pinecone/core-2020-05-10-deduplication huggingface dataset:
On the size of the fibers of spectral maps induced by semialgebraic embeddings

Let S(M) be the ring of (continuous) semialgebraic functions on a semialgebraic set M and S*(M) its subring of bounded semialgebraic functions. In this work we compute the size of the fibers of the spectral maps Spec(j)1:Spec(S(N))→Spec(S(M)) and Spec(j)2:Spec(S*(N))→Spec(S*(M)) induced by the inclusion j:N M of a semialgebraic subset N of M. The ring S(M) can be understood as the localization of S*(M) at the multiplicative subset WM of those bounded semialgebraic functions on M with empty zero set. This provides a natural inclusion iM:Spec(S(M)) Spec(S*(M)) that reduces both problems above to an analysis of the fibers of the spectral map Spec(j)2:Spec(S*(N))→Spec(S*(M)). If we denote Z:=ClSpec(S*(M))(M N), it holds that the restriction map Spec(j)2|:Spec(S*(N)) Spec(j)2-1(Z)→Spec(S*(M)) Z is a homeomorphism. Our problem concentrates on the computation of the size of the fibers of Spec(j)2 at the points of Z. The size of the fibers of prime ideals "close" to the complement Y:=M N provides valuable information concerning how N is immersed inside M. If N is dense in M, the map Spec(j)2 is surjective and the generic fiber of a prime ideal p∈Z contains infinitely many elements. However, finite fibers may also appear and we provide a criterium to decide when the fiber Spec(j)2-1(p) is a finite set for p∈Z. If such is the case, our procedure allows us to compute the size s of Spec(j)2-1(p). If in addition N is locally compact and M is pure dimensional, s coincides with the number of minimal prime ideals contained in p. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Equiaffine geometry of level sets and ruled hypersurfaces with
  equiaffine mean curvature zero

Basic aspects of the equiaffine geometry of level sets are developed
systematically. As an application there are constructed families of
$2n$-dimensional nondegenerate hypersurfaces ruled by $n$-planes, having
equiaffine mean curvature zero, and solving the affine normal flow. Each
carries a symplectic structure with respect to which the ruling is Lagrangian.Comment: Corrected multiple typos in displayed equation (2.22) in Remark 2.7
  (Remark 2.13 in the published version) and a sign error in the final line of
  the second paragraph of Example 2.9 (Example 2.17 in the published version).
  Neither correction is consequential, but the errors in the formulas could
  have made comparison with other sources confusin
A Mehta-Ramanathan theorem for linear systems with basepoints

Let $(X, H)$ be a normal complex projective polarized variety and $\mathscr
E$ an $H$-semistable sheaf on $X$. We prove that the restriction $\mathscr
E\big|_C$ to a sufficiently positive general complete intersection curve $C
\subset X$ passing through a prescribed finite set of points $S \subset X$
remains semistable, provided that at each $p \in S$, the variety $X$ is smooth
and the factors of a Jordan-H\"older filtration of $\mathscr E$ are locally
free. As an application, we obtain a generalization of Miyaoka's generic
semipositivity theorem.Comment: Mostly minor changes. Improved Example 1.9. To appear in
  Mathematische Nachrichte
Moment Representations of the Exceptional $X_1$-Laguerre Orthogonal
  Polynomials

Exceptional orthogonal Laguerre polynomials can be viewed as an extension of
the classical Laguerre polynomials per excluding polynomials of certain
order(s) from being eigenfunctions for the corresponding exceptional
differential operator. We are interested in the (so-called) Type I
$X_1$-Laguerre polynomial sequence $\{L_n^\alpha\}_{n=1}^\infty$, $\text{deg}
\,p_n = n$ and $\alpha>0$, where the constant polynomial is omitted.
  We derive two representations for the polynomials in terms of moments by
using determinants. The first representation in terms of the canonical moments
is rather cumbersome. We introduce adjusted moments and find a second, more
elegant formula. We deduce a recursion formula for the moments and the adjusted
ones. The adjusted moments are also expressed via a generating function. We
observe a certain detachedness of the first two moments from the others.Comment: 19 page
Asymptotics for the best Sobolev constants and their extremal functions

Let $\Omega$ be a bounded domain of $\mathbf{R}^{N},$ $N\geq2.$ Let, for
$p>N,$ \[ \Lambda_{p}(\Omega):=\inf\left\{ \left\Vert \nabla u\right\Vert
_{p}^{p}:u\in W_{0}^{1,p}(\Omega)\quad and\quad\left\Vert u\right\Vert
_{\infty}=1\right\} . \] We first prove that \[
\lim_{p\rightarrow\infty}\Lambda_{p}(\Omega)^{\frac{1}{p}}=\frac{1}{\left\Vert
\rho\right\Vert _{\infty}}, \] where $\rho$ denotes the distance function to
the boundary. Then, we show that, up to subsequences, the extremal functions of
$\Lambda_{p}(\Omega)$ converge (as $p\rightarrow\infty$) to the viscosity
solutions of a specific Dirichlet problem involving the infinity Laplacian in
the punctured $\Omega.
Sliding block codes between shift spaces over infinite alphabets

Recently Ott, Tomforde and Willis introduced a notion of one-sided shifts
over infinite alphabets and proposed a definition for sliding block codes
between such shift spaces. In this work we propose a more general definition
for sliding block codes between Ott-Tomforde-Willis shift spaces and then we
prove Curtis-Hedlund-Lyndon type theorems for them, finding sufficient and
necessary conditions under which the class of the sliding block codes coincides
with the class of continuous shift-commuting maps.Comment: 15 pages. Revised tex
The quantization for Markov-type measures on a class of ratio-specified
  graph directed fractals

We study the asymptotic quantization error of order $r$ for Markov-type
measures $\mu$ on a class of ratio-specified graph directed fractals. We show
that the quantization dimension of $\mu$ exists and determine its exact value
$s_{r}$ in terms of spectral radius of a related matrix. We prove that the
$s_{r}$-dimensional lower quantization coefficient of $\mu$ is always positive.
Moreover, inspired by Mauldin-Williams's work on the Hausdorff measure of graph
directed fractals, we establish a necessary and sufficient condition for the
$s_{r}$-dimensional upper quantization coefficient of $\mu$ to be finite
A Friedrichs-Maz'ya inequality for functions of bounded variation

The aim of this short note is to give an alternative proof, which applies to
functions of bounded variation in arbitrary domains, of an inequality by Maz'ya
that improves Friedrichs inequality. A remarkable feature of such a proof is
that it is rather elementary, if the basic background in the theory of
functions of bounded variation is assumed. Never the less, it allows to extend
all the previously known versions of this fundamental inequality to a
completely general version. In fact the inequality presented here is optimal in
several respects.
  As already observed in previous proofs, the crucial step is to provide
conditions under which a function of bounded variation on a bounded open set,
extended to zero outside, has bounded variation on the whole space. We push
such conditions to their limits. In fact, we give a sufficient and necessary
condition if the open set has a boundary with $\sigma$-finite surface measure
and a sufficient condition if the open set is fully arbitrary. Via a
counterexample we show that such a general sufficient condition is sharp.Comment: 12 pages. To appear in Mathematische Nachrichte
Minimal energy problems for strongly singular Riesz kernels

We study minimal energy problems for strongly singular Riesz kernels math formula, where math formula and math formula, considered for compact math formula-dimensional math formula-manifolds Γ immersed into math formula. Based on the spatial energy of harmonic double layer potentials, we are motivated to formulate the natural regularization of such minimization problems by switching to Hadamard's partie finie integral operator which defines a strongly elliptic pseudodifferential operator of order math formula on Γ. The measures with finite energy are shown to be elements from the Sobolev space math formula, math formula, and the corresponding minimal energy problem admits a unique solution. We relate our continuous approach also to the discrete one, which has been worked out earlier by D. P. Hardin and E. B. Saff
Geometric properties of the Cassinian metric

In this paper we prove a sharp distortion property of the Cassinian metric
under M\"obius transformations of a punctured ball onto another punctured ball.
The paper also deals with discussion on local convexity properties of the
Cassinian metric balls in some specific subdomains of $\mathbb{R}^n$. Inclusion
properties of the Cassinian metric balls with other hyperbolic-type metric
balls are also investigated. In particular, several conjectures are also stated
in response to sharpness of the inclusion relations.Comment: 16 pages, 2 figure
On the structure of sets with positive reach

We give a complete characterization of compact sets with positive reach
(=proximally $C^1$ sets) in the plane and of one-dimensional sets with positive
reach in ${\mathbb R}^d$. Further, we prove that if $\emptyset \neq
A\subset{\mathbb R}^d$ is a set of positive reach of topological dimension $0<
k \leq d$, then $A$ has its "$k$-dimensional regular part" $\emptyset \neq R
\subset A$ which is a $k$-dimensional "uniform" $C^{1,1}$ manifold open in $A$
and $A\setminus R$ can be locally covered by finitely many $(k-1)$-dimensional
DC surfaces. We also show that if $A \subset {\mathbb R}^d$ has positive reach,
then $\partial A$ can be locally covered by finitely many semiconcave
hypersurfaces
Geometry and arithmetic of primary Burniat surfaces

We study the geometry and arithmetic of so-called primary Burniat surfaces, a
family of surfaces of general type arising as smooth bidouble covers of a del
Pezzo surface of degree 6 and at the same time as \'etale quotients of certain
hypersurfaces in a product of three elliptic curves. We give a new explicit
description of their moduli space and determine their possible automorphism
groups. We also give an explicit description of the set of curves of geometric
genus 1 on each primary Burniat surface. We then describe how one can try to
obtain a description of the set of rational points on a given primary Burniat
surface $S$ defined over $\mathbb Q$. This involves an explicit description of
the relevant twists of the \'etale covering of $S$ coming from the second
construction mentioned above and methods for finding the set of rational points
on a given twist.Comment: v3: Some changes following referee's suggestions; in particular, the
  title was changed and Section 2 was shortened. v2: added abstract and a
  paragraph at the beginning of the introduction, plus various minor edits. 35
  pages, several figures, Mathematische Nachrichten 2017 (online
On the discretisation in time of the stochastic Allen-Cahn equation

We consider the stochastic Allen--Cahn equation perturbed by smooth additive
Gaussian noise in a spatial domain with smooth boundary in dimension $d\le 3$,
and study the semidiscretisation in time of the equation by an Euler type
split-step method. We show that the method converges strongly with a rate
$O(\Delta t^{\frac12}) $. By means of a perturbation argument, we also
establish the strong convergence of the standard backward Euler scheme with the
same rate.Comment: 32 pages. Several typos fixed, the statement and proof of Lemma 3.2
  are updated and so is the proof of Lemma 5.2. The proof of Lemma 5.1 is
  omitte
The automorphism group of a rigid affine variety

An irreducible algebraic variety $X$ is rigid if it admits no nontrivial
action of the additive group of the ground field. We prove that the
automorphism group $\text{Aut}(X)$ of a rigid affine variety contains a unique
maximal torus $\mathbb{T}$. If the grading on the algebra of regular functions
$\mathbb{K}[X]$ defined by the action of $\mathbb{T}$ is pointed, the group
$\text{Aut}(X)$ is a finite extension of $\mathbb{T}$. As an application, we
describe the automorphism group of a rigid trinomial affine hypersurface and
find all isomorphisms between such hypersurfaces.Comment: 12 page
Eigenvalues of Robin Laplacians in infinite sectors

For $\alpha\in(0,\pi)$, let $U_\alpha$ denote the infinite planar sector of
opening $2\alpha$, \[ U_\alpha=\big\{ (x_1,x_2)\in\mathbb R^2:
\big|\arg(x_1+ix_2) \big|<\alpha \big\}, \] and $T^\gamma_\alpha$ be the
Laplacian in $L^2(U_\alpha)$, $T^\gamma_\alpha u= -\Delta u$, with the Robin
boundary condition $\partial_\nu u=\gamma u$, where $\partial_\nu$ stands for
the outer normal derivative and $\gamma>0$. The essential spectrum of
$T^\gamma_\alpha$ does not depend on the angle $\alpha$ and equals
$[-\gamma^2,+\infty)$, and the discrete spectrum is non-empty iff
$\alpha<\frac\pi 2$. In this case we show that the discrete spectrum is always
finite and that each individual eigenvalue is a continous strictly increasing
function of the angle $\alpha$. In particular, there is just one discrete
eigenvalue for $\alpha \ge \frac{\pi}{6}$. As $\alpha$ approaches $0$, the
number of discrete eigenvalues becomes arbitrary large and is minorated by
$\kappa/\alpha$ with a suitable $\kappa>0$, and the $n$th eigenvalue
$E_n(T^\gamma_\alpha)$ of $T^\gamma_\alpha$ behaves as \[
E_n(T^\gamma_\alpha)=-\dfrac{\gamma^2}{(2n-1)^2 \alpha^2}+O(1) \] and admits a
full asymptotic expansion in powers of $\alpha^2$. The eigenfunctions are
exponentially localized near the origin. The results are also applied to
$\delta$-interactions on star graphs.Comment: 34 page
Extension of Whitney jets of controlled growth

We revisit Whitney's extension theorem in the ultradifferentiable Roumieu
setting. Based on the description of ultradifferentiable classes by weight
matrices, we extend results on how growth constraints on Whitney jets on
arbitrary compact subsets in $\mathbb R^n$ are preserved by their extensions to
$\mathbb R^n$. More precisely, for any admissible class $\mathcal C$ of
ultradifferentiable functions on $\mathbb R^n$ we determine a class $\mathcal
C'$ such that all ultradifferentiable Whitney jets of class $\mathcal C'$ on
arbitrary compact subsets admit extensions in $\mathcal C$. The class $\mathcal
C'$ can be explicitly computed from $\mathcal C$.Comment: 21 pages; minor changes, some references added; accepted for
  publication in Math. Nach
Recovery of periodicities hidden in heavy-tailed noise

We address a parametric joint detection-estimation problem for discrete
signals of the form $x(t) = \sum_{n=1}^{N} \alpha_n e^{-i \lambda_n t } +
\epsilon_t$, $t \in \mathbb{N}$, with an additive noise represented by
independent centered complex random variables $\epsilon_t$. The distributions
of $\epsilon_t$ are assumed to be unknown, but satisfying various sets of
conditions. We prove that in the case of a heavy-tailed noise it is possible to
construct asymptotically strongly consistent estimators for the unknown
parameters of the signal, i.e., the frequencies $\lambda_n$, their number $N$,
and complex amplitudes $\alpha_n$. For example, one of considered classes of
noise is the following: $\epsilon_t$ are independent identically distributed
random variables with $\mathbb{E} (\epsilon_t) = 0$ and $\mathbb{E}
(|\epsilon_t| \ln |\epsilon_t|) < \infty$. The construction of estimators is
based on detection of singularities of anti-derivatives for $Z$-transforms and
on a two-level selection procedure for special discretized versions of
superlevel sets. The consistency proof relies on the convergence theory for
random Fourier series. We discuss also decaying signals and the case of
infinite number of frequencies.Comment: This e-print differs in style, formatting, pagination, and small
  non-mathematical details from the version of this paper accepted for
  publication in "Mathematische Nachrichten" (Wiley-VCH). In comparison with
  the previous version, the following changes have been made: The introduction
  section 1 was split into two sections 1 and 2. The new section 5 was added.
  The algorithm 4.1 was adde
The Ces\`aro operator in weighted $\ell_1$ spaces

Unlike for $\ell_p$, $1<p\leq\infty$, the discrete Ces\`aro operator $C$ does
not map $\ell_1$ into itself. We identify precisely those weights $w$ such that
$C$ does map $\ell_1(w)$ continuously into itself. For these weights a complete
description of the eigenvalues and the spectrum of $C$ are presented. It is
also possible to identify all $w$ such that $C$ is a compact operator in
$\ell_1(w)$. The final section investigates the mean ergodic properties of $C$
in $\ell_1(w)$. Many examples are presented in order to supplement the results
and to illustrate the phenomena that occur
Algebraic cycles and EPW cubes

Let $X$ be a hyperk\"ahler variety with an anti-symplectic involution
$\iota$. According to Beauville's conjectural "splitting property", the Chow
groups of $X$ should split in a finite number of pieces such that the Chow ring
has a bigrading. The Bloch-Beilinson conjectures predict how $\iota$ should act
on certain of these pieces of the Chow groups. We verify part of this
conjecture for a $19$-dimensional family of hyperk\"ahler sixfolds that are
"double EPW cubes" (in the sense of Iliev-Kapustka-Kapustka-Ranestad). This has
interesting consequences for the Chow ring of the quotient $X/\iota$, which is
an "EPW cube" (in the sense of Iliev-Kapustka-Kapustka-Ranestad).Comment: 32 pages, to appear in Math. Nachrichten, feedback welcom
Applications of Livingston-type inequalities to the generalized Zalcman
  functional

We obtain sharp estimates for a generalized Zalcman coefficient functional
with a complex parameter for the Hurwitz class and the Noshiro-Warschawski
class of univalent functions as well as for the closed convex hulls of the
convex and starlike functions by using an inequality from [6]. In particular,
we generalize an inequality proved by Ma for starlike functions and answer a
question from his paper [16]. Finally, we prove an asymptotic version of the
generalized Zalcman conjecture for univalent functions and discuss various
related or equivalent statements which may shed further light on the problem.Comment: This manuscript differs significantly in content from our earlier
  unpublished manuscript arXiv:1403.5240, cited here as [6]. In this version, a
  misprint has been corrected and a reference adde
On automorphisms of Enriques surfaces and their entropy

Consider an arbitrary automorphism of an Enriques surface with its lift to
the covering K3 surface. We prove a bound of the order of the lift acting on
the anti-invariant cohomology sublattice of the Enriques involution. We use it
to obtain some mod 2 constraint on the original automorphism. As an
application, we give a necessary condition for Salem numbers to be dynamical
degrees on Enriques surfaces and obtain a new lower bound on the minimal value.
In the Appendix, we give a complete list of Salem numbers that potentially may
be the minimal dynamical degree on Enriques surfaces and for which the
existence of geometric automorphisms is unknown.Comment: 16 pages / v2: some refinements on the theorems and the proofs, and
  also attached plain text lists of Salem numbers related to the proble
Spectral Heat Content for L\'evy Processes

In this paper we study the spectral heat content for various L\'evy
processes. We establish the asymptotic behavior of the spectral heat content
for L\'{e}vy processes of bounded variation in $\mathbb{R}^{d}$, $d\geq 1$. We
also study the spectral heat content for arbitrary open sets of finite Lebesgue
measure in $\mathbb{R}$ with respect to L\'{e}vy processes of unbounded
variation under certain conditions on their characteristic exponents. Finally
we establish that the asymptotic behavior of the spectral heat content is
stable under integrable perturbations to the L\'{e}vy measure.Comment: 19 page
Developing Heuristic-Based Quality Judgements: Attention Blocking in Consumer Choice

Through a series of experiments we illustrate how the sequential order in which
consumers receive information can influence the way this information is processed
and affect consumers’ decisions. Specifically, when participants initially receive information regarding brand/quality or price/quality associations, these associations
can block consumers’ attention to more relevant quality-determining physical attributes.
Moreover, this process of attention blocking can carry-over to affect quality
judgements pertaining to similarly branded or priced products beyond the product
in which blocking was initiated. This implies that consumers judgements of quality
may be heavily dependent on “first impressions” which develop into brand and price
heuristics.
"This is who I am": Identity expressiveness and the theory of planned behavior

-"This is the peer reviewed version of the following article: Thorbjørnsen, H., Pedersen, P. E. and Nysveen, H. (2007), “This is who i am”: Identity expressiveness and the theory of planned behavior. Psychol. Mark., 24: 763–785, which has been published in final form at doi: 10.1002/mar.20183. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."This paper explores the role of self-identity expressiveness and social identity expressiveness in the context of Multimedia Messaging (MMS) adoption. An extended version of the Theory of Planned Behavior (TPB) including a wider array of identity and social influences is developed and tested. As hypothesized, self-identity expressiveness and social identity expressiveness prove to be significant determinants of intentions to use. Moreover, the extended TPB model explains 62% of the variance in usage intentions. The paper also investigates the relationship between self identity expressiveness and attitude and between social identity expressiveness and subjective norm. The study results indicate that the concept of subjective norm alone is insufficient to capture the rich universe of identity and social influences driving behavioral intentions. Implications for marketing managers and scholars are discussed. © 2007 Wiley Periodicals, Inc
The electronic service quality model : the moderating effect of customer self-efficacy

The research in the area has largely ignored the moderating effects of the customer trait, self-efficacy, on the electronic service quality model. This study examines the degree to which electronic service quality dimensions influence overall service quality, which in turn affects customer satisfaction and loyalty. On the basis of self-efficacy theory, this paper argues that outcome quality is the most important predictor of overall quality, whereas environment quality is the least important predictor of overall quality, particularly when self-efficacy is high. Additionally, the paper demonstrates that self-efficacy strengthens the link between customer satisfaction and both repurchase intention and word of mouth. Data collected from 162 participants provide support for most of these hypotheses
Does "Passing the Courvoisier" Always Pay Off? Positive and Negative Evaluative Conditioning Effects of Brand Placements in Rap Videos

The proliferation of brands in television programming has\ud
abounded in recent times. Especially in rap videos, actors frequently depict brands and products. One mechanism by which placements can affect consumers’ attitudes is evaluative conditioning. Given that in rap videos brands are paired with liked as well as disliked actors, there is a high potential for positive and negative conditioning effects. In an experiment with an authentic rap video, the\ud
appearance of placements and the image of the rap actors were varied. The results indicate that the pairing of a brand with positively evaluated artists produces positive attitudes toward the brand. In contrast, a negative conditioning procedure results in negative attitudes toward the brand. Further analyses demonstrate that conditioning effects are even stronger when preference for rap music is high and recognition of the brand rather low