bluuebunny/crossref_metadata_2025 huggingface dataset:
Surfaces in $G(1,5)$ with one apparent double point
Authors: Sierra José Carlos
Published: September 2016

In this work we characterize the smooth surfaces that can be embedded in the Grassmannian of lines $G(1,5)$ with one apparent double point, i.e., such that the general linear projection to $G(1,3)$ produces just one double point. The result is that such a surface must be either a rational scroll of degree $4$ or $5$ or a Del Pezzo surface of degree $6$ or $7$.
Estimations des solutions de l'équation de Bezout dans les algèbres de Beurling analytiques
Authors: El-Fallah O. , Zarrabi M.
Published: September 2016

Let $A$ be a unitary commutative Banach algebra with unit $e$. For $f\in A$ we denote by $\hat f$ the Gelfand transform of $f$ defined on $\hat A$, the set of maximal ideals of $A$. Let $(f_1,\dots,f_n)\in A^n$ be such that $\sum_{i=1}^n\|f_i\|^2 \leq 1$. We study here the existence of solutions $(g_1,\dots,g_n)\in A^n$ to the Bezout equation $f_1g_1+\cdots+f_ng_n=e$, whose norm is controlled by a function of $n$ and $\delta=\inf_{\chi\in\hat A}(|\hat f_1(\chi)|^2+\cdots+|\hat f_n(\chi)|^2)^{1/2}$. We treat this problem for the analytic Beurling algebras and their quotient by closed ideals. The general Banach algebras with compact Gelfand transform are also considered.
Tiles with no spectra in dimension 4
Authors: Farkas Bálint , Szilárd Gy. Révész
Published: September 2016

We show by a counterexample that the "tiling $\Rightarrow$ spectral" part of Fuglede's Spectral Set Conjecture fails already in $\mathsf{Z}^4$ and $\mathsf {R}^4$.
Time-frequency partitions for the Gelfand triple $(S_0,L^2,S_0')$
Authors: Dörfler Monika , Feichtinger Hans G. , Gröchenig Karlheinz
Published: September 2016

We give a new characterization of the Gelfand triple of function spaces in $(S_0, L^2, S_0')$ by means of a family of time-frequency localization operators. The localization operators are defined by the short-time Fourier transform and determine the local time-frequency behavior, whereas the global time-frequency distribution is characterized by a sequence space norm. We also show that the alternative time-frequency localization method with the Weyl transform fails to yield a similar characterization of time-frequency distribution.
Amenable representations and coefficient subspaces of Fourier-Stieltjes algebras
Authors: Stokke Ross
Published: September 2016

Amenable unitary representations of a locally compact group, $G$, are studied in terms of associated coefficient subspaces of the Fourier-Stieltjes algebra $B(G)$, and in terms of the existence of invariant and multiplicative states on associated von Neumann and $C^*$-algebras. We introduce Fourier algebras and reduced Fourier-Stieltjes algebras associated to arbitrary representations, and study amenable representations in relation to these algebras.
Fenchel equalities and bilinear minmax equalities
Authors: Greco G.H. , Flores-Franulic A. , Román-Flores H.
Published: September 2016

Chief objects here are pairs $(X,F)$ of convex subsets in a Hilbert space, satisfying the bilinear minmax equality 26737 \inf_{x\in X}\sup_{y\in F} \langle x,y\rangle=\sup_{y\in F}\inf_{x\in X} \langle x,y\rangle. 26737 Specializing $F$ to be an affine closed subspace we recover and restate crucial concepts of convex duality, revolving around Fenchel equalities, biconjugation, and inf-convolution. The resulting perspective reinforces the strong links between minmax, set-theoretic, and functional aspects of convex analysis.
Holomorphic Fock spaces for positive linear transformations
Authors: Fabec R. , Ólafsson G. , Sengupta A.N.
Published: September 2016

Suppose $A$ is a positive real linear transformation on a finite dimensional complex inner product space $V$. The reproducing kernel for the Fock space of square integrable holomorphic functions on $V$ relative to the Gaussian measure $d\mu_A(z)=\frac {\sqrt{\det A}} {\pi^n}e^{-\Re\langle Az,z\rangle}\,dz$ is described in terms of the linear and antilinear decomposition of the linear operator $A$. Moreover, if $A$ commutes with a conjugation on $V$, then a restriction mapping to the real vectors in $V$ is polarized to obtain a Segal-Bargmann transform, which we also study in the Gaussian-measure setting.
Gin and lex of certain monomial ideals
Authors: Murai Satoshi , Hibi Takayuki
Published: September 2016

Let $A = K[x_1,\ldots, x_n]$ denote the polynomial ring in $n$ variables over a field $K$ of characteristic $0$ with each $\deg x_i = 1$. Given arbitrary integers $i$ and $j$ with $2 \leq i \leq n$ and $3 \leq j \leq n$, we will construct a monomial ideal $I \subset A$ such that (i) $\beta_k(I) < \beta_k(\mathrm{Gin}(I))$ for all $k < i$, (ii) $\beta_i(I)= \beta_i(\mathrm{Gin}(I))$, (iii) $\beta_\ell((\mathrm{Gin}(I)) < \beta_\ell((\mathrm{Lex}(I))$ for all $\ell < j$ and (iv) $\beta_j(\mathrm{Gin}(I)) = \beta_j(\mathrm{Lex}(I))$, where $\mathrm{Gin}(I)$ is the generic initial ideal of $I$ with respect to the reverse lexicographic order induced by $x_1 > \cdots > x_n$ and where $\mathrm{Lex}(I)$ is the lexsegment ideal with the same Hilbert function as $I$.
On the fractional parts of lacunary sequences
Authors: Dubickas Arturas
Published: September 2016

In this paper, we prove that if $t_0, t_1, t_2, \dots$ is a lacunary sequence, namely, $t_{n+1}/t_n\geq 1+r^{-1}$ for each $n\geq 0$, where $r$ is a fixed positive number, then there are two positive constants $c(r)=\max(1-r, 2(3r+6)^{-2})$ and $\xi=\xi(t_0, t_1,\dots)$ such that the fractional parts $\{\xi t_n\}$, $n=0,1,2,\dots$, all belong to a subinterval of $[0,1)$ of length $1-c(r)$. Some applications of this theorem to the chromatic numbers of certain graphs and to some fast growing sequences are discussed. We prove, for instance, that the number $\sqrt{10}$ can be written as a quotient of two positive numbers whose decimal expansions contain the digits $0$, $1$, $2$, $3$ and $4$ only.
The complement of a d-tree is Cohen-Macaulay
Authors: Ferrarello Daniela
Published: September 2016

In this work we obtain the result that the complement of a $d$-tree is a Cohen-Macaulay graph. To do this we use a theorem by Fröberg that estabilishes a condition for a Stanley-Reisner ring of a simplicial complex to be Cohen-Macaulay and a useful lemma to pass from a Stanley-Reisner ideal of a simplicial complex to an edge ideal of a graph.
Ideal structure and $C^*$-algebras of low rank
Authors: Brown Lawrence G. , Pedersen Gert K.
Published: September 2016

We explore various constructions with ideals in a $C^*$-algebra $A$ in relation to the notions of real rank, stable rank and extremal richness. In particular we investigate the maximum ideals of low rank. And we investigate the relationship between existence of infinite or properly infinite projections in an extremally rich $C^*$-algebra and non-existence of ideals or quotients of stable rank one.
Evans-Kishimoto type argument for actions of discrete amenable groups on McDuff factors
Authors: Masuda Toshihiko
Published: September 2016

We apply the Evans-Kishimoto type argument to centrally free actions of discrete amenable groups on McDuff factors, and classify them. Especially, we present a different proof that the Connes-Takesaki modules are complete cocycle conjugacy invariants for centrally free actions of discrete amenable groups on injective factors.
Global Schauder decompositions of locally convex spaces
Authors: Venkova Milena
Published: September 2016

We define global Schauder decompositions of locally convex spaces and prove a necessary and sufficient condition for two spaces with global Schauder decompositions to be isomorphic. These results are applied to spaces of entire functions on a locally convex space.
Rings with finite Gorenstein global dimension
Authors: Enochs E. , Estrada S. , Iacob A.
Published: September 2016

We find new classes of non noetherian rings which have the same homological behavior as Gorenstein rings.
Grand Orlicz spaces and global integrability of the Jacobian
Authors: Capone C. , Fiorenza A. , Karadzhov G. E.
Published: September 2016

We introduce and investigate the grand Orlicz spaces and the grand Lorentz-Orlicz spaces. An application to the problem of global integrability of the Jacobian of orientation preserving mappings is given.
An example of a bounded $\mathsf C$-convex domain which is not biholomorphic to a convex domain
Authors: Nikolov Nikolai , Pflug Peter , Zwonek W{\l}odzimierz
Published: September 2016

We show that the symmetrized bidisc is a $\mathsf C$-convex domain. This provides an example of a bounded $\mathsf C$-convex domain which cannot be exhausted by domains biholomorphic to convex domains.
Sharpened forms of a von Neumann inequality for $\rho$-contractions
Authors: Cassier Gilles , Suciu Nicolae
Published: September 2016

The purpose of this paper is to give some sharpened forms of the von Neumann inequality for strict $\rho$-contractions which were obtained earlier. Also, some sharpened forms of the Schwarz inequality for strict $\rho$-contractions will be given, and as applications, corresponding inequalities for strict contractions and for uniformly stable operators will be derived. In particular, we recover the results of K. Fan covering the strict contractions, and in the scalar context we find an improved form of the interior Schwarz inequality quoted by R. Osserman .
Toeplitz operators on weighted spaces of holomorphic functions
Authors: Harutyunyan Anahit , Lusky Wolfgang
Published: September 2016

We define a notion of Toeplitz operator on certain spaces of holomorphic functions on the unit disk and on the complex plane which are endowed with a weighted sup-norm. We establish boundedness and compactness conditions, give norm estimates and characterize the essential spectrum of these operators for many symbols.
Composition, numerical range and Aron-Berner extension
Authors: Choi Yun Sung , García Domingo , Kim Sung Guen , Maestre Manuel
Published: September 2016

Given an entire mapping $f\in \mathcal{H}_b(X,X)$ of bounded type from a Banach space $X$ into $X$, we denote by $\overline{f}$ the Aron-Berner extension of $f$ to the bidual $X^{\ast\ast}$ of $X$. We show that $\overline{g\circ f} = \overline{g}\circ \overline{f}$ for all $f, g\in \mathcal{H}_b(X,X)$ if $X$ is symmetrically regular. We also give a counterexample on $l_1$ such that the equality does not hold. We prove that the closure of the numerical range of $f$ is the same as that of $\bar{f}$.
Absolutely convergent Fourier series and generalized Zygmund classes of functions
Authors: Móricz Ferenc
Published: September 2016

We investigate the order of magnitude of the modulus of smoothness of a function $f$ with absolutely convergent Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that $f$ belongs to one of the generalized Zygmund classes $(\mathrm{Zyg}(\alpha, L)$ and $(\mathrm{Zyg} (\alpha, 1/L)$, where $0\le \alpha\le 2$ and $L= L(x)$ is a positive, nondecreasing, slowly varying function and such that $L(x) \to \infty$ as $x\to \infty$. A continuous periodic function $f$ with period $2\pi$ is said to belong to the class $(\mathrm{Zyg} (\alpha, L)$ if 26740 |f(x+h) - 2f(x) + f(x-h)| \le C h^\alpha L\left(\frac{1}{h}\right)\qquad \text{for all $x\in \mathsf T$ and $h>0$}, 26740 where the constant $C$ does not depend on $x$ and $h$; and the class $(\mathrm{Zyg} (\alpha, 1/L)$ is defined analogously. The above sufficient conditions are also necessary in case the Fourier coefficients of $f$ are all nonnegative.
Linearity defect and regularity over a Koszul algebra
Authors: Yanagawa Kohji
Published: September 2016

Let $A = \bigoplus_{i\in \mathsf{N}}A_i$ be a Koszul algebra over a field $K = A_0$, and $*\operatorname{mod} A$ the category of finitely generated graded left $A$-modules. The linearity defect $\mathrm{ld}_A(M)$ of $M \in *\operatorname{mod} A$ is an invariant defined by Herzog and Iyengar. An exterior algebra $E$ is a Koszul algebra which is the Koszul dual of a polynomial ring. Eisenbud et al. showed that $\mathrm{ld}_E(M) < \infty$ for all $M \in *\operatorname{mod} E$. Improving this, we show that the Koszul dual $A^!$ of a Koszul commutative algebra $A$ satisfies the following. Let $M \in *\operatorname{mod} A^!$. If $\{\dim_K M_i \mid i \in {\mathsf Z}\}$ is bounded, then $\mathrm{ld}_{A^!}(M) < \infty$. If $A$ is complete intersection, then $\mathrm{reg}_{A^!}(M) < \infty$ and $\mathrm{ld}_{A^!}(M) < \infty$ for all $M \in *\operatorname{mod} A^!$. If $E=\bigwedge \langle y_1, \ldots, y_n\rangle$ is an exterior algebra, then $\mathrm{ld}_E(M)\leq c^{n!} 2^{(n-1)!}$ for $M \in *\operatorname{mod} E$ with $c := \max \{\dim_K M_i \mid i \in{\mathsf Z}\}$.
Inclusions of unital $C^*$-algebras of index-finite type with depth 2 induced by saturated actions of finite dimensional $C^*$-Hopf algebras
Authors: Kodaka Kazunori , Teruya Yamotsu
Published: September 2016

Let $B$ be a unital $C^*$-algebra and $H$ a finite dimensional $C^*$-Hopf algebra with its dual $C^*$-Hopf algebra $H^0$. We suppose that there is a saturated action of $H$ on $B$ and we denote by $A$ its fixed point $C^*$-subalgebra of $B$. Let $E$ be the canonical conditional expectation from $B$ onto $A$. In the present paper, we shall give a necessary and sufficient condition that there are a weak action of $H^0$ on $A$ and a unitary cocycle $\sigma$ of $H^0 \otimes H^0 $ to $A$ satisfying that there is an isomorphism $\pi$ of $A\rtimes_{\sigma}H^0 $ onto $B$, which is the twisted crossed product of $A$ by the weak action of $H^0$ on $A$ and the unitary cocycle $\sigma$, such that $F=E\circ \pi$, where $F$ is the canonical conditional expectation from $A\rtimes_{\sigma}H^0 $ onto $A$.
$C^*$-algebras of labelled graphs II - simplicity results
Authors: Bates Teresa , Pask David
Published: September 2016

We prove simplicity and pure infiniteness results for a certain class of labelled graph $C^*$-algebras. We show, by example, that this class of unital labelled graph $C^*$-algebras is strictly larger than the class of unital graph $C^*$-algebras.
Composition operators on some holomorphic Banach function spaces
Authors: El-Sayed Ahmed A. , Bakhit M.A.
Published: September 2016

In this paper, we study composition operators on some Möbius invariant Banach function spaces like Bloch and $F(p,q,s)$ spaces. We give a Carleson measure characterization on $F(p,q,s)$ spaces, then we use this Carleson measure characterization of the compact compositions on $F(p,q,s)$ spaces to show that every compact composition operator on $F(p,q,s)$ spaces is compact on a Bloch space. Also, we give conditions to clarify when the converse holds.
Corrigendum to: The Daugavet property for spaces of Lipschitz functions
Authors: Ivakhno Yevgen , Kadets Vladimir , Werner Dirk
Published: September 2016

Corrigendum to our paper The Daugavet property for spaces of Lipschitz functions, Math. Scand. 101 (2007), 261-279.
Acyclic complexes of finitely generated free modules over local rings
Authors: Hughes Meri T. , Jorgensen David A. , Sega Liana M.
Published: September 2016

We consider the question of how minimal acyclic complexes of finitely generated free modules arise over a commutative local ring. A standard construction gives that every totally reflexive module yields such a complex. We show that for certain rings this construction is essentially the only method of obtaining such complexes. We also give examples of rings which admit minimal acyclic complexes of finitely generated free modules which cannot be obtained by means of this construction.
Cofiniteness and coassociated primes of local cohomology modules
Authors: Aghapournahr Moharram , Melkersson Leif
Published: September 2016

Let $R$ be a noetherian ring, $\mathfrak a$ an ideal of $R$ such that $\dim R/{\mathfrak a}=1$ and $M$ a finite $R$-module. We will study cofiniteness and some other properties of the local cohomology modules $H^{i}_{{\mathfrak a}}(M)$. For an arbitrary ideal $\mathfrak a$ and an $R$-module $M$ (not necessarily finite), we will characterize $\mathfrak a$-cofinite artinian local cohomology modules. Certain sets of coassociated primes of top local cohomology modules over local rings are characterized.
On the spectrum of the generalized Gelfand pair $(u(p,q), h_{n})$, $p+q=n$
Authors: Godoy Tomás , Saal Linda
Published: September 2016

It is known that the spectrum of the Gelfand pair $(U(n), H_{n})$ is homeomorphic to the Heisenberg fan. In this paper after defining a suitable notion of spectrum, we prove an analogous result for the generalized Gelfand pair $(U(p,q), H_{n})$, $p+q=n$.
Analysis of the quadratic term in the backscattering transformation
Authors: Beltita Ingrid , Melin Anders
Published: September 2016

The quadratic term in the Taylor expansion at the origin of the backscattering transformation in odd dimensions $n\ge 3$ gives rise to a symmetric bilinear operator $B_2$ on $C_0^\infty({\mathsf R}^n)\times C_0^\infty({\mathsf R}^n)$. In this paper we prove that $B_2$ extends to certain Sobolev spaces with weights and show that it improves both regularity and decay.
Homological aspects of semidualizing modules
Authors: Takahashi Ryo , White Diana
Published: September 2016

We investigate the notion of the $C$-projective dimension of a module, where $C$ is a semidualizing module. When $C=R$, this recovers the standard projective dimension. We show that three natural definitions of finite $C$-projective dimension agree, and investigate the relationship between relative cohomology modules and absolute cohomology modules in this setting. Finally, we prove several results that demonstrate the deep connections between modules of finite projective dimension and modules of finite $C$-projective dimension. In parallel, we develop the dual theory for injective dimension and $C$-injective dimension.
On the heart of hypermodules
Authors: Anvariyeh S.M. , Davvaz B.
Published: September 2016

This paper presents some types of hypermodules, associated to an arbitrary hypermodule, studying properties and characterizing their hearts. Also, we establish a few results concerning the sequence of heart, which can be associated to a hypermodule, in connection with subhypermodules generated by a non-empty set, by a union of subhypermodules or by the intersection of subhypermodules. Finally, we study several properties of $1$-hypermodules.
On essential and continuous spectra of the linearized water-wave problem in a finite pond
Authors: Nazarov Sergey A. , Taskinen Jari
Published: September 2016

We show that the spectrum of the Laplace equation with the Steklov spectral boundary condition, in the connection of the linearized theory of water-waves, can have a nontrivial essential component even in case of a bounded basin with a horizontal water surface. The appearance of the essential spectrum is caused by the boundary irregularities of the type of a rotational cusp or a cuspidal edge. In a previous paper the authors have proven a similar result for the Steklov spectral problem in a bounded domain with a sharp peak.
Approximate weak amenability of abstract Segal algebras
Authors: Samea H.
Published: September 2016

In this paper the approximate weak amenability of abstract Segal algebras is investigated. Applications to compact groups are given. Also an open problem raised by Ghahramani and Lau is answered negatively.
On subordination results for classes of analytic functions with a convolution structure
Authors: Prajapat J. K. , Raina R. K.
Published: September 2016

By adapting a familiar convolution structure of analytic functions, we define and investigate in this paper certain new classes of analytic functions. Among the various results studied (by using the methods of differential subordinations) are some of the useful properties and characteristics attributed to these function classes. Several consequences of the main results are considered and relevant connections with some known results are also pointed out.
A note on fractional integral operators defined by weights and non-doubling measures
Authors: Blasco Oscar , Casanova Vicente , Motos Joaquín
Published: September 2016

Given a metric measure space $(X,d,\mu)$, a weight $w$ defined on $(0,\infty)$ and a kernel $k_w(x,y)$ satisfying the standard fractional integral type estimates, we study the boundedness of the operators $K_w f(x)=\int_X k_w(x,y)f(y)\,d\mu(y)$ and $\tilde K_w f(x)=\int_X (k_w(x,y)-k_w(x_0,y))f(y)\,d\mu(y)$ on Lebesgue spaces $L^p(\mu)$ and generalized Lipschitz spaces $\mathrm{Lip}_\phi$, respectively, for certain range of the parameters depending on the $n$-dimension of $\mu$ and some indices associated to the weight $w$.
$C^*$-Algebra relations
Authors: Loring Terry A.
Published: September 2016

We investigate relations on elements in $C^{*}$-algebras, including $*$-polynomial relations, order relations and all relations that correspond to universal $C^{*}$-algebras. We call these $C^{*}$-relations and define them axiomatically. Within these are the compact $C^{*}$-relations, which are those that determine universal $C^{*}$-algebras, and we introduce the more flexible concept of a closed $C^{*}$-relation. In the case of a finite set of generators, we show that closed $C^{*}$-relations correspond to the zero-sets of elements in a free $\sigma$-$C^{*}$-algebra. This provides a solid link between two of the previous theories on relations in $C^{*}$-algebras. Applications to lifting problems are briefly considered in the last section.
Convergence in capacity and applications
Authors: Hiep Pham Hoang
Published: September 2016

In this article we prove that if $u_j, v_j, w\in\mathcal{E}(\Omega)$ such that $u_j,v_j\geq w$, $\forall\ j\geq 1$, and $|u_j-v_j|\to 0$ in $C_n$-capacity, then $\lim_{j\to\infty}h(\varphi_1,\ldots,\varphi_m) [(dd^cu_j)^n-(dd^cv_j)^n]=0$ in the weak-topology of measures for all $\varphi_1,\ldots ,\varphi_m\in{\operatorname{PSH}}\cap L_{\operatorname {loc}}^\infty (\Omega)$, $h\in C(\mathsf{R}^m)$. We shall then use this result to give some applications.
Advantages of the Hausdorff centered measure from the computability point of view
Authors: Llorente Marta , Morán Manuel
Published: September 2016

In this paper we study Hausdorff centered measures, a useful tool in fractal geometry. The definition of Hausdorff centered measure is based on efficient coverings centered at the given set, playing a dual role to packing measures. We show that, at least in the self-similar setting, it has some advantages, from a computational point of view, over other measures based on coverings, such as the Hausdorff measure or the Hausdorff spherical measure. We also extend our results to general Hausdorff centered measures with gauge functions for which the measures scale.
Differential geometry of matrix inversion
Authors: Huhtanen Marko
Published: September 2016

Essentially, there exists just the dimension segregating (square) matrix subspaces. In view of algebraic operations, this quantity is not particularly descriptive. For differential geometric information on matrix inversion, the second fundamental form is found for the set of inverses of the invertible elements of a matrix subspace. Several conditions for this form to vanish are given, such as being equivalent to a Jordan subalgebra. Global measures of curvature are introduced in terms of an analogy of the Nash fiber.
Boundary interpolation and approximation by infinite Blaschke products
Authors: Chalendar Isabelle , Gorkin Pamela , Partington Jonathan R.
Published: September 2016

This paper considers the problem of boundary interpolation (in the sense of non-tangential limits) by Blaschke products and interpolating Blaschke products. Simple and constructive proofs, which also work in the more general situation of $H^\infty(\Omega)$ where $\Omega$ is a more general domain, are given of a number of results showing the existence of Blaschke products solving certain interpolation problems at a countable set of points on the circle. A variant of Frostman's theorem is also presented.
A charaterization of commutators for parabolic singular integrals
Authors: Chen Yanping , Ding Yong
Published: September 2016

In this paper, the authors give a characterization of the $L^p$-boundedness of the commutators for the parabolic singular integrals. More precisely, the authors prove that if $b\in \mathrm{BMO}_\varphi(\mathsf{R}^n,\rho)$, then the commutator $[b,T]$ is a bounded operator from $L^p(\mathsf{R}^n)$ to the Orlicz space $L_\psi(\mathsf{R}^n)$, where the kernel function $\Omega$ has no any smoothness on the unit sphere $S^{n-1}$. Conversely, if assuming on $\Omega$ a slight smoothness on $S^{n-1}$, then the boundedness of $[b,T]$ from $L^p(\mathsf{R}^n)$ to $L_\psi(\mathsf{R}^n)$ implies that $b\in \mathrm{BMO}_\varphi(\mathsf{R}^n,\rho)$. The results in this paper improve essentially and extend some known conclusions.
Metric inhomogeneous Diophantine approximation in positive characteristic
Authors: Kristensen S.
Published: September 2016

We obtain asymptotic formulae for the number of solutions to systems of inhomogeneous linear Diophantine inequalities over the field of formal Laurent series with coefficients from a finite fields, which are valid for almost every such system. Here "almost every" is with respect to Haar measure of the coefficients of the homogeneous part when the number of variables is at least two (singly metric case), and with respect to the Haar measure of all coefficients for any number of variables (doubly metric case). As consequences, we derive zero-one laws in the spirit of the Khintchine-Groshev Theorem and zero-infinity laws for Hausdorff measure in the spirit of Jarník's Theorem. The latter result depends on extending a recently developed slicing technique of Beresnevich and Velani to the present setup.
Littlewood-Paley spaces
Authors: Ho Kwok-Pun
Published: September 2016

We introduce the Littlewood-Paley spaces in which the Lebesgue spaces, the Hardy spaces, the Orlicz spaces, the Lorentz-Karamata spaces, the r.-i. quasi-Banach function spaces and the Morrey spaces reside. The Littlewood-Paley spaces provide a unified framework for the study of some important function spaces arising in analysis.
Hypersurfaces of Lorentzian para-Sasakian manifolds
Authors: Perktas Selcen Yüksel , Kiliç Erol , Keles Sadik
Published: September 2016

In this paper we study the invariant and noninvariant hypersurfaces of $(1,1,1)$ almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an $(1,1,1)$ almost contact manifold admits an almost product structure. We investigate hypersurfaces of affinely cosymplectic and normal $(1,1,1)$ almost contact manifolds. It is proved that a noninvariant hypersurface of a Lorentzian almost paracontact manifold is an almost product metric manifold. Some necessary and sufficient conditions have been given for a noninvariant hypersurface of a Lorentzian para-Sasakian manifold to be locally product manifold. We establish a Lorentzian para-Sasakian structure for an invariant hypersurface of a Lorentzian para-Sasakian manifold. Finally we give some examples for invariant and noninvariant hypersurfaces of a Lorentzian para-Sasakian manifold.
The Howe-Moore property for real and $p$-adic groups
Authors: Cluckers Raf , Cornulier Yves , Louvet Nicolas , Tessera Romain , Valette Alain
Published: September 2016

We consider in this paper a relative version of the Howe-Moore property, about vanishing at infinity of coefficients of unitary representations. We characterize this property in terms of ergodic measure-preserving actions. We also characterize, for linear Lie groups or $p$-adic Lie groups, the pairs with the relative Howe-Moore property with respect to a closed, normal subgroup. This involves, in one direction, structural results on locally compact groups all of whose proper closed characteristic subgroups are compact, and, in the other direction, some results about the vanishing at infinity of oscillatory integrals.
Certain results on subordinations associated with a differintegral operator
Authors: Dziok Jacek , Raina Ravinder Krishna , Sokól Janusz
Published: September 2016

We investigate some interesting properties on subordinations for classes of multivalent analytic functions associated with a linear differintegral operator of J. Dziok [3]. Some applications and important consequences of the main results are also discussed.
Condition number and eccentricity of a closed convex cone
Authors: Henrion René , Seeger Alberto
Published: September 2016

We discuss some extremality issues concerning the circumradius, the inradius, and the condition number of a closed convex cone in $\mathsf{R}^n$. The condition number refers to the ratio between the circumradius and the inradius. We also study the eccentricity of a closed convex cone, which is a coefficient that measures to which extent the circumcenter differs from the incenter.
Localisation and colocalisation of triangulated categories at thick subcategories
Authors: Inassaridze Hvedri , Kandelaki Tamaz , Meyer Ralf
Published: September 2016

Given a thick subcategory of a triangulated category, we define a colocalisation and a natural long exact sequence that involves the original category and its localisation and colocalisation at the subcategory. Similarly, we construct a natural long exact sequence containing the canonical map between a homological functor and its total derived functor with respect to a thick subcategory.
Face numbers of pseudomanifolds with isolated singularities
Authors: Novik Isabella , Swartz Ed
Published: September 2016

We investigate the face numbers of simplicial complexes with Buchsbaum vertex links, especially pseudomanifolds with isolated singularities. This includes deriving Dehn-Sommerville relations for pseudomanifolds with isolated singularities and establishing lower and upper bound theorems when the singularities are also homologically isolated. We give formulas for the Hilbert function of a generic Artinian reduction of the face ring when the singularities are homologically isolated and for any pure two-dimensional complex. Some examples of spaces where the $f$-vector can be completely characterized are described. We also show that the Hilbert function of a generic Artinian reduction of the face ring of a simplicial complex $\Delta$ with isolated singularities minus the $h$-vector of $\Delta$ is a PL-topological invariant.
On Dirichlet's principle and problem
Authors: Åhag Per , Cegrell Urban , Czyz Rafal
Published: September 2016

The aim of this paper is to give a new proof of the complete characterization of measures for which there exists a solution of the Dirichlet problem for the complex Monge-Ampere operator in the set of plurisubharmonic functions with finite pluricomplex energy. The proof uses variational methods.
Siebeck curves and two refinements of the
Authors: Casas-Alvero Eduardo
Published: September 2016

We prove two results which improve the well known Gauss-Lucas theorem by locating the roots of the derivative of a complex polynomial $f$ in sets smaller than the convex hull of the roots of $f$.
Weighted spaces of holomorphic functions on the upper halfplane
Authors: Ardalani Mohammad Ali , Lusky Wolfgang
Published: September 2016

We discuss weighted spaces $Hv(\mathbf{G})$ of holomorphic functions on the upper halfplane $\mathbf{G}$ where $v(w) = v(i \operatorname{Im} w)$, $w \in \mathbf{G}$, $\lim_{t\to 0} v(it)=0$ and $v(it)$ is increasing in $t$. We characterize those weights $v$ with moderate growth where $Hv(\mathbf{G})$ is isomorphic to $l_{\infty}$ and we show that this is never the case if $v$ is bounded.
Involutions on a Tropical Line
Authors: Roé Joaquim
Published: September 2016

Tropical involutive linear maps and pencils of degree 2 on the tropical projective line are introduced and studied. Both concepts are related in a similar way to linear involutions and $g^1_2$'s in the classical (algebraic) projective line, and tropicalization relates the algebraic phenomena to the tropical ones.
The Chow Motives of Relative Fulton-Macpherson Space
Authors: Sato Fumitoshi
Published: September 2016

Suppose that $X$ is a complex nonsingular projective variety and $D$ is a smooth divisor. Compactifications of configuration spaces of distinct and non-distinct $n$ points in $X$ away from $D$ were constructed by the author and B. Kim in "A generalization of Fulton-MacPherson configuration spaces" by using the method of wonderful compactification. In this paper, we give explicit presentations of Chow motives and Chow groups of these configuration spaces.
Uniform Domains and Uniform Domain Decomposition Property in Real Normed Vector Spaces
Authors: Huang M. , Wang X.
Published: September 2016

Let $E$ be a real normed vector space with $\dim(E)\geq 2$, $D$ a proper subdomain of $E$. In this paper we characterize uniform domains in $E$ in terms of the uniform domain decomposition property. In addition, we discuss the relation between quasiballs and domains with the quasiball decomposition property in $\mathsf{R}^n$.
Perturbations of Planar Algebras
Authors: Das Paramita , Ghosh Shamindra Kumar , Gupta Ved Prakash
Published: September 2016

We analyze the effect of pivotal structures (on a $2$-category) on the planar algebra associated to a $1$-cell as in [8] and come up with the notion of perturbations of planar algebras by weights (a concept that appeared earlier in Michael Burns' thesis [6]); we establish a one-to-one correspondence between weights and pivotal structures. Using the construction of [8], to each bifinite bimodule over $\mathit{II}_1$-factors, we associate a bimodule planar algebra in such a way that extremality of the bimodule corresponds to sphericality of the planar algebra. As a consequence of this, we reproduce an extension of Jones' theorem ([13]) (of associating 'subfactor planar algebras' to extremal subfactors). Conversely, given a bimodule planar algebra, we construct a bifinite bimodule whose associated bimodule planar algebra is the one which we start with, using perturbations and Jones-Walker-Shlyakhtenko-Kodiyalam-Sunder method of reconstructing an extremal subfactor from a subfactor planar algebra. The perturbation technique helps us to construct an example of a family of non-spherical planar algebras starting from a particular spherical one; we also show that this family is associated to a known family of subfactors constructed by Jones.
Toric Ideals of Finite Graphs and Adjacent 2-Minors
Authors: Ohsugi Hidefumi , Hibi Takayuki
Published: September 2016

We study the problem when an ideal generated by adjacent $2$-minors is the toric ideal of a finite graph.
Strict U-Ideals and U-Summands in Banach Spaces
Authors: Abrahamsen Trond A.
Published: September 2016

For a strict u-ideal $X$ in a Banach space $Y$ we show that the set of points in the dual unit ball $B_{X^{\ast}}$, strongly exposed by points in the range $\it TY$ of the unconditional extension operator $T$ from $Y$ into the bidual $X^{\ast\ast}$ of $X$, is contained in the weak$^{\ast}$ denting points in $B_{X^{\ast}}$. We also prove that a u-embedded space is a u-summand if and only if it contains no copy of $c_0$ if and only if it is weakly sequentially complete.
Contractive Spectral Triples for Crossed Products
Authors: Paterson Alan L. T.
Published: September 2016

Connes showed that spectral triples encode (noncommutative) metric information. Further, Connes and Moscovici in their metric bundle construction showed that, as with the Takesaki duality theorem, forming a crossed product spectral triple can substantially simplify the structure. In a recent paper, Bellissard, Marcolli and Reihani (among other things) studied in depth metric notions for spectral triples and crossed product spectral triples for $Z$-actions, with applications in number theory and coding theory. In the work of Connes and Moscovici, crossed products involving groups of diffeomorphisms and even of étale groupoids are required. With this motivation, the present paper develops part of the Bellissard-Marcolli-Reihani theory for a general discrete group action, and in particular, introduces coaction spectral triples and their associated metric notions. The isometric condition is replaced by the contractive condition.
On the Category of Weakly Laskerian Cofinite Modules
Authors: Bahmanpour Kamal
Published: September 2016

Let $R$ denote a commutative Noetherian (not necessarily local) ring and $I$ be an ideal of $R$. The main purpose of this note is to show that the category $\mathscr{WL}(R, I)_{\it cof}$ of $I$-cofinite weakly Laskerian $R$-modules forms an Abelian subcategory of the category of all $R$-modules.
A Lifting Characterization of Rfd C*-Algebras
Authors: Hadwin Don
Published: September 2016

We prove a conjecture of Terry Loring that characterizes separable RFD C*-algebras in terms of a lifting property. In addition we introduce and study generalizations of RFD algebras. If $k$ is an infinite cardinal, we say a C*-algebra is residually less than $k$ dimensional, if the family of representations on Hilbert spaces of dimension less than $k$ separates the points of the algebra. We give characterizations of this property and prove that this class is closed under free products in the nonunital category. For free products in the unital category, the results depend on the cardinal $k$.
Some Sharp Estimates for the Haar System and Other Bases In $L^1(0,1)$
Authors: Osȩkowski Adam
Published: September 2016

Let $h=(h_k)_{k\geq 0}$ denote the Haar system of functions on $[0,1]$. It is well known that $h$ forms an unconditional basis of $L^p(0,1)$ if and only if $1
0$ we identify the best constant $\beta=\beta_h(\lambda)\in [0,1]$ such that the following holds. If $n$ is an arbitrary nonnegative integer and $a_0$, $a_1$, $a_2$, $\ldots$, $a_n$ are real numbers such that $\bigl\|\sum_{k=0}^n a_kh_k\bigr\|_1\leq 1$, then \[ \Bigl|\Bigl\{x\in [0,1]:\Bigl|\sum_{k=0}^n \varepsilon_ka_kh_k(x)\Bigr|\geq \lambda\Bigr\}\Bigr|\leq \beta, \] for any sequence $\varepsilon_0, \varepsilon_1, \varepsilon_2,\ldots, \varepsilon_n$ of signs. A related bound for an arbitrary basis of $L^1(0,1)$ is also established. The proof rests on the construction of the Bellman function corresponding to the problem.
Some Sufficient Conditions for Heegaard Genera to Be Additive Under Annulus Sum
Authors: Li Fengling , Lei Fengchun , Yang Guoqiu
Published: September 2016

Let $M_{i}$ be a compact orientable 3-manifold, and $A_{i}$ an incompressible annulus on a component $F_i$ of $\partial M_i$, $i=1,2$. Suppose $A_{1}$ is separating on $F_{1}$ and $A_{2}$ is non-separating on $F_{2}$. Let $M$ be the annulus sum of $M_1$ and $M_2$ along $A_1$ and $A_2$. In the present paper we show that if $M_{i}$ has a Heegaard splitting $V_{i}\cup_{S_{i}}W_{i}$ with Heegaard distance $d(S_{i})\geq2g(M_{i})+5$ for $i=1,2$, then $g(M)=g(M_{1})+g(M_{2})$. Moreover, when $g(F_{2})\geq 2$, the minimal Heegaard splitting of $M$ is unique up to isotopy.
Maximal Operator in Variable Exponent Lebesgue Spaces on Unbounded Quasimetric Measure Spaces
Authors: Adamowicz Tomasz , Harjulehto Petteri , Hästö Peter
Published: September 2016

We study the Hardy-Littlewood maximal operator $M$ on $L^{p({\cdot})}(X)$ when $X$ is an unbounded (quasi)metric measure space, and $p$ may be unbounded. We consider both the doubling and general measure case, and use two versions of the $\log$-Hölder condition. As a special case we obtain the criterion for a boundedness of $M$ on $L^{p({\cdot})}({\mathsf{R}^n},\mu)$ for arbitrary, possibly non-doubling, Radon measures.
Orlicz Regularity for Non-Divergence Parabolic Systems with Partially Vmo Coefficients
Authors: Zhu Maochun , Niu Pengcheng , Feng Xiaojing
Published: September 2016

This work treats the interior Orlicz regularity for strong solutions of a class of non-divergence parabolic systems with coefficients just measurable in time and VMO in the spatial variables.
The Algebra of Semigroups of Sets
Authors: Aigner Mats , Chatyrko Vitalij A. , Nyagahakwa Venuste
Published: September 2016

We study the algebra of semigroups of sets (i.e. families of sets closed under finite unions) and its applications. For each $n > 1$ we produce two finite nested families of pairwise different semigroups of sets consisting of subsets of $\mathsf{R}^n$ without the Baire property.
On the Generating Hypothesis in Noncommutative Stable Homotopy
Authors: Mahanta Snigdhayan
Published: September 2016

Freyd's Generating Hypothesis is an important problem in topology with deep structural consequences for finite stable homotopy. Due to its complexity some recent work has examined analogous questions in various other triangulated categories. In this short note we analyze the question in noncommutative stable homotopy, which is a canonical generalization of finite stable homotopy. Along the way we also discuss Spanier-Whitehead duality in this extended setup.
Topological Amenability Is a Borel Property
Authors: Renault Jean
Published: September 2016

We establish that a $\sigma$-compact locally compact groupoid possessing a continuous Haar system is topologically amenable if and only if it is Borel amenable. We give some examples and applications.
The Square Terms in Generalized Lucas Sequence with Parameters $P$ And $Q$
Authors: Şi̇ar Zafer , Keski̇n Refi̇k
Published: September 2016

Let $P$ and $Q$ be nonzero integers. Generalized Lucas sequence is defined as follows: $V_{0}=2$, $V_{1}=P$, and $V_{n+1}=PV_{n}+QV_{n-1}$ for $n\geq 1$. We assume that $P$ and $Q$ are odd relatively prime integers. Firstly, we determine all indices $n$ such that $V_{n}=kx^{2}$ and $V_{n}=2kx^{2}$ when $k|P$. Then, as an application of our these results, we find all solutions of the equations $V_{n}=3x^{2}$ and $V_{n}=6x^{2}$. Moreover, we find integer solutions of some Diophantine equations.
Affine Modules and the Drinfeld Center
Authors: Das Paramita , Ghosh Shamindra Kumar , Gupta Ved Prakash
Published: September 2016

Given a finite index subfactor, we show that the affine morphisms at zero level in the affine category over the planar algebra associated to the subfactor is isomorphic to the fusion algebra of the subfactor as a $*$-algebra. This identification paves the way to analyze the structure of affine $P$-modules with weight zero for any subfactor planar algebra $P$ (possibly having infinite depth). Further, for irreducible depth two subfactor planar algebras, we establish an additive equivalence between the category of affine $P$-modules and the center of the category of $N$-$N$-bimodules generated by $L^2(M)$; this partially verifies a conjecture of Jones and Walker.
Regularity and Free Resolution of Ideals Which Are Minimal To $d$-Linearity
Authors: Morales M. , Pour A. A. Yazdan , Zaare-Nahandi R.
Published: September 2016

For given positive integers $n\geq d$, a $d$-uniform clutter on a vertex set $[n]=\{1,\dots,n\}$ is a collection of distinct $d$-subsets of $[n]$. Let $\mathscr{C}$ be a $d$-uniform clutter on $[n]$. We may naturally associate an ideal $I(\mathscr{C})$ in the polynomial ring $S=k[x_1,\dots,x_n]$ generated by all square-free monomials \smash{$x_{i_1}\cdots x_{i_d}$} for $\{i_1,\dots,i_d\}\in\mathscr{C}$. We say a clutter $\mathscr{C}$ has a $d$-linear resolution if the ideal \smash{$I(\overline{\mathscr{\mathscr{C}}})$} has a $d$-linear resolution, where \smash{$\overline{\mathscr{C}}$} is the complement of $\mathscr{C}$ (the set of $d$-subsets of $[n]$ which are not in $\mathscr C$). In this paper, we introduce some classes of $d$-uniform clutters which do not have a linear resolution, but every proper subclutter of them has a $d$-linear resolution. It is proved that for any two $d$-uniform clutters $\mathscr{C}_1$, $\mathscr{C}_2$ the regularity of the ideal $I(\overline{\mathscr{C}_1 \cup \mathscr{C}_2})$, under some restrictions on their intersection, is equal to the maximum of the regularities of $I(\overline{\mathscr{C}}_1)$ and $I(\overline{\mathscr{C}}_2)$. As applications, alternative proofs are given for Fröberg's Theorem on linearity of edge ideals of graphs with chordal complement as well as for linearity of generalized chordal hypergraphs defined by Emtander. Finally, we find minimal free resolutions of the ideal of a triangulation of a pseudo-manifold and a homology manifold explicitly.
A Deformation of the Orlik-Solomon Algebra
Authors: Heckenberger István , Welker Volkmar
Published: September 2016

A deformation of the Orlik-Solomon algebra of a matroid $\mathfrak{M}$ is defined as a quotient of the free associative algebra over a commutative ring $R$ with $1$. It is shown that the given generators form a Gröbner basis and that after suitable homogenization the deformation and the Orlik-Solomon have the same Hilbert series as $R$-algebras. For supersolvable matroids, equivalently fiber type arrangements, there is a quadratic Gröbner basis and hence the algebra is Koszul.
On Plane Curves with Double and Triple Points
Authors: Abdallah Nancy
Published: September 2016

We describe in simple geometric terms the Hodge filtration on the cohomology $H^*(U)$ of the complement $U=\mathsf{P}^2 \setminus C$ of a plane curve $C$ with ordinary double and triple points. Relations to Milnor algebra, syzygies of the Jacobian ideal and pole order filtration on $H^2(U)$ are given.
Marstrand's Approximate Independence of Sets and Strong Differentiation of the Integral
Authors: Cabral Raquel
Published: September 2016

A constructive proof is given for the existence of a function belonging to the product Hardy space $H^1(\mathsf{R} \times \mathsf{R})$ and the Orlicz space $L(\log L)^{\epsilon}(\mathsf{R}^{2})$ for all $0<\epsilon <1$, for all whose integral is not strongly differentiable almost everywhere on a set of positive measure. It consists of a modification of a non-negative function created by J. M. Marstrand. In addition, we generalize the claim concerning "approximately independent sets" that appears in his work in relation to hyperbolic-crosses. Our generalization, which holds for any sets with boundary of sufficiently low complexity in any Euclidean space, has a version of the second Borel-Cantelli Lemma as a corollary.
Newtonian Spaces Based on Quasi-Banach Function Lattices
Authors: Malý Lukáš
Published: September 2016

In this paper, first-order Sobolev-type spaces on abstract metric measure spaces are defined using the notion of (weak) upper gradients, where the summability of a function and its upper gradient is measured by the "norm" of a quasi-Banach function lattice. This approach gives rise to so-called Newtonian spaces. Tools such as moduli of curve families and Sobolev capacity are developed, which allows us to study basic properties of these spaces. The absolute continuity of Newtonian functions along curves and the completeness of Newtonian spaces in this general setting are established.
Fjernt og tæt på: Telemedicinens forskellige facetter
Authors: Bossen Claus , Ballegaard Stinne Aaløkke
Published: September 2016

Introduktion til Tidsskrift for Forskning i Sygdom og Samfund