pinecone/core-2020-05-10-deduplication huggingface dataset:
On the solutions of a second-order difference equations in terms of
  generalized Padovan sequences

This paper deals with the solution, stability character and asymptotic
behavior of the rational difference equation \begin{equation*}
x_{n+1}=\frac{\alpha x_{n-1}+\beta}{ \gamma x_{n}x_{n-1}},\qquad n \in
\mathbb{N}_{0}, \end{equation*} where $\mathbb{N}_{0}=\mathbb{N}\cup
\left\{0\right\}$, $\alpha,\beta,\gamma\in\mathbb{R}^{+}$, and the initial
conditions $x_{-1}$ and $x_{0}$ are non zero real numbers such that their
solutions are associated to generalized Padovan numbers. Also, we investigate
the two-dimensional case of the this equation given by \begin{equation*}
  x_{n+1} = \frac{\alpha x_{n-1} + \beta}{\gamma y_n x_{n-1}}, \qquad y_{n+1} =
\frac{\alpha y_{n-1} +\beta}{\gamma x_n y_{n-1}} ,\qquad n\in \mathbb{N}_0,
\end{equation*} and this generalizes the results presented in \cite{yazlik}Comment: 17 pages, 2 figure
Can information be spread as a virus? Viral Marketing as epidemiological
  model

In epidemiology, an epidemic is defined as the spread of an infectious
disease to a large number of people in a given population within a short period
of time. In the marketing context, a message is viral when it is broadly sent
and received by the target market through person-to-person transmission. This
specific marketing communication strategy is commonly referred as viral
marketing. Due to this similarity between an epidemic and the viral marketing
process and because the understanding of the critical factors to this
communications strategy effectiveness remain largely unknown, the mathematical
models in epidemiology are presented in this marketing specific field. In this
paper, an epidemiological model SIR (Susceptible- Infected-Recovered) to study
the effects of a viral marketing strategy is presented. It is made a comparison
between the disease parameters and the marketing application, and Matlab
simulations are performed. Finally, some conclusions are carried out and their
marketing implications are exposed: interactions across the parameters suggest
some recommendations to marketers, as the profitability of the investment or
the need to improve the targeting criteria of the communications campaigns.Comment: Please cite this paper as: Rodrigues, Helena Sofia and Fonseca,
  Manuel Jos\'e (2016) . Can information be spread as a virus? Viral Marketing
  as epidemiological model, Mathematical Methods in the Applied Sciences, 39:
  4780--4786. arXiv admin note: substantial text overlap with arXiv:1507.0698
A cluster of many small holes with negative imaginary surface impedances
  may generate a negative refraction index

We deal with the scattering of an acoustic medium modeled by an index of
refraction $n$ varying in a bounded region $\Omega$ of $\mathbb{R}^3$ and equal
to unity outside $\Omega$. This region is perforated with an extremely large
number of small holes $D_m$'s of maximum radius $a$, $a<<1$, modeled by surface
impedance functions. Precisely, we are in the regime described by the number of
holes of the order $M:=O(a^{\beta-2})$, the minimum distance between the holes
is $d\sim a^t$ and the surface impedance functions of the form $\lambda_m \sim
\lambda_{m,0} a^{-\beta}$ with $\beta >0$ and $\lambda_{m,0}$ being constants
and eventually complex numbers. Under some natural conditions on the parameters
$\beta, t$ and $\lambda_{m,0}$, we characterize the equivalent medium
generating, approximately, the same scattered waves as the original perforated
acoustic medium. We give an explicit error estimate between the scattered waves
generated by the perforated medium and the equivalent one respectively, as $a
\rightarrow 0$. As applications of these results, we discuss the following
findings:
  1. If we choose negative valued imaginary surface impedance functions,
attached to each surface of the holes, then the equivalent medium behaves as a
passive acoustic medium only if it is an acoustic metamaterial with index of
refraction $\tilde{n}(x)=-n(x),\; x \in \Omega$ and $\tilde{n}(x)=1,\; x \in
\mathbb{R}^3\setminus{\overline{\Omega}}$. This means that, with this process,
we can switch the sign of the index of the refraction from positive to negative
values.
  2. We can choose the surface impedance functions attached to each surface of
the holes so that the equivalent index of refraction $\tilde{n}$ is
$\tilde{n}(x)=1,\; x \in \mathbb{R}^3$. This means that the region $\Omega$
modeled by the original index of refraction $n$ is approximately cloaked.Comment: arXiv admin note: text overlap with arXiv:1504.0694
A new approach to the Pontryagin maximum principle for nonlinear
  fractional optimal control problems

In this paper, we discuss a new general formulation of fractional optimal
control problems whose performance index is in the fractional integral form and
the dynamics are given by a set of fractional differential equations in the
Caputo sense. We use a new approach to prove necessary conditions of optimality
in the form of Pontryagin maximum principle for fractional nonlinear optimal
control problems. Moreover, a new method based on a generalization of the
Mittag-Leffler function is used to solving this class of fractional optimal
control problems. A simple example is provided to illustrate the effectiveness
of our main result.Comment: Reasons for replacing: (i) change of the email of the corresponding
  author, (ii) added references dor section 2, (iii) minor English corrections,
  (iv) typos adde
Modelling some real phenomena by fractional differential equations

This paper deals with fractional differential equations, with dependence on a
Caputo fractional derivative of real order. The goal is to show, based on
concrete examples and experimental data from several experiments, that
fractional differential equations may model more efficiently certain problems
than ordinary differential equations. A numerical optimization approach based
on least squares approximation is used to determine the order of the fractional
operator that better describes real data, as well as other related parameters.Comment: This is a preprint. The final form will appear in Mathematical
  Methods in the Applied Science
Global regularity for the 2D Oldroyd-B model in the corotational case

This paper is dedicated to the Oldroyd-B model with fractional dissipation
$(-\Delta)^{\alpha}\tau$ for any $\alpha>0$. We establish the global smooth
solutions to the Oldroyd-B model in the corotational case with arbitrarily
small fractional powers of the Laplacian in two spatial dimensions. The methods
described here are quite different from the tedious iterative approach used in
recent paper \cite{XY}. Moreover, in the Appendix we provide some a priori
estimates to the Oldroyd-B model in the critical case which may be useful and
of interest for future improvement. Finally, the global regularity to to the
Oldroyd-B model in the corotational case with $-\Delta u$ replaced by
$(-\Delta)^{\gamma}u$ for $\gamma>1$ are also collected in the Appendix.
Therefore our result is more closer to the resolution of the well-known global
regularity issue on the critical 2D Oldroyd-B model.Comment: 23 pages, Submitted August 201
Predicting and controlling the Ebola infection

We present a comparison between two different mathematical models used in the
description of the Ebola virus propagation currently occurring in West Africa.
In order to improve the prediction and the control of the propagation of the
virus, numerical simulations and optimal control of the two models for Ebola
are investigated. In particular, we study when the two models generate similar
results.Comment: This is a preprint of a paper whose final and definite form will be
  published in Mathematical Methods in the Applied Sciences, ISSN 0170-4214.
  Submitted 31-Aug-2015; revised 16-Nov-2015; accepted 19-Nov-201
On well-posedness for some thermo-piezoelectric coupling models

There is an increasing reliance on mathematical modelling to assist in the design of piezoelectric ultrasonic transducers since this provides a cost-effective and quick way to arrive at a first prototype. Given a desired operating envelope for the sensor the inverse problem of obtaining the associated design parameters within the model can be considered. It is therefore of practical interest to examine the well-posedness of such models. There is a need to extend the use of such sensors into high temperature environments and so this paper shows, for a broad class of models, the well-posedness of the magneto-electro-thermo-elastic problem. Due to its widespread use in the literature, we also show the well-posedness of the quasi-electrostatic case
On the Caginalp phase-field systems with two temperatures and the Maxwell–Cattaneo law

This is the peer reviewed version of the following article: Miranville, A., and Quintanilla, R. (2016) On the Caginalp phase-field systems with two temperatures and the Maxwell–Cattaneo law. Math. Meth. Appl. Sci., 39: 4385–4397, which has been published in final form at http://dx.doi.org/10.1002/mma.3867. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-ArchivingOur aim in this paper is to study generalizations of the nonconserved and conserved Caginalp phase-¿eld systems based on the Maxwell–Cattaneo law with two temperatures for heat conduction. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators.Peer ReviewedPostprint (author's final draft
Kolmogorov Space in Time Series Data

We provide the proof that the space of time series data is a Kolmogorov space
with $T_{0}$-separation axiom using the loop space of time series data. In our
approach we define a cyclic coordinate of intrinsic time scale of time series
data after empirical mode decomposition. A spinor field of time series data
comes from the rotation of data around price and time axis by defining a new
extradimension to time series data. We show that there exist hidden eight
dimensions in Kolmogorov space for time series data. Our concept is realized as
the algorithm of empirical mode decomposition and intrinsic time scale
decomposition and it is subsequently used for preliminary analysis on the real
time series data.Comment: 22 pages, 20 figure
Propagation and filtering of elastic and electromagnetic waves in
  piezoelectric composite structures

In this article we discuss the modelling of elastic and electromagnetic wave
propagation through one- and two-dimensional structured piezoelectric solids.
Dispersion and the effect of piezoelectricity on the group velocity and
positions of stop bands are studied in detail. We will also analyze the
reflection and transmission associated with the problem of scattering of an
elastic wave by a heterogeneous piezoelectric stack. Special attention is given
to the occurrence of transmission resonances in finite stacks and their
dependence on a piezoelectric effect. A 2D doubly-periodic piezoelectric
checkerboard structure is subsequently introduced, for which the dispersion
surfaces for Bloch waves have been constructed and analysed, with the emphasis
on the dynamic anisotropy and special features of standing waves within the
piezoelectric structure.Comment: 24 pages, 18 figures, 3 tables. Preprint version of a research
  article, accepted for publication in "Mathematical Methods in the Applied
  Science (2016)
An asymptotic model for the deformation of a transversely isotropic, transversely monogeneous biphasic cartilage layer

In the present paper, an asymptotic model is constructed for the short-time deformation of an articular cartilage layer modeled as transversely isotropic, transversely homogeneous biphasic material. It is assumed that the layer thickness is relatively small compared with the characteristic size of the normal surface load applied to the upper surface of the cartilage layer, while the bottom surface is assumed to be firmly attached to a rigid impermeable substrate. In view of applications to articular contact problems, it is assumed that the interstitial fluid is not allowed to escape through the articular surface. Copyright ? 2016 John Wiley & Sons, LtdauthorsversionPeer reviewe
Structured populations with distributed recruitment: from PDE to delay
  formulation

In this work first we consider a physiologically structured population model
with a distributed recruitment process. That is, our model allows newly
recruited individuals to enter the population at all possible individual
states, in principle. The model can be naturally formulated as a first order
partial integro-differential equation, and it has been studied extensively. In
particular, it is well-posed on the biologically relevant state space of
Lebesgue integrable functions. We also formulate a delayed integral equation
(renewal equation) for the distributed birth rate of the population. We aim to
illustrate the connection between the partial integro-differential and the
delayed integral equation formulation of the model utilising a recent spectral
theoretic result. In particular, we consider the equivalence of the steady
state problems in the two different formulations, which then leads us to
characterise irreducibility of the semigroup governing the linear partial
integro-differential equation. Furthermore, using the method of
characteristics, we investigate the connection between the time dependent
problems. In particular, we prove that any (non-negative) solution of the
delayed integral equation determines a (non-negative) solution of the partial
differential equation and vice versa. The results obtained for the particular
distributed states at birth model then lead us to present some very general
results, which establish the equivalence between a general class of partial
differential and delay equation, modelling physiologically structured
populations.Comment: 28 pages, to appear in Mathematical Methods in the Applied Science
Carleman estimate for Biot consolidation system in poro-elasticity and
  application to inverse problems

In this paper, we consider a coupled system of mixed hyperbolic-parabolic
type which describes the Biot consolidation model in poro-elasticity. We
establish a local Carleman estimate for Biot consilidation system. Using this
estimate, we prove the uniqueness and a H\"older stability in determining on
the one hand a physical parameter arising in connection with secondary
consolidation effects $\lambda^*$ and on the other hand the two spatially
varying density by a single measurement of solution over $\omega \times (0,
T)$, where $T>0$ is a sufficiently large time and a suitable subbdomain
$\omega$ satisfying $\p \omega \supset \p \Omega$
Inverse Problems of Combined Photoacoustic and Optical Coherence
  Tomography

Optical coherence tomography (OCT) and photoacoustic tomography (PAT) are
emerging non-invasive biological and medical imaging techniques. It is a recent
trend in experimental science to design experiments that perform PAT and OCT
imaging at once. In this paper we present a mathematical model describing the
dual experiment.
  Since OCT is mathematically modelled by Maxwell's equations or some
simplifications of it, whereas the light propagation in quantitative
photoacoustics is modelled by (simplifications of) the radiative transfer
equation, the first step in the derivation of a mathematical model of the dual
experiment is to obtain a unified mathematical description, which in our case
are Maxwell's equations. As a by-product we therefore derive a new mathematical
model of photoacoustic tomography based on Maxwell's equations.
  It is well known by now, that without additional assumptions on the medium,
it is not possible to uniquely reconstruct all optical parameters from either
one of these modalities alone. We show that in the combined approach one has
additional information, compared to a single modality, and the inverse problem
of reconstruction of the optical parameters becomes feasible.Comment: 26 pages, 4 table
Schatten class and Berezin transform of quaternionic linear operators

In this paper we introduce the Schatten class of operators and the Berezin
transform of operators in the quaternionic setting. The first topic is of great
importance in operator theory but it is also necessary to study the second one
because we need the notion of trace class operators, which is a particular case
of the Schatten class. Regarding the Berezin transform, we give the general
definition and properties. Then we concentrate on the setting of weighted
Bergman spaces of slice hyperholomorphic functions. Our results are based on
the S-spectrum for quaternionic operators, which is the notion of spectrum that
appears in the quaternionic version of the spectral theorem and in the
quaternionic S-functional calculus
Exact solutions for fractional DDEs via auxiliary equation method coupled with the fractional complex transform

Dynamical behavior of many nonlinear systems can be described by fractional-order equations. This study is devoted to fractional differential–difference equations of rational type. Our focus is on the construction of exact solutions by means of the (G'/G)-expansion method coupled with the so-called fractional complex transform. The solution procedure is elucidated through two generalized time-fractional differential–difference equations of rational type. As a result, three types of discrete solutions emerged: hyperbolic, trigonometric, and rational. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd
Projector operators in clustering

In a recent paper the notion of {\em quantum perceptron} has been introduced
in connection with projection operators. Here we extend this idea, using these
kind of operators to produce a {\em clustering machine}, i.e. a framework which
generates different clusters from a set of input data. Also, we consider what
happens when the orthonormal bases first used in the definition of the
projectors are replaced by frames, and how these can be useful when trying to
connect some noised signal to a given cluster
On the coupling of regularization techniques and the boundary element
  method for a hemivariational inequality modelling a delamination problem

In this paper, we couple regularization techniques of nondifferentiable
optimization with the h-version of the boundary element method (h-BEM) to solve
nonsmooth variational problems arising in contact mechanics. As a model example
we consider the delamination problem. The variational formulation of this
problem leads to a hemivariational inequality (HVI)with a nonsmooth functional
defined on the contact boundary. This problem is first regularized and then
discretized by a h-BEM. We prove convergence of the h-BEM Galerkin solution of
the regularized problem in the energy norm, provide an a-priori error estimate
and give a numerical example.Comment: 22 p., 8 figures. arXiv admin note: substantial text overlap with
  arXiv:1510.0634
Regularity and a priori error analysis of a Ventcel problem in
  polyhedral domains

We consider the regularity of a mixed boundary value problem for the Laplace
operator on a polyhedral domain, where Ventcel boundary conditions are imposed
on one face of the polyhedron and Dirichlet boundary conditions are imposed on
the complement of that face in the boundary. We establish improved regularity
estimates for the trace of the variational solution on the Ventcel face, and
use them to derive a decomposition of the solution into a regular and a
singular part that belongs to suitable weighted Sobolev spaces. This
decomposition, in turn, via interpolation estimates both in the interior as
well as on the Ventcel face, allows us to perform an a priori error analysis
for the Finite Element approximation of the solution on anisotropic graded
meshes. Numerical tests support the theoretical analysis.Comment: 18 pages, 2 figure
Localized Boundary-Domain Singular Integral Equations of Dirichlet
  Problem for Self-adjoint Second Order Strongly Elliptic PDE Systems

The paper deals with the three-dimensional Dirichlet boundary value problem
(BVP) for a second order strongly elliptic self-adjoint system of partial
differential equations in the divergence form with variable coefficients and
develops the integral potential method based on a localized parametrix. Using
Green's representation formula and properties of the localized layer and volume
potentials, we reduce the Dirichlet BVP to a system of localized
boundary-domain integral equations (LBDIEs). The equivalence between the
Dirichlet BVP and the corresponding LBDIE system is studied. We establish that
the obtained localized boundary-domain integral operator belongs to the Boutet
de Monvel algebra. With the help of the Wiener-Hopf factorization method we
investigate corresponding Fredholm properties and prove invertibility of the
localized operator in appropriate Sobolev (Bessel potential) spaces.Comment: 31 pages, Math. Meth. Appl. Sci., 2016, 21
Weighted pseudo-almost periodic functions on time scales with
  applications to cellular neural networks with discrete delays

In this paper, we first propose a concept of weighted pseudo-almost periodic
functions on time scales and study some basic properties of weighted
pseudo-almost periodic functions on time scales. Then, we establish some
results about the existence of weighted pseudo-almost periodic solutions to
linear dynamic equations on time scales. Finally, as an application of our
results, we study the existence and global exponential stability of weighted
pseudo-almost periodic solutions for a class of cellular neural networks with
discrete delays on time scales. The results of this paper are completely new.Comment: 25 page
Factorization of the transition matrix for the general Jacobi system

The Jacobi system on a full-line lattice is considered when it contains
additional weight factors. A factorization formula is derived expressing the
scattering from such a generalized Jacobi system in terms of the scattering
from its fragments. This is done by writing the transition matrix for the
generalized Jacobi system as an ordered matrix product of the transition
matrices corresponding to its fragments. The resulting factorization formula
resembles the factorization formula for the Schr\"odinger equation on the full
line.Comment: 18 page
An $hp$-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear
  Boundary Value Problems

In this paper we develop an $hp$-adaptive procedure for the numerical
solution of general, semilinear elliptic boundary value problems in 1d, with
possible singular perturbations. Our approach combines both a prediction-type
adaptive Newton method and an $hp$-version adaptive finite element
discretization (based on a robust a posteriori residual analysis), thereby
leading to a fully $hp$-adaptive Newton-Galerkin scheme. Numerical experiments
underline the robustness and reliability of the proposed approach for various
examples.Comment: arXiv admin note: text overlap with arXiv:1408.522
Computation Methods for combinatorial sums and Euler type numbers
  related to new families of numbers

The aim of this article is to define some new families of the special
numbers. These numbers provide some further motivation for computation of
combinatorial sums involving binomial coefficients and the Euler kind numbers
of negative order. We can show that these numbers are related to the well-known
numbers and polynomials such as the Stirling numbers of the second kind and the
central factorial numbers, the array polynomials, the rook numbers and
polynomials, the Bernstein basis functions and others. In order to derive our
new identities and relations for these numbers, we use a technique including
the generating functions and functional equations. Finally, we not only give a
computational algorithm for these numbers, but also some numerical values of
these numbers and the Euler numbers of negative order with tables. We also give
some combinatorial interpretations of our new numbers.Comment: arXiv admin note: text overlap with arXiv:1604.0560