r$ set $s_t(E)$:= sup $\lbrace t$(deg($E$)) - $r$(deg($F$)), where $F$ is a rank $t$ subsheaf of $E \rbrace $. Here we construct rank $r$ stable vector bundles $E$ on $X$ such that the sequence $ \lbrace s_t(E) \rbrace _{1 \leq t<r}$ has a prescribed value and the set of all subsheaves of $E$ with maximal degree may be explicitely described.
On the classification and bifurcation of multigerms of maps from surfaces to 3-space
Authors: Hobbs C. A. , Kirk N. P.
Published: September 2016

The $\mathcal A$-classification of multigerm singularities is discussed, based on the theory of complete transversals. An $\mathcal A$-classification of $r$-multigerms from the plane to 3-space of $\mathcal A-\text{codimension} \leq 6-r$ is carried out and the bifurcation geometry of these singularities analysed. This work has applications to the study of two-dimensional spatial motions, giving local models for the singularities which appear on general trajectories of rigid body motions from the plane to 3-space. In addition, our classification is extensive enough to give the full list of simple multigerm singularities from the plane to 3-space.
Transferring algebra structures up to homology equivalence
Authors: Johansson Leif , Lambe Larry
Published: September 2016

Given a strong deformation retract $M$ of an algebra $A$, there are several apparently distinct ways ([9],[19],[13],[24],[15],[18],[17]) of constructing a coderivation on the tensor coalgebra of $M$ in such a way that the resulting complex is quasi isomorphic to the classical (differential tor) [17] bar construction of $A$. We show that these methods are equivalent and are determined combinatorially by an inductive formula first given in a very special setting in [16]. Applications to de Rham theory and Massey products are given.
Twisted properties of banach spaces
Authors: Castillo Jesús M. F. , Gonzáles Manuel , Plichko Anatolij M. , Yost David
Published: September 2016

If $\mathcal P$, $\mathcal Q$ are two linear topological properties, say that a Banach space $X$ has the property $\mathcal P$-by-$\mathcal Q$ (or is a $\mathcal P$-by-$\mathcal Q$ space) if $X$ has a subspace $Y$ with property $\mathcal P$ such that the corresponding quotient $X/Y$ has property $\mathcal Q$. The choices $\mathcal P,\mathcal Q \in\{\hbox{separable, reflexive}\}$ lead naturally to some new results and new proofs of old results concerning weakly compactly generated Banach spaces. For example, every extension of a subspace of $L_1(0,1)$ by a WCG space is WCG. They also give a simple new example of a Banach space property which is not a 3-space property but whose dual is a 3-space property.
Purely Infinite, Simple $C^*$-Algebras Arising from Free Product Constructions, II
Authors: Dykema Kenneth J.
Published: September 2016

Certain reduced free products of $C^*$-algebras with respect to faithful states are simple and purely infinite.
Bratteli-Vershik models for Cantor minimal systems associated to interval exchange transformations
Authors: Gjerde Richard , Johansen Ørjan
Published: September 2016

We construct Bratteli-Vershik models for minimal interval exchange transformations. We use this to show that the interval exchange transformations over quadratic fields, recently studied by Boshernitzan and Carroll, actually are (conjugate to) substitution minimal systems. We also prove a partial converse to this. Furthermore, these systems are orbit equivalent to Sturmian systems.
Gaussian bounds for reduced heat kernels of subelliptic operators on nilpotent Lie groups
Authors: Elst A. F. M. Ter , Prado Humberto
Published: September 2016

We obtain Gaussian estimates for the kernels of the semigroups generated by a class of subelliptic operators $H$ acting on $L_p(\boldsymbol R^k)$. The class includes anharmonic oscillators and Schrödinger operators with external magnetic fields. The estimates imply an $H_\infty$-functional calculus for the operator $H$ on $L_p$ with $p \in \langle 1,\infty\rangle$ and in many cases the spectral $p$-independence. Moreover, we show for a subclass of operators satisfying a homogeneity property that the Riesz transforms of all orders are bounded.
Dubrovin equations and integrable systems on hyperelliptic curves
Authors: Gesztesy Fritz , Holden Helge
Published: September 2016

We introduce the most general version of Dubrovin-type equations for divisors on a hyperelliptic curve $\mathcal K_g$ of arbitrary genus $g\in\boldsymbol N$, and provide a new argument for linearizing the corresponding completely integrable flows. Detailed applications to completely integrable systems, including the KdV, AKNS, Toda, and the combined sine-Gordon and mKdV hierarchies, are made. These investigations uncover a new principle for $1+1$-dimensional integrable soliton equations in the sense that the Dubrovin equations, combined with appropriate trace formulas, encode all hierarchies of soliton equations associated with hyperelliptic curves. In other words, completely integrable hierarchies of soliton equations determine Dubrovin equations and associated trace formulas and, vice versa, Dubrovin-type equations combined with trace formulas permit the construction of hierarchies of soliton equations.
Discreteness of subgroups of $\mathrm{SL}(2,\boldsymbol{C})$ containing elliptic elements
Authors: Tukia Pekka , Wang Xiantao
Published: September 2016

The following result is the main result of the paper. Let $G\subset \boldsymbol{SL}(2,\boldsymbol C)$ be non-elementary. If $G$ contains an elliptic element of order at least 3, then $G$ is discrete if and only if each non-elementary subgroup generated by two elliptic elements of $G$ is discrete.
Topological triviality of families of real isolated singularities and their Milnor fibrations
Authors: Santos Raimundo Nonato Araújo Dos
Published: September 2016

The aim of this paper is to study the topological triviality and the topological equivalence of the Milnor fibrations for families of real analytic map germs with no coalescing of critical points.
Strong perforation in infinitely generated $\mathrm{K}_0$-groups of simple $C^*$-algebras
Authors: Toms Andrew S.
Published: September 2016

Let $(G,G^{+})$ be an ordered abelian group. We say that $G$ has strong perforation if there exists $x \in G$, $x \notin G^{+}$, such that $nx \in G^{+}$, $nx \neq 0$ for some natural number $n$. Otherwise, the group is said to be weakly unperforated. Examples of simple $C^{*}$-algebras whose ordered $\mathrm{K}_0$-groups have this property and for which the entire order structure on $\mathrm{K}_0$ is known have, until now, been restricted to the case where $\mathrm{K}_0$ is group isomorphic to the integers. We construct simple, separable, unital $C^{*}$-algebras with strongly perforated $\mathrm{K}_0$-groups group isomorphic to an arbitrary infinitely generated subgroup of the rationals, and determine the order structure on $\mathrm{K}_0$ in each case.
Unconditional bases in tensor products of Hilbert spaces
Authors: Pérez-García David , Villanueva Ignacio
Published: September 2016

We prove that a tensor norm $\alpha$ (defined on tensor products of Hilbert spaces) is the Hilbert-Schmidt norm if and only if $\ell_2\otimes\cdots\otimes \ell_2$, endowed with the norm $\alpha$, has an unconditional basis. This extends a classical result of Kwapień and Pełczyński. The symmetric version of that statement follows, and this extends a recent result of Defant, Díaz, García and Maestre.
Galois embedding problems and symmetric powers
Authors: Crespo Teresa , Hajto Zbigniew
Published: September 2016

We consider a Galois embedding problem given by a finite projective group and its special linear lifting. We give an equivalent condition to the solvability of such an embedding problem and a method of construction of its solutions.
Integration of simplicial forms and Deligne cohomology
Authors: Dupont Johan L. , Ljungmann Rune
Published: September 2016

We present two approaches to constructing an integration map along the fiber for smooth Deligne cohomology. The first is defined in the simplicial model, where a class in Deligne cohomology is represented by a simplicial form, and the second in a related but more combinatorial model .
$C^*$-algebras associated with the fundamental groups of graphs of groups
Authors: Okayasu Rui
Published: September 2016

We construct a nuclear $C^*$-algebra associated with the fundamental group of a graph of groups of finite type. It is well-known that every word-hyperbolic group with zero-dimensional boundary, in other words, every group acting trees with finite stabilizers is given by the fundamental group of such a graph of groups. We show that our $C^*$-algebra is $*$-isomorphic to the crossed product arising from the associated boundary action and is also given by a Cuntz-Pimsner algebra. We also compute the K-groups and determine the ideal structures of our $C^*$-algebras.
On the stable rank and real rank of group $C^*$-algebras of nilpotent locally compact groups
Authors: Archbold Robert J. , Kaniuth Eberhard
Published: September 2016

It is shown that if $G$ is an almost connected nilpotent group then the stable rank of $C^*(G)$ is equal to the rank of the abelian group $G/[G,G]$. For a general nilpotent locally compact group $G$, it is shown that finiteness of the rank of $G/[G,G]$ is necessary and sufficient for the finiteness of the stable rank of $C^*(G)$ and also for the finiteness of the real rank of $C^*(G)$.
The first Szegö limit theorem for non-selfadjoint operators in the Følner algebra
Authors: Böttcher Albrecht , Otte Peter
Published: September 2016

We determine the first order asymptotics of the trace of $f(P_nUP_n)$ and the determinant $\det P_nUP_n$ for operators $U$ belonging to the Følner algebra associated with the sequence $\{P_n\}$ and satisfying an "index zero" condition. We present three different proofs of the main result in the case where $U$ is a normal operator.
Degenerations of $(1,7)$-polarized abelian surfaces
Authors: Melliez F. , Ranestad K.
Published: September 2016

The moduli space of $(1,7)$-polarized abelian surfaces with a level structure was shown by Manolache and Schreyer to be rational with compactification the variety of powersum presentations of the Klein quartic curve. In this paper the possible degenerations of the abelian surfaces corresponding to degenerations of powersum presentations are classified.
A Monge-Ampère norm for delta-plurisubharmonic functions
Authors: Cegrell Urban , Wiklund Jonas
Published: September 2016

We consider differences of plurisubharmonic functions in the energy class $\mathcal{F}$ as a linear space, and equip this space with a norm, depending on the generalized complex Monge-Ampère operator, turning the linear space into a Banach space $\delta \mathcal{F}$. Fundamental topological questions for this space is studied, and we prove that $\delta\mathcal{F}$ is not separable. Moreover we investigate the dual space. The study is concluded with comparison between $\delta \mathcal{F}$ and the space of delta-plurisubharmonic functions, with norm depending on the total variation of the Laplace mass, studied by the first author in an earlier paper [7].
Embeddings for monotone functions and $B_p$ weights, between discrete and continuous
Authors: Garcia-Domingo Josep L.
Published: September 2016

We characterize the embedding for general weighted Lebesgue spaces of monotone functions by using the analog embedding for discrete monotone sequences indexed over the integers. We then use these results to obtain the boundedness of the discrete Hardy operator and to study the connections with the Hardy classical operator in the continuous setting.
Asymptotically sharp dimension estimates for $k$-porous sets
Authors: Järvenpää E. , Järvenpää M. , Käenmäki A. , Suomala V.
Published: September 2016

In ${\mathsf R}^n$, we establish an asymptotically sharp upper bound for the upper Minkowski dimension of $k$-porous sets having holes of certain size near every point in $k$ orthogonal directions at all small scales. This bound tends to $n-k$ as $k$-porosity tends to its maximum value.
A floating body approach to Fefferman's hypersurface measure
Authors: Barrett David E.
Published: September 2016

The floating body approach to affine surface area is adapted to a holomorphic context providing an alternate approach to Fefferman's invariant hypersurface measure.
Regularization by erasement
Authors: Martínez-Legaz Juan-Enrique , Penot Jean-Paul
Published: September 2016

We study an approximation method for sets and functions which erases corners but keeps smooth parts. Basic properties of such a method are pointed out in a general and simple way. Several convergence results are provided, essentially in the framework of variational analysis.
Existence results for Volterra-Stieltjes quadratic integral equations on an unbounded interval
Authors: Banas Jósef
Published: September 2016

We prove a few existence results for a nonlinear quadratic Volterra-Stieltjes integral equation on an unbounded interval. Our proof depends on suitable combination of the technique of measures of noncompactness and the Schauder fixed point principle. Such an approach permits us to obtain existence theorems under rather general assumptions.
Odd Riemannian symmetric spaces associated to four-forms
Authors: Cortés Vicente
Published: September 2016

To any four-form $\Omega$ satisfying certain system of quadratic equations a Lie superalgebra $\mathfrak{g} = \mathfrak{g}_0 + \mathfrak{g}_1$ endowed with an invariant scalar superproduct is associated. The geometric structure of the corresponding odd symmetric superspace, which is of hyper-Kähler type, is described. Finally, some classes of solutions to the quadratic system are discussed.
An integral duality formula
Authors: Grecu Bogdan C. , Ryan Raymond A.
Published: September 2016

We establish an integral formula for the duality between multilinear forms/homogeneous polynomials and tensor products for dual spaces with the approximation property and for which the injective tensor products of their preduals is separable and does not contain a copy of $\ell_1$. We deduce some multilinear Bishop-Phelps-type results.
Infinite dimensional analysis of pure jump Lévy processes on the Poisson space
Authors: Løkka Arne , Proske Frank Norbert
Published: September 2016

We develop a white noise calculus for pure jump Lévy processes on the Poisson space. This theory covers the treatment of Lévy processes of unbounded variation. The starting point of the theory is the construction of a distribution space. This space has many of the same nice properties as the classical Schwartz space, but is modified in a certain way in order to be more suitable for pure jump Lévy processes. We apply Minlos's theorem to this space and obtain a white noise measure which satisfies the first condition of analyticity, and which is non-degenerate. Furthermore, we obtain generalized Charlier polynomials for all Lévy measures. We introduce Kondratiev test function and distribution spaces, the $\mathcal{S}$-transform and the Wick product. We proceed by using a transfer principle on Poisson spaces to establish a differential calculus.
Factorization for bounded analytic functions in the unit disk and an application to prime ideals
Authors: Mortini Raymond
Published: September 2016

We prove several factorization theorems for bounded analytic functions in the open unit disk and present a very simple new proof of two conjectures of Frank Forelli and the author on the structure of finitely generated, respectively countably generated prime ideals in $H^{\infty}$.
Functional composition in $B_{p,k}$ spaces and applications
Authors: Jornet David , Oliaro Alessandro
Published: September 2016

Let $f(x,z)$, $x\in\mathsf{R}^N$, $z\in \mathsf{C}^M$, be a smooth function in the sense that its Fourier transform has a good behaviour. We study the composition $f(x,u(x))$, where $u$ is in a generalized Hörmander $B_{p,k}$ space in the sense of Björck [1]. As a consequence we obtain results of local solvability and hypoellipticity of semilinear equations of the type $P(D)u+f(x,Q_1(D)u,\ldots,Q_M(D)u)=g$, with $g\in B_{p,k}$, and fully nonlinear elliptic equations.
AF-equivalence relations
Authors: Molberg Mats
Published: September 2016

Let $R=\lim\limits_{\longrightarrow}R_{n}$ be the inductive limit of an ascending sequence of étale finite equivalence relations $R_n$ on the zero-dimensional space $X$. We prove that $R$ is an AF-equivalence relation.
Monotone operator functions, gaps and power moment problem
Authors: Osaka Hiroyuki , Silvestrov Sergei , Tomiyama Jun
Published: September 2016

The article is devoted to investigation of the classes of functions belonging to the gaps between classes $P_{n+1}(I)$ and $P_{n}(I)$ of matrix monotone functions for full matrix algebras of successive dimensions. In this paper we address the problem of characterizing polynomials belonging to the gaps $P_{n}(I) \setminus P_{n+1}(I)$ for bounded intervals $I$. We show that solution of this problem is closely linked to solution of truncated moment problems, Hankel matrices and Hankel extensions. Namely, we show that using the solutions to truncated moment problems we can construct continuum many polynomials in the gaps. We also provide via several examples some first insights into the further problem of description of polynomials in the gaps that are not coming from the truncated moment problem. Also, in this article, we deepen further in another way into the structure of the classes of matrix monotone functions and of the gaps between them by considering the problem of position in the gaps of certain interesting subclasses of matrix monotone functions that appeared in connection to interpolation of spaces and in a proof of the Löwner theorem on integral representation of operator monotone functions.
Multiplicative properties of positive maps
Authors: Størmer Erling
Published: September 2016

Let $\phi$ be a positive unital normal map of a von Neumann algebra $M$ into itself. It is shown that with some faithfulness assumptions on $\phi$ there exists a largest Jordan subalgebra $C_{\phi}$ of $M$ such that the restriction of $\phi$ to $C_{\phi}$ is a Jordan automorphism and each weak limit point of $(\phi^n (a))$ for $a\in M$ belongs to $C_{\phi}$.
Brown measures of unbounded operators affiliated with a finite von Neumann algebra
Authors: Haagerup Uffe , Schultz Hanne
Published: September 2016

In this paper we generalize Brown's spectral distribution measure to a large class of unbounded operators affiliated with a finite von Neumann algebra. Moreover, we compute the Brown measure of all unbounded $R$-diagonal operators in this class. As a particular case, we determine the Brown measure $z=xy^{-1}$, where $(x,y)$ is a circular system in the sense of Voiculescu, and we prove that for all $n\in \mathsf N$, $z^n\in L^p$ if and only if $0<p<\frac{2}{n+1}$.
An analogue of the Baum-Connes isomorphism for coactions of compact groups
Authors: Meyer Ralf , Nest Ryszard
Published: September 2016

We formulate and prove the analogue of the Baum-Connes conjecture for coactions of connected compact groups.
Projective multi-resolution analyses arising from direct limits of Hilbert modules
Authors: Larsen Nadia S. , Raeburn Iain
Published: September 2016

The authors have recently shown how direct limits of Hilbert spaces can be used to construct multi-resolution analyses and wavelets in $L^2(\mathsf R)$. Here they investigate similar constructions in the context of Hilbert modules over $C^*$-algebras. For modules over $C(\mathsf T^n)$, the results shed light on work of Packer and Rieffel on projective multi-resolution analyses for specific Hilbert $C(\mathsf T^n)$-modules of functions on $\mathsf R^n$. There are also new applications to modules over $C(C)$ when $C$ is the infinite path space of a directed graph.
Dual of the Auslander-Bridger formula and GF-perfectness
Authors: Sahandi Parviz , Sharif Tirdad
Published: September 2016

Ext-finite modules were introduced and studied by Enochs and Jenda. We prove under some conditions that the depth of a local ring is equal to the sum of the Gorenstein injective dimension and Tor-depth of an Ext-finite module of finite Gorenstein injective dimension. Let $(R,\mathfrak m)$ be a local ring. We say that an $R$-module $M$ with $\dim_R M=n$ is a Grothendieck module if the $n$-th local cohomology module of $M$ with respect to $\mathfrak m$, $\mathrm{H}_{\mathfrak m}^n (M)$, is non-zero. We prove the Bass formula for this kind of modules of finite Gorenstein injective dimension and of maximal Krull dimension. These results are dual versions of the Auslander-Bridger formula for the Gorenstein dimension. We also introduce GF-perfect modules as an extension of quasi-perfect modules introduced by Foxby.
A general energy formula
Authors: Hare Kathryn E. , Mohanty Parasar , Roginskaya Maria
Published: September 2016

An analogue of the formula relating the Riesz energy of a measure on the torus with a weighted $l^{2}$ norm of its Fourier transform is given for energies arising from more general kernels. This involves estimating the Fourier transform of the kernel. The formula is used to study certain measures of (classical) energy dimension zero.
On the Nagell-Ljunggren equation $(x^n - 1)/(x - 1) = y^q$
Authors: Bugeaud Yann , Mihailescu Preda
Published: September 2016

We establish several new results on the Nagell-Ljunggren equation $(x^n - 1)/(x-1) = y^q$. Among others, we prove that, for every solution $(x, y, n, q)$ to this equation, $n$ has at most four prime divisors, counted with their multiplicities.
Spaces of absolutely summing polynomials
Authors: Barbosa J.A. , Botelho G. , Diniz D. , Pellegrino D.
Published: September 2016

This paper has a twofold purpose: to prove a much more general Dvoretzky-Rogers type theorem for absolutely summing polynomials and to introduce a more convenient norm on the space of everywhere summing polynomials.
Quasimonotone embedding of one-sided Lipschitz continuous functions
Authors: Herzog Gerd
Published: September 2016

We prove that one-sided Lipschitz continuous functions can be embedded into quasimonotone increasing functions, in a quite natural way. As a consequence of this result, quasimontonicity methods can be used to study initial and boundary value problems in Banach spaces if one-sided Lipschitz continuous functions are involved.
On Rørdam's classification of certain $C^*$-algebras with one non-trivial ideal, II
Authors: Restorff Gunnar , Ruiz Efren
Published: September 2016

In this paper we extend the classification results obtained by Rørdam in the paper [16]. We prove a strong classification theorem for the unital essential extensions of Kirchberg algebras, a classification theorem for the non-stable, non-unital essential extensions of Kirchberg algebras, and we characterize the range in both cases. The invariants are cyclic six term exact sequences together with the class of some unit.
An Euler characteristic for modules of finite G-dimension
Authors: Sather-Wagstaff Sean , White Diana
Published: September 2016

We extend Auslander and Buchsbaum's Euler characteristic from the category of finitely generated modules of finite projective dimension to the category of modules of finite G-dimension using Avramov and Martsinkovsky's notion of relative Betti numbers. We prove analogues of some properties of the classical invariant and provide examples showing that other properties do not translate to the new context. One unexpected property is in the characterization of the extremal behavior of this invariant: the vanishing of the Euler characteristic of a module $M$ of finite G-dimension implies the finiteness of the projective dimension of $M$. We include two applications of the Euler characteristic as well as several explicit calculations.
Fell bundles associated to groupoid morphisms
Authors: Deaconu Valentin , Kumjian Alex , Ramazan Birant
Published: September 2016

Given a continuous open surjective morphism $\pi :G\rightarrow H$ of étale groupoids with amenable kernel, we construct a Fell bundle $E$ over $H$ and prove that its $C^*$-algebra $C^*_r(E)$ is isomorphic to $C^*_r(G)$. This is related to results of Fell concerning $C^*$-algebraic bundles over groups. The case $H=X$, a locally compact space, was treated earlier by Ramazan. We conclude that $C^*_r(G)$ is strongly Morita equivalent to a crossed product, the $C^*$-algebra of a Fell bundle arising from an action of the groupoid $H$ on a $C^*$-bundle over $H^0$. We apply the theory to groupoid morphisms obtained from extensions of dynamical systems and from morphisms of directed graphs with the path lifting property. We also prove a structure theorem for abelian Fell bundles.
A note on the restriction theorem and geometry of hypersurfaces
Authors: Nicola Fabio
Published: September 2016

A necessary condition is established for the optimal $(L^p,L^2)$ restriction theorem to hold on a hypersurface $S$, in terms of its Gaussian curvature. For some classes of flat hypersurface we give sharp thresholds for the range of admissible exponents $p$, depending on the specific geometry.
On Banach ideals satisfying $c_0(\mathcal{A}(X,Y))=\mathcal{A}(X,c_0(Y))$
Authors: Delgado J. M. , Piñeiro C.
Published: September 2016

We characterize Banach ideals $[\mathcal{A},a]$ satisfying the equality $c_0(\mathcal{A}(X,Y))= \mathcal{A}(X,c_0(Y))$ for all Banach spaces $X$ and $Y$. Among other results we have proved that $\mathcal{K}$ (the normed operator ideal of all compact operators with the operator norm) is the only injective Banach ideal satisfying the equality.
Logarithms and sectorial projections for elliptic boundary problems
Authors: Gaarde Anders , Grubb Gerd
Published: September 2016

On a compact manifold with boundary, consider the realization $B$ of an elliptic, possibly pseudodifferential, boundary value problem having a spectral cut (a ray free of eigenvalues), say $\mathsf{R}_{-}$. In the first part of the paper we define and discuss in detail the operator $\log B$; its residue (generalizing the Wodzicki residue) is essentially proportional to the zeta function value at zero, $\zeta (B,0)$, and it enters in an important way in studies of composed zeta functions $\zeta (A,B,s)= {\operatorname {Tr}}(AB^{-s})$ (pursued elsewhere). There is a similar definition of the operator $\log_{\theta}B$, when the spectral cut is at a general angle $\theta$. When $B$ has spectral cuts at two angles $\theta <\varphi$, one can define the sectorial projection $\Pi_{\theta,\varphi} (B)$ whose range contains the generalized eigenspaces for eigenvalues with argument in $\left]\theta,\varphi \right[$; this is studied in the last part of the paper. The operator $\Pi_{\theta ,\varphi}(B)$ is shown to be proportional to the difference between $\log_{\theta}B$ and $\log_{\varphi} B$, having slightly better symbol properties than they have. We show by examples that it belongs to the Boutet de Monvel calculus in many special cases, but lies outside the calculus in general.
Quaternionic discrete series for $Sp(1,1)$
Authors: Seppänen Henrik
Published: September 2016

In this paper we study the analytic realization of the discrete series representations for the group $G=Sp(1,1)$ as a subspace of the space of square integrable sections in a homogeneous vector bundle over the symmetric space $G/K:=Sp(1,1) /(Sp(1) \times Sp(1))$. We use the Szegő map to give expressions for the restrictions of the $K$-types occurring in the representation spaces to the submanifold $AK/K$.
Classification of rational surfaces of degree 11 and sectional genus 11 in ${\mathsf P}^{4}$
Authors: Graf von Bothmer Hans-Christian , Ranestad Kristian
Published: September 2016

We use the BGG-correspondence to show that there are at most three possible Hilbert functions for smooth rational surfaces of degree 11 and sectional genus 11. Surfaces with one of these Hilbert functions have been classified by Popescu. The classification for a second one is done in this paper. For the third Hilbert function the classification is still open.
On the $KK$-theory of strongly self-absorbing $C^{*}$-algebras
Authors: Dadarlat Marius , Winter Wilhelm
Published: September 2016

Let $\mathcal D$ and $A$ be unital and separable $C^{*}$-algebras; let $\mathcal D$ be strongly self-absorbing. It is known that any two unital ${}^*$-homomorphisms from $\mathcal D$ to $A \otimes \mathcal D$ are approximately unitarily equivalent. We show that, if $\mathcal D$ is also $K_{1}$-injective, they are even asymptotically unitarily equivalent. This in particular implies that any unital endomorphism of $\mathcal D$ is asymptotically inner. Moreover, the space of automorphisms of $\mathcal D$ is compactly-contractible (in the point-norm topology) in the sense that for any compact Hausdorff space $X$, the set of homotopy classes $[X,(\mathrm{Aut}(\mathcal D)]$ reduces to a point. The respective statement holds for the space of unital endomorphisms of $\mathcal D$. As an application, we give a description of the Kasparov group $KK(\mathcal D, A\otimes \mathcal D)$ in terms of $^*$-homomorphisms and asymptotic unitary equivalence. Along the way, we show that the Kasparov group $KK(\mathcal D, A\otimes \mathcal D)$ is isomorphic to $K_0(A\otimes \mathcal D)$.
Pushing down infinite Loeb measures
Authors: Ross David A.
Published: September 2016

Sufficient conditions are given under which the standard part map on an arbitrary Hausdorff space can be used to push down an infinite nonstandard measure. This makes it easier to construct standard infinite Borel measures using nonstandard techniques.
Representations of Banach algebras as algebras of completely bounded maps
Authors: Oikhberg Timur
Published: September 2016

We use the notion of $\Pi_2$-hyperreflexivity to construct, for a wide variety of Banach algebras $\mathcal A$, an operator space $X$ and a representation $\pi : {\mathcal A} \to CB(X)$, such that $CB(X)$ consists of $2$-summing perturbations of $\pi({\mathcal A})$. This gives rise to some examples of operator spaces with interesting properties.
Maximal operators of Schrödinger type with a complex parameter
Authors: Sjölin Per
Published: September 2016

Maximal operators of Schrödinger type but with a complex parameter are considered. For these operators we obtain results which in a certain sense lie between the results for the corresponding maximal operators for solutions to the Schrödinger equation and for solutions to the heat equation.
On the asymptotic expansion of the logarithm of Barnes triple gamma function
Authors: Koumandos Stamatis , Pedersen Henrik L.
Published: September 2016

It is shown that the remainders in an asymptotic expansion of the logarithm of Barnes triple gamma function give rise to completely monotonic functions. Furthermore, error bounds are found.
Weak compactness in the dual space of a JB*-triple is commutatively determined
Authors: Fernández-Polo Francisco J. , Peralta Antonio M.
Published: September 2016

We prove the following criterium of weak compactness in the dual of a JB*-triple: a bounded set $K$ in the dual of a JB*-triple $E$ is not relatively weakly compact if and only if there exist a sequence of pairwise orthogonal elements $(a_n)$ in the closed unit ball of $E$, a sequence $(\varphi_{n} )$ in $K$, and $\vartheta >0$ satisfying that $|\varphi_{n}(a_{n})|>\vartheta$ for all $n \in {\mathsf N}$. This solves a question stimulated by the main result in [11] and posed in [9].
A class of hypergraphs that generalizes chordal graphs
Authors: Emtander Eric
Published: September 2016

In this paper we introduce a class of hypergraphs that we call chordal. We also extend the definition of triangulated hypergraphs, given by H. T. Hà and A. Van Tuyl, so that a triangulated hypergraph, according to our definition, is a natural generalization of a chordal (rigid circuit) graph. R. Fröberg has showed that the chordal graphs corresponds to graph algebras, $R/I(\mathcal{G})$, with linear resolutions. We extend Fröberg's method and show that the hypergraph algebras of generalized chordal hypergraphs, a class of hypergraphs that includes the chordal hypergraphs, have linear resolutions. The definitions we give, yield a natural higher dimensional version of the well known flag property of simplicial complexes. We obtain what we call $d$-flag complexes.
Pointwise multipliers in Hardy-Orlicz spaces, and interpolation
Authors: Hartmann Andreas
Published: September 2016

We study multipliers of Hardy-Orlicz spaces ${\mathcal H}_{\Phi}$ which are strictly contained between $\bigcup_{p>0}H^p$ and so-called "big" Hardy-Orlicz spaces. Big Hardy-Orlicz spaces, carrying an algebraic structure, are equal to their multiplier algebra, whereas in classical Hardy spaces $H^p$, the multipliers reduce to $H^{\infty}$. For Hardy-Orlicz spaces ${\mathcal H}_{\Phi}$ between these two extremal situations and subject to some conditions, we exhibit multipliers that are in Hardy-Orlicz spaces the defining functions of which are related to $\Phi$. In general it cannot be expected to obtain a characterization of the multiplier algebra in terms of Hardy-Orlicz spaces since these are in general not algebras. Nevertheless, some examples show that we are not very far from such a characterization. In certain situations we see how the multiplier algebra grows in a sense from $H^{\infty}$ to big Hardy-Orlicz spaces when we go from classical $H^p$ spaces to big Hardy-Orlicz spaces. However, the multiplier algebras are not always ordered as their underlying Hardy-Orlicz spaces. Such an ordering holds in certain situations, but examples show that there are large Hardy-Orlicz spaces for which the multipliers reduce to $H^{\infty}$ so that the multipliers do in general not conserve the ordering of the underlying Hardy-Orlicz spaces. We apply some of the multiplier results to construct Hardy-Orlicz spaces close to $\bigcup_{p>0}H^p$ and for which the free interpolating sequences are no longer characterized by the Carleson condition which is well known to characterize free interpolating sequences in $H^p$, $p>0$.
Topological quivers as multiplicity free relations
Authors: Brenken Berndt
Published: September 2016

For a $C^*$-correspondence $\mathcal{E}$ over a $C^*$-algebra $A$ the restricted correspondence $\mathcal{R}(\mathcal{E})$ over the ideal $I=\overline{\langle\mathcal{E},\mathcal{E}\rangle}$ of $A$ is introduced. The Cuntz-Pimsner algebra $\mathcal{O}_{\mathcal{R}(\mathcal{E})}$ is the unaugmented $C^*$-algebra associated with $\mathcal{E}$. For a topological quiver $G$ an associated multiplicity free quiver, or topological relation, $G^{1}$ is introduced. The Cuntz-Pimsner algebra $\mathcal{O}_{\mathcal{R}(\mathcal{E})}$ of the correspondence $\mathcal{E}$ associated with $G$ is contained in the algebra $\mathcal{O}_{\mathcal{R}(\mathcal{E}^{1})}$ for the correspondence $\mathcal{E}^{1}$ associated with $G^{1}$ if the source map for the quiver is proper on an appropriate codomain. The unaugmented Cuntz-Pimsner algebras for $G$ and $G^{1}$ are isomorphic if the left action for the correspondence $\mathcal{R}(\mathcal{E})$ is by compact adjointable maps and if the kernel for the left action is complemented in $I$. There are counter examples if either condition fails.
Decomposable projections related to the Fourier and flip automorphisms
Authors: Walters S.
Published: September 2016

In this paper we classify Fourier invariant projections $g$ in the irrational rotation $C^*$-algebra that can be decomposed in the form 26741 g = f + \sigma(f) + \sigma^2(f) + \sigma^3(f) 26741 for some Fourier orthogonal projection $f$, where $\sigma$ is the Fourier transform automorphism. The analogous result is shown for the flip automorphism as well as the existence of flip-orthogonal projections. Both classifications are achieved by means of topological invariants (given by unbounded traces) and the canonical trace. We also show (in both the flip and Fourier cases) that invariant projections $h$ are subprojections of orthogonal decompositions $g$ for some projection $f$ such that $\tau(f) = \tau(h)$ (where $\tau$ is the canonical trace).
On the weak differentiability of $u\circ f^{-1}$
Authors: Hencl Stanislav
Published: September 2016

Let $p\geq n-1$ and suppose that $f:\Omega\to{\mathsf R}^n$ is a homeomorphism in the Sobolev space $W^{1,p}_{(\mathrm{loc}}(\Omega,{\mathsf R}^n)$. Further let $u\in W^{1,q}_{(\mathrm{loc}}(\Omega)$ where $q=\frac{p}{p-(n-1)}$ and for $q>n$ we also assume that $u$ is continuous. Then $u\circ f^{-1}\in (\mathrm{BV}_{(\mathrm{loc}}(f(\Omega))$ and if we moreover assume that $f$ is a mapping of finite distortion, then $u\circ f^{-1}\in W^{1,1}_{(\mathrm{loc}}(f(\Omega))$.
Asymptotics of eigenvalues of regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition for integrable potential
Authors: Coskun Haskiz , Baskaya Elif
Published: September 2016

In this paper we obtain asymptotic estimates of eigenvalues for regular Sturm-Liouville problems having the eigenparameter in the boundary condition without smoothness conditions on $q$.
Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces
Authors: Guliyev Vagif S. , Hasanov Javanshir J. , Samko Stefan G.
Published: September 2016

We consider generalized Morrey spaces ${\mathcal M}^{p(\cdot),\omega}(\Omega)$ with variable exponent $p(x)$ and a general function $\omega (x,r)$ defining the Morrey-type norm. In case of bounded sets $\Omega \subset {\mathsf R}^n$ we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev-Adams type ${\mathcal M}^{p(\cdot),\omega} (\Omega)\rightarrow {\mathcal M}^{q(\cdot),\omega} (\Omega)$-theorem for the potential operators $I^{\alpha(\cdot)}$, also of variable order. The conditions for the boundedness are given it terms of Zygmund-type integral inequalities on $\omega(x,r)$, which do not assume any assumption on monotonicity of $\omega(x,r)$ in $r$.
Lattice gauge field theory and prismatic sets
Authors: Akyar B. , Dupont J. L.
Published: September 2016

We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set $S$ and the prismatic star of $S$. Both have the same homotopy type as $S$ and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group $G$ and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying space of $G$. In turn this defines a $G$-bundle over the prismatic star.
Poincaré type inequality for Dirichlet spaces and application to the uniqueness set
Authors: Kellay Karim
Published: September 2016

We give an extension of Poincaré's type capacitary inequality for Dirichlet spaces and provide an application to study the uniqueness sets on the unit circle for these spaces.
Uniform metric spaces, annular quasiconvexity and pointed tangent spaces
Authors: Herron David A.
Published: September 2016

We establish Väisälä's tangent space characterization for uniformity in the doubling metric space setting. We present similar results for other geometric properties.