pinecone/core-2020-05-10-deduplication huggingface dataset:
Linear spectral transformations and Laurent polynomials

17 pages, 2 figures.-- MSC2000 codes: Primary 42C05; Secondary 15A23.In this manuscript we analyze some linear spectral transformations of a Hermitian linear functional using the multiplication by some class of Laurent polynomials. We focus our attention in the behavior of the Verblunsky parameters of the perturbed linear functional. Some illustrative examples are pointed out.The work of the first author has been supported by a grant of Universidad Autónoma de Tamaulipas. The work of the second author has been supported by Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain, grant MTM06-13000-C03-02. Both authors have been supported by project CCG07-UC3M/ESP-3339 with the financial
support of Comunidad de Madrid-Universidad Carlos III de Madrid.Publicad
The geometry of systems of third order differential equations induced by
  second order Lagrangians

A dynamical system on the total space of the fibre bundle of second order
accelerations, $T^2M$, is defined as a third order vector field $S$ on $T^2M$,
called semispray, which is mapped by the second order tangent structure into
one of the Liouville vector field. For a regular Lagrangian of second order we
prove that this semispray is uniquely determined by two associated
Cartan-Poincar\'e one-forms. To study the geometry of this semispray we
construct a nonlinear connection, which is a Lagrangian subbundle for the
presymplectic structure. Using this semispray and the associated nonlinear
connection we define covariant derivatives of first and second order. With
respect to this, the second order dynamical derivative of the Lagrangian metric
tensor vanishes
A new approach to transport equations associated to a regular field: trace results and well-posedness.

30 pages.International audienceWe generalize known results on transport equations associated to a Lipschitz field $\mathbf{F}$ on some subspace of $\mathbb{R}^N$ endowed with some general space measure $\mu$. We provide a new definition of both the transport operator and the trace measures over the incoming and outgoing parts of $\partial \Omega$ generalizing known results from the literature. We also prove the well-posedness of some suitable boundary-value transport problems and describe in full generality the generator of the transport semigroup with no-incoming boundary conditions
An Invariant Theory of Spacelike Surfaces in the Four-dimensional
  Minkowski Space

We consider spacelike surfaces in the four-dimensional Minkowski space and
introduce geometrically an invariant linear map of Weingarten-type in the
tangent plane at any point of the surface under consideration. This allows us
to introduce principal lines and an invariant moving frame field. Writing
derivative formulas of Frenet-type for this frame field, we obtain eight
invariant functions. We prove a fundamental theorem of Bonnet-type, stating
that these eight invariants under some natural conditions determine the surface
up to a motion. We show that the basic geometric classes of spacelike surfaces
in the four-dimensional Minkowski space, determined by conditions on their
invariants, can be interpreted in terms of the properties of the two geometric
figures: the tangent indicatrix, and the normal curvature ellipse. We apply our
theory to a class of spacelike general rotational surfaces.Comment: 23 pages; to appear in Mediterr. J. Math., Vol. 9 (2012
Vector Risk Functions

The paper introduces a new notion of vector-valued risk function, a crucial notion in Actuarial and Financial Mathematics. Both deviations and expectation bounded or coherent risk measures are defined and analyzed. The relationships with both scalar and vector risk functions of previous literature are discussed, and it is pointed out that this new approach seems to appropriately integrate several preceding points of view. The framework of the study is the general setting of Banach lattices and Bochner integrable vector-valued random variables. Sub-gradient linked representation theorems and practical examples are provided.This research was partially supported by “Ministerio de Ciencia en Innovación”
(Spain), Grant ECO2009 − 14457 − C04Publicad
Multiple Solutions of Semilinear Elliptic Problems with Degenerate Boundary Conditions

The purpose of this paper is to study a class of semilinear elliptic boundary value problems with degenerate boundary conditions which include as particular cases the Dirichlet and Robin problems. The approach here is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of partial differential equations. By making use of the Leray–Schauder degree, we prove very exact results on the number of solutions of our problem. The results here extend earlier theorems due to Berger–Podolak, Castro–Lazer and Ambrosetti–Mancini to the degenerate case
On a sum of modified Bessel functions

In this paper we consider a sum of modified Bessel functions of the first
kind of which particular case is used in the study of Kanter's sharp modified
Bessel function bound for concentrations of some sums of independent symmetric
random vectors. We present some monotonicity and convexity properties for that
sum of modified Bessel functions of the first kind, as well as some Tur\'an
type inequalities, lower and upper bounds. Moreover, we point out an error in
Kanter's paper [Ka] and at the end of the paper we pose an open problem, which
may be of interest for further research.Comment: 8 page
Exponential quadrature rules for linear fractional differential
  equations

This paper focuses on the numerical solution of initial value problems for
fractional differential equations of linear type. The approach we propose
grounds on expressing the solution in terms of some integral weighted by a
generalized Mittag-Leffler function. Then suitable quadrature rules are devised
and order conditions of algebraic type are derived. Theoretical findings are
validated by means of numerical experiments and the effectiveness of the
proposed approach is illustrated by means of comparisons with other standard
methods
Filter convergence and decompositions for vector lattice-valued measures

Filter convergence of vector lattice-valued measures is considered, in order
to deduce theorems of convergence for their decompositions. First the
$\sigma$-additive case is studied, without particular assumptions on the
filter; later the finitely additive case is faced, first assuming uniform
$s$-boundedness (without restrictions on the filter), then relaxing this
condition but imposing stronger properties on the filter. In order to obtain
the last results, a Schur-type convergence theorem is used.Comment: 18 page
Some Monotonicity Properties of Convex Functions with Applications

We mainly establish a monotonicity property between some special Riemann sums
of a convex function $f$ on $[a,b]$, which in particular yields that
$\frac{b-a}{n+1}\sum_{i=0}^n f\left(a+i\frac{b-a}{n}\right)$ is decreasing
while $\frac{b-a}{n-1}\sum_{i=1}^{n-1} f\left(a+i\frac{b-a}{n}\right)$ is an
increasing sequence. These give us a new refinement of the Hermitt-Hadamard
inequality.
  Moreover, we give a refinement of the classical Alzer's inequality together
with a suitable converse to it. Applications regarding to some important convex
functions are also included
S-Cobordism Classification of $4$-Manifolds Through the Group of
  Homotopy Self-Equivalences

The aim of this paper is to give an $s$-cobordism classification of
topological $4$-manifolds in terms of the standard invariants using the group
of homotopy self-equivalences. Hambleton and Kreck constructed a braid to study
the group of homotopy self-equivalences of $4$-manifolds. Using this braid
together with the modified surgery theory of Kreck, we give an $s$-cobordism
classification for certain $4$-manifolds with fundamental group $\pi$, such
that cd $\pi \leq 2$.Comment: appears in Mediterr. J. Math. (2015
Almost Kaehler Ricci Flows and Einstein and Lagrange-Finsler Structures
  on Lie Algebroids

In this work we investigate Ricci flows of almost Kaehler structures on Lie
algebroids when the fundamental geometric objects are completely determined by
(semi) Riemannian metrics, or effective) regular generating Lagrange/ Finsler,
functions. There are constructed canonical almost symplectic connections for
which the geometric flows can be represented as gradient ones and characterized
by nonholonomic deformations of Grigory Perelman's functionals. The first goal
of this paper is to define such thermodynamical type values and derive almost
K\"ahler - Ricci geometric evolution equations. The second goal is to study how
fixed Lie algebroid, i.e. Ricci soliton, configurations can be constructed for
Riemannian manifolds and/or (co) tangent bundles endowed with nonholonomic
distributions modelling (generalized) Einstein or Finsler - Cartan spaces.
Finally, there are provided some examples of generic off-diagonal solutions for
Lie algebroid type Ricci solitons and (effective) Einstein and Lagrange-Finsler
algebroids.Comment: This version is accepted by Mediterranian J. Math. and modified
  following editor/referee's requests. File latex2e 11pt generates 29 page
A method to generate first integrals from infinitesimal symmetries

We propose a method to construct first integrals of a dynamical system,
starting with a given set of independent infinitesimal symmetries. In the case
of two infinitesimal symmetries, a rank two Poisson structure on the ambient
space it is found, such that the vector field that generates the dynamical
system, becomes a Poisson vector field. Moreover, the symplectic leaves and the
Casimir functions of the associated Poisson manifold are characterized.
Explicit conditions that guarantee Hamilton-Poisson realizations of the
dynamical system are also given.Comment: 14 page
Maximal area integral problem for certain class of univalent analytic
  functions

One of the classical problems concerns the class of analytic functions $f$ on
the open unit disk $|z|<1$ which have finite Dirichlet integral $\Delta(1,f)$,
where $$\Delta(r,f)=\iint_{|z|<r}|f'(z)|^2 \, dxdy \quad (0<r\leq 1). $$ The
class ${\mathcal S}^*(A,B)$ of normalized functions $f$ analytic in $|z|<1$ and
satisfies the subordination condition $zf'(z)/f(z)\prec (1+Az)/(1+Bz)$ in
$|z|<1$ and for some $-1\leq B\leq 0$, $A\in {\mathbb C}$ with $A\neq B$, has
been studied extensively. In this paper, we solve the extremal problem of
determining the value of $$\max_{f\in {\mathcal S}^*(A,B)}\Delta(r,z/f)$$ as a
function of $r$. This settles the question raised by Ponnusamy and Wirths in
[11]. One of the particular cases includes solution to a conjecture of
Yamashita which was settled recently by Obradovi\'{c} et. al [9].Comment: 16 pages, 8 figures, 3 table
Higher Affine Connections

For a smooth manifold $M$, it was shown in \cite{BPH} that every affine
connection on the tangent bundle $TM$ naturally gives rise to covariant
differentiation of multivector fields (MVFs) and differential forms along MVFs.
In this paper, we generalize the covariant derivative of \cite{BPH} and
construct covariant derivatives along MVFs which are not induced by affine
connections on $TM$. We call this more general class of covariant derivatives
\textit{higher affine connections}. In addition, we also propose a framework
which gives rise to non-induced higher connections; this framework is obtained
by equipping the full exterior bundle $\wedge^\bullet TM$ with an associative
bilinear form $\eta$. Since the latter can be shown to be equivalent to a set
of differential forms of various degrees, this framework also provides a link
between higher connections and multisymplectic geometry.Comment: 37 pages; main definition and results generalized; substantial
  changes after section
Real-Linear Isometries and Jointly Norm-Additive Maps on Function Algebras

In this paper, we describe into real-linear isometries defined between (not necessarily unital) function algebras and show, based on an example, that this type of isometries behaves differently from surjective real-linear isometries and from classical linear isometries. Next we introduce jointly norm-additive mappings and apply our results on real-linear isometries to provide a complete description of these mappings when defined between function algebras which are not necessarily unital or uniformly closed.Research of J. J. Font was partially supported by Universitat Jaume I (Projecte P1-1B2014-35)
Harmonic and Spectral Analysis of Abstract Parabolic Operators in
  Homogeneous Function Spaces

We use methods of harmonic analysis and group representation theory to study
the spectral properties of the abstract parabolic operator $\mathscr L =
-d/dt+A$ in homogeneous function spaces. We provide sufficient conditions for
invertibility of such operators in terms of the spectral properties of the
operator $A$ and the semigroup generated by $A$. We introduce a homogeneous
space of functions with absolutely summable spectrum and prove a generalization
of the Gearhart-Pr\"uss Theorem for such spaces. We use the results to prove
existence and uniqueness of solutions of a certain class of non-linear
equations
Inducing maps between Gromov boundaries

It is well known that quasi-isometric embeddings of Gromov hyperbolic spaces
induce topological embeddings of their Gromov boundaries. A more general
question is to detect classes of functions between Gromov hyperbolic spaces
that induce continuous maps between their Gromov boundaries. In this paper we
introduce the class of visual functions $f$ that do induce continuous maps
$\tilde f$ between Gromov boundaries. Its subclass, the class of radial
functions, induces Hoelder maps between Gromov boundaries. Conversely, every
Hoelder map between Gromov boundaries of visual hyperbolic spaces induces a
radial function. We study the relationship between large scale properties of f
and small scale properties of $f$, especially related to the dimension theory.
In particular, we prove a form of the dimension raising theorem. We give a
natural example of a radial dimension raising map and we also give a general
class of radial functions that raise asymptotic dimension
Elasticae in Killing submersions

Classical elastic curves (elastica) are variational objects with many applications in physics and engineering. Elastica in real space forms are well understood, but in other ambient spaces there are few known explicit examples, except geodesics. In this work, we study elastica living in the total space of a Killing submersion focusing on those curves whose osculating plane forms a constant angle with the vertical foliation (slant elastica). First, we compute the Euler–Lagrange equations for elastica and construct new examples of slant elastica in Killing submersions. Then, we completely classify the two main families of slant elastica in Bianchi–Cartan–Vranceanu ambient spaces (giving also explicit parametrizations)
On the locus of smooth plane curves with a fixed automorphism group

In this paper, we study some aspects of the irreducibility of
$\widetilde{M_g^{Pl}(G)}$ and its interrelation with the existence of "normal
forms", i.e. non-singular plane equations (depending on a set of parameters)
such that a specialization of the parameters gives a certain non-singular plane
model associated to the elements of $\widetilde{M_g^{Pl}(G)}$. In particular,
we introduce the concept of being equation strongly irreducible
(ES-Irreducible) for which the locus $\widetilde{M_g^{Pl}(G)}$ is represented
by a single "normal form". Henn, and Komiya-Kuribayashi, observed that
$\widetilde{M_3^{Pl}(G)}$ is ES-Irreducible. In this paper we prove that this
phenomena does not occur for any odd $d>4$. More precisely, let
$\mathbb{Z}/m\mathbb{Z}$ be the cyclic group of order $m$, we prove that
$\widetilde{M_g^{Pl}(\mathbb{Z}/(d-1)\mathbb{Z})}$ is not ES-Irreducible for
any odd integer $d\geq5$, and the number of its irreducible components is at
least two. Furthermore, we conclude the previous result when $d=6$ for the
locus $\widetilde{M_{10}^{Pl}(\mathbb{Z}/3\mathbb{Z})}$.
  Lastly, we prove the analogy of these statements when $K$ is any
algebraically closed field of positive characteristic $p$ such that
$p>(d-1)(d-2)+1$.Comment: This paper is a recent version of chapter 1 of arXiv:1503.0114
Towers and fibered products of model structures

Given a left Quillen presheaf of localized model structures, we study the
homotopy limit model structure on the associated category of sections. We focus
specifically on towers and fibered products (pullbacks) of model categories. As
applications we consider Postnikov towers of model categories, chromatic towers
of spectra and Bousfield arithmetic squares of spectra. For stable model
categories, we show that the homotopy fiber of a stable left Bousfield
localization is a stable right Bousfield localization.Comment: 20 pages. The paper "Bousfield localisations along Quillen bifunctors
  and applications" (arXiv:1411.0500v1) has been divided into two parts:
  "Towers and fibered products of model structures", which is this arXiv
  submission, and "Bousfield localisations along Quillen bifunctors"
  (arXiv:1411.0500v2
On a Moser-Steffensen type method for nonlinear systems of equations

This paper is devoted to the construction and analysis of a Moser–Steffensen iterative scheme. The method has quadratic convergence without evaluating any derivative nor inverse operator. We present a complete study of the order of convergence for systems of equations, hypotheses ensuring the local convergence, and finally, we focus our attention to its numerical behavior. The conclusion is that the method improves the applicability of both Newton and Steffensen methods having the same order of convergence.Peer ReviewedPostprint (author's final draft
Invariant metrizability and projective metrizability on Lie groups and
  homogeneous spaces

In this paper we study the invariant metrizability and projective
metrizability problems for the special case of the geodesic spray associated to
the canonical connection of a Lie group. We prove that such canonical spray is
projectively Finsler metrizable if and only if it is Riemann metrizable. This
result means that this structure is rigid in the sense that considering
left-invariant metrics, the potentially much larger class of projective Finsler
metrizable canonical sprays, corresponding to Lie groups, coincides with the
class of Riemann metrizable canonical sprays. Generalisation of these results
for geodesic orbit spaces are given.Comment: final version, accepted by MJO
Solitary wave simulations of the Boussinesq Systems

In the study, the collocation method based on exponential cubic B-spline
functions is proposed to solve one dimensional Boussinesq systems numerically.
Two initial boundary value problems for Regularized and Classical Boussinesq
systems modeling motion of traveling waves are considered. The accuracy of the
method is validated by measuring the error between the numerical and analytical
solutions. The numerical solutions obtained by various values of free parameter
$p$ are compared with some solutions in literature.Comment: 13 pages, 4 figure
Higher order tangent bundles

The tangent bundle $T^kM$ of order $k$, of a smooth Banach manifold $M$
consists of all equivalent classes of curves that agree up to their
accelerations of order $k$. For a Banach manifold $M$ and a natural number $k$
first we determine a smooth manifold structure on $T^kM$ which also offers a
fiber bundle structure for $(\pi_k,T^kM,M)$. Then we introduce a particular
lift of linear connections on $M$ to geometrize $T^kM$ as a vector bundle over
$M$. More precisely based on this lifted nonlinear connection we prove that
$T^kM$ admits a vector bundle structure over $M$ if and only if $M$ is endowed
with a linear connection. As a consequence applying this vector bundle
structure we lift Riemannian metrics and Lagrangians from $M$ to $T^kM$. Also,
using the projective limit techniques, we declare a generalized Fr\'echet
vector bundle structure for $T^\infty M$ over $M$
Tabulation of prime knots in lens spaces

Using computational techniques we tabulate prime knots up to five crossings
in the solid torus and the infinite family of lens spaces $L(p,q)$. For these
knots we calculate the second and third skein module and establish which prime
knots in the solid torus are amphichiral. Most knots are distinguished by the
skein modules. For the handful of cases where the skein modules fail to detect
inequivalent knots, we calculate and compare the hyperbolic structures of the
knot complements. We were unable to resolve a handful of 5-crossing cases for
$p\geq 13$.Comment: To appear in Mediterr. J. Mat
Meridian Surfaces with Constant Mean Curvature in Pseudo-Euclidean
  4-space with Neutral Metric

In the present paper we consider a special class of Lorentz surfaces in the
four-dimensional pseudo-Euclidean space with neutral metric which are
one-parameter systems of meridians of rotational hypersurfaces with timelike or
spacelike axis and call them meridian surfaces. We give the complete
classification of minimal and quasi-minimal meridian surfaces. We also classify
the meridian surfaces with non-zero constant mean curvature.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1606.0004
Simply Connected 3-Manifolds with a Dense Set of Ends of Specified Genus

We show that for every sequence $(n_i)$, where each $n_i$ is either an
integer greater than 1 or is $\infty$, there exists a simply connected open
3-manifold $M$ with a countable dense set of ends $\{e_i\}$ so that, for every
$i$, the genus of end $e_i$ is equal to $n_i$. In addition, the genus of the
ends not in the dense set is shown to be less than or equal to 2. These simply
connected 3-manifolds are constructed as the complements of certain Cantor sets
in $S^3$. The methods used require careful analysis of the genera of ends and
new techniques for dealing with infinite genus
On Biconservative Lorentz Hypersurface with non-diagonalizable shape
  operator

In this paper, we obtain some properties of biconservative Lorentz
hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ having shape operator with complex
eigen values. We prove that every biconservative Lorentz hypersurface
$M_{1}^{n}$ in $E_{1}^{n+1}$ whose shape operator has complex eigen values with
at most five distinct principal curvatures has constant mean curvature. Also,
we investigate such type of hypersurface with constant length of second
fundamental form having six distinct principal curvatures
Second order time dependent tangent bundles and their applications

The aim of this paper is to geometrize time dependent Lagrangian mechanics in
a way that the framework of second order tangent bundles plays an essential
role. To this end, we first introduce the concepts of time dependent
connections and time dependent semisprays on a manifold $M$ and their induced
vector bundle structures on the second order time dependent tangent bundle
$\R\times T^2M$. Then we turn our attention to regular time Lagrangians and
their interaction with $\R\times T^2M$ in different situations such as
mechanical systems with potential fields, external forces and holonomic
constraints. Finally we propose an examples to support our theory
On the geometry of almost Golden Riemannian manifolds

An almost Golden Riemannian structure $(\varphi ,g)$ on a manifold is given
by a tensor field $\varphi $ of type (1,1) satisfying the Golden section
relation $\varphi ^{2}=\varphi +1$, and a pure Riemannian metric $g$, i.e., a
metric satisfying $g(\varphi X,Y)=g(X,\varphi Y)$. We study connections adapted
to such a structure, finding two of them, the first canonical and the well
adapted, which measure the integrability of $\varphi $ and the integrability of
the $G$-structure corresponding to $(\varphi ,g)$