pinecone/core-2020-05-10-deduplication huggingface dataset:
The Play Operator, the Truncated Variation and the Generalisation of the
  Jordan Decomposition

The play operator minimalizes the total variation on intervals $[0,T], T> 0$,
of functions approximating uniformly given regulated function with given
accuracy and starting from a given point. In this article we link the play
operator with so called truncated variation functionals, introduced recently by
the second-named author, and provide a semi-explicit expression for the play
operator in terms of these functionals. Generalisation for time-dependent
boundaries is also considered. This gives the best possible lower bounds for
the total variation of the outputs of the play operator and its Jordan-like
decomposition
On Integro-Differential Inclusions with Operator-valued Kernels

We study integro-differential inclusions in Hilbert spaces with
operator-valued kernels and give sufficient conditions for the well-posedness.
We show that several types of integro-differential equations and inclusions are
covered by the class of evolutionary inclusions and we therefore give criteria
for the well-posedness within this framework. As an example we apply our
results to the equations of visco-elasticity and to a class of nonlinear
integro-differential inclusions describing Phase Transition phenomena in
materials with memory.Comment: arXiv admin note: substantial text overlap with arXiv:1210.172
On Stability of Hyperbolic Thermoelastic Reissner-Mindlin-Timoshenko
  Plates

In the present article, we consider a thermoelastic plate of
Reissner-Mindlin-Timoshenko type with the hyperbolic heat conduction arising
from Cattaneo's law. In the absense of any additional mechanical dissipations,
the system is often not even strongly stable unless restricted to the
rotationally symmetric case, etc. We present a well-posedness result for the
linear problem under general mixed boundary conditions for the elastic and
thermal parts. For the case of a clamped, thermally isolated plate, we show an
exponential energy decay rate under a full damping for all elastic variables.
Restricting the problem to the rotationally symmetric case, we further prove
that a single frictional damping merely for the bending compoment is sufficient
for exponential stability. To this end, we construct a Lyapunov functional
incorporating the Bogovski\u{i} operator for irrotational vector fields which
we discuss in the appendix.Comment: 27 page
A Mixed ODE-PDE Model for Vehicular Traffic

We present a traffic flow model consisting of a gluing between the
Lighthill-Whitham and Richards macroscopic model with a first order microscopic
follow the leader model. The basic analytical properties of this model are
investigated. Existence and uniqueness are proved, as well as the basic
estimates on the dependence of solutions from the initial data. Moreover,
numerical integrations show some qualitative features of the model, in
particular the transfer of information among regions where the different models
are used
Generalized fractional operators for nonstandard Lagrangians

In this note we study the application of generalized fractional operators to
a particular class of nonstandard Lagrangians. These are typical of dissipative
systems and the corresponding Euler-Lagrange and Hamilton equations are
analyzed. The dependence of the equation of motion on the generalized kernel
permits to obtain a wide range of different configurations of motion. Some
examples are discussed and analyzed.Comment: This is a preprint of a paper whose final and definite form will
  appear in Mathematical Methods in the Applied Sciences, ISSN 0170-4214. Paper
  submitted 31/Jan/2014; revised 23/Apr/2014; accepted for publication
  25/Apr/201
On the geometry of spatial biphoton correlation in spontaneous
  parametric down-conversion

Analytical expressions are derived for the distribution rates of spatial
coincidences in the counting of photons produced by spontaneous parametric down
conversion (SPDC). Gaussian profiles are assumed for the wave function of the
idler and signal light created in type-I SPDC. The distribution rates describe
ellipses on the detection planes that are oriented at different angles
according to the photon coincidences in either horizontal-horizontal,
vertical-vertical, horizontal-vertical or vertical-horizontal position
variables. The predictions are in agreement with the experimental data obtained
with a type-I BBO crystal that is illuminated by a 100 mW violet pump laser as
well as with the results obtained from the geometry defined by the
phase-matching conditions
High-energy and smoothness asymptotic expansion of the scattering
  amplitude for the Dirac equation and applications

We obtain an explicit formula for the diagonal singularities of the
scattering amplitude for the Dirac equation with short-range electromagnetic
potentials. Using this expansion we uniquely reconstruct an electric potential
and magnetic field from the high-energy limit of the scattering amplitude.
Moreover, supposing that the electric potential and magnetic field are
asymptotic sums of homogeneous terms we give the unique reconstruction
procedure for these asymptotics from the scattering amplitude, known for some
energy $E.$ Furthermore, we prove that the set of the averaged scattering
solutions to the Dirac equation is dense in the set of all solutions to the
Dirac equation that are in $L^{2}\left( \Omega\right) ,$ where $\Omega$ is any
connected bounded open set in $\mathbb{R}^{3}$ with smooth boundary, and we
show that if we know an electric potential and a magnetic field for
$\mathbb{R}^{3}\setminus\Omega$, then the scattering amplitude, given for some
energy $E$, uniquely determines these electric potential and magnetic field
everywhere in $\mathbb{R}^{3}$. Combining this uniqueness result with the
reconstruction procedure for the asymptotics of the electric potential and the
magnetic field we show that the scattering amplitude, known for some $E$,
uniquely determines a electric potential and a magnetic field, that are
asymptotic sums of homogeneous terms, which converges to the electric potential
and the magnetic field, respectively. Moreover, we discuss the symmetries of
the kernel of the scattering matrix, which follow from the parity,
charge-conjugation and time-reversal transformations for the Dirac operator
Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data

We apply the trial method for the solution of Bernoulli’s free boundary problem when the Dirichlet boundary condition is imposed for the solution of the underlying Laplace equation and the free boundary is updated according to the Neumann boundary condition. The Dirichlet boundary value problem for the Laplacian is solved by an exponentially convergent boundary element method. The update rule for the free boundary is derived from the linearization of the Neumann data around the actual free boundary. With the help of shape sensitivity analysis and Banach’s fixed-point theorem, we shed light on the convergence of the respective trial method. Especially, we derive a stabilized version of this trial method. Numerical examples validate the theoretical findings
Traffic flow optimization on roundabouts

International audienceThe aim of this article is to propose an optimization strategy for traffic flow on roundabouts using a macroscopic approach. The roundabout is modeled as a sequence of 2 × 2 junctions with one main-lane and secondary incoming and outgoing roads. We consider two cost functionals: the total travel time and the total waiting time, which give an estimate of the time spent by drivers on the network section. These cost functionals are minimized with respect to the right of way parameter of the incoming roads. For each cost functional, the analytical expression is given for each junction. We then solve numerically the optimization problem and show some numerical results
Numerical implementation for reconstruction of inhomogeneous
  conductivities via Generalized Polarization Tensors

This paper deals with numerical methods for reconstruction of inhomogeneous
conductivities. We use the concept of Generalized Polarization Tensors, which
were introduced in [3], to do reconstruction. Basic resolution and stability
analysis are presented. Least square norm methods with respect to Generalized
Polarization Tensors are used for reconstruction of conductivities. Finally,
reconstruction of three different types of conductivities in the plane is
demonstrated.Comment: 23pages, 8 figures; 3 big figures are not listed due to size limit
Understanding Chicken Walks on n x n Grid: Hamiltonian Paths, Discrete
  Dynamics and Rectifiable Paths

Understanding animal movements and modelling the routes they travel can be
essential in studies of pathogen transmission dynamics. Pathogen biology is
also of crucial importance, defining the manner in which infectious agents are
transmitted. In this article we investigate animal movement with relevance to
pathogen transmission by physical rather than airborne contact, using the
domestic chicken and its protozoan parasite Eimeria as an example. We have
obtained a configuration for the maximum possible distance that a chicken can
walk through straight and non-overlapping paths (defined in this paper) on
square grid graphs. We have obtained preliminary results for such walks which
can be practically adopted and tested as a foundation to improve understanding
of non-airborne pathogen transmission. Linking individual non-overlapping walks
within a grid-delineated area can be used to support modeling of the frequently
repetitive, overlapping walks characteristic of the domestic chicken, providing
a framework to model faecal deposition and subsequent parasite dissemination by
faecal/host contact.We also pose an open problem on multiple walks on finite
grid graphs. These results grew from biological insights and have potential
applications. Keywords: Spread of bird diseases, Eimeria, Maximum walks,
longest paths, NP-Complete. MSC: 92A17, 68Q1
Seasonality effects on Dengue: basic reproduction number, sensitivity
  analysis and optimal control

Dengue is a vector-borne disease transmitted from an infected human to an
Aedes mosquito, during a blood-meal. Dengue is still a major public health
problem. A model for the disease transmission is presented, composed by human
and mosquitoes compartments. The aim is to simulate the effects of seasonality,
on the vectorial capacity and, consequently, on the disease development. Using
entomological information about the mosquito behavior under different
temperatures and rainfall, simulations are carried out and the repercussions
analyzed. The basic reproduction number of the model is given, as well as a
sensitivity analysis of model's parameters. Finally, an optimal control problem
is proposed and solved, illustrating the difficulty of making a trade-off
between reduction of infected individuals and costs with insecticide.Comment: Several typos detected by the authors while reading the proofs were
  corrected. This is a preprint of a paper whose final and definite form is
  published in 'Mathematical Methods in the Applied Sciences', ISSN 0170-4214
  (see http://dx.doi.org/10.1002/mma.3319). Paper submitted 22/July/2014;
  revised 11/Sept/2014; accepted for publication 12/Sept/201
Existence and stability of nonconstant positive steady states of
  morphogenesis models

In this paper, We study an one--dimensional morphogenesis model considered by
C. Stinner et al. in (Math. Meth. Appl. Sci. 2012,35 (445-465). Under
homogeneous boundary conditions, we prove the existence of nonconstant positive
steady states through local bifurcation theories. We also rigorously study the
stability of the nonconstant solutions when the sensitivity function are chosen
to be linear and logarithmic function respectively. Finally, we present
numerical solutions to illustrate the formation of stable spatially
inhomogeneous patterns. Our numerical simulations suggests that this model can
develop very complicated and interesting structures even over one--dimensional
finite domains
The Allen-Cahn equation with dynamic boundary conditions and mass
  constraints

The Allen-Cahn equation, coupled with dynamic boundary conditions, has
recently received a good deal of attention. The new issue of this paper is the
setting of a rather general mass constraint which may involve either the
solution inside the domain or its trace on the boundary. The system of
nonlinear partial differential equations can be formulated as variational
inequality. The presence of the constraint in the evolution process leads to
additional terms in the equation and the boundary condition containing a
suitable Lagrange multiplier. A well-posedness result is proved for the related
initial value problem.Comment: Key words: Allen-Cahn equation, dynamic boundary condition, mass
  constraint, variational inequality, Lagrange multiplie
Zero-Hopf bifurcation in the Fitzhugh-Nagumo system

Agraïments: The first author is supported by the FAPESP-BRAZIL grants 2010/18015-6 and 2012/05635-1. The third author is partially supported by Dirección de Investigación DIUBB 120408 4/R.We characterize the values of the parameters for which a zero–Hopf equilibrium point takes place at the singular points, namely, O (the origin), P+ and P− in the FitzHugh-Nagumo system. Thus we find two 2–parameter families of the FitzHugh-Nagumo system for which the equilibrium point at the origin is a zero-Hopf equilibrium. For these two families we prove the existence of a periodic orbit bifurcating from the zero–Hopf equilibrium point O. We prove that exist three 2–parameter families of the FitzHughNagumo system for which the equilibrium point at P+ and P− is a zero-Hopf equilibrium point. For one of these families we prove the existence of 1, or 2, or 3 periodic orbits borning at P+ and P−
Bilaplacian problems with a sign-changing coefficient

International audienceWe investigate the properties of the operator ∆(σ∆·) : H^2_0 (Ω) → H^{−2}(Ω), where σ is a given parameter whose sign can change on the bounded domain Ω. Here, H^2_0 (Ω) denotes the subspace of H^2(Ω) made of the functions v such that v = ν · ∇v = 0 on ∂Ω. The study of this problem arises when one is interested in some configurations of the Interior Transmission Eigenvalue Problem. We prove that ∆(σ∆·) : H^2_0 (Ω) → H^{−2}(Ω) is a Fredholm operator of index zero as soon as σ ∈ L^∞(Ω), with σ^{−1}∈ L^∞(Ω), is such that σ remains uniformly positive (or uniformly negative) in a neighbourhood of ∂Ω. We also study configurations where σ changes sign on ∂Ω and we prove that Fredholm property can be lost for such situations. In the process, we examine in details the features of a simpler problem where the boundary condition ν · ∇v = 0 is replaced by σ∆v = 0 on ∂Ω
Simultaneous quasi-optimal convergence in FEM-BEM coupling

We consider the symmetric FEM-BEM coupling that connects two linear elliptic
second order partial differential equations posed in a bounded domain $\Omega$
and its complement, where the exterior problem is restated by an integral
equation on the coupling boundary $\Gamma=\partial\Omega$. We assume that the
corresponding transmission problem admits a shift theorem for data in
$H^{-1+s}$, $s \in [-1,-1+s_0]$, $s_0 > 1/2$. We analyze the discretization by
piecewise polynomials of degree $k$ for the domain variable and piecewise
polynomials of degree $k-1$ for the flux variable on the coupling boundary.
Given sufficient regularity we show that (up to logarithmic factors) the
optimal convergence $O(h^{k+1/2})$ in the $H^{-1/2}(\Gamma)$-norm is obtained
for the flux variable, while classical arguments by C\'ea-type quasi-optimality
and standard approximation results provide only $O(h^k)$ for the overall error
in the natural product norm on $H^1(\Omega)\times H^{-1/2}(\Gamma)$
Canonical systems in $\mathbb{R}^2$ with periodic potentials and
  vanishing instability intervals

Canonical systems in $\mathbb{R}^2$ with absolutely continuous real symmetric
$\pi$-periodic potentials matrices are considered. A through analysis of the
discriminant is given along with the indexing and interlacing of the
eigenvalues of the periodic, anti-periodic and Dirichlet-type boundary value
problems on $[0,\pi]$. The periodic and anti-periodic eigenvalues are
characterized in terms of Dirichlet type eigenvalues. It is shown that all
instability intervals vanish if and only if the potential is the product of an
absolutely continuous real valued function with the identity matrix
Exponential decay in nonsimple thermoelasticity of type III

This is the peer reviewed version of the following article: Magaña, A., and Quintanilla, R. (2016) Exponential decay in nonsimple thermoelasticity of type III. Math. Meth. Appl. Sci., 39: 225–235. doi: 10.1002/mma.3472, which has been published in final form at http://dx.doi.org/10.1002/mma.3472. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-ArchivingThis paper deals with the model proposed for nonsimple materials\ud
with heat conduction of type III.We analyze  rst the general system of equations, determine the behavior of its solutions with respect to the time and show that the semigroup associated with the system is not analytic. Two limiting cases of the model are studied later.Peer ReviewedPostprint (author's final draft
Nonsymmetric and Symmetric Fractional Calculi on Arbitrary Nonempty
  Closed Sets

We introduce a nabla, a delta, and a symmetric fractional calculus on
arbitrary nonempty closed subsets of the real numbers. These fractional calculi
provide a study of differentiation and integration of noninteger order on
discrete, continuous, and hybrid settings. Main properties of the new
fractional operators are investigated, and some fundamental results presented,
illustrating the interplay between discrete and continuous behaviors.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 05/March/2014; revised 24/Feb/2015; accepted 25/Feb/2015. arXiv
  admin note: text overlap with arXiv:1405.281
A new approach toward boundedness in a two-dimensional parabolic
  chemotaxis system with singular sensitivity

We consider the parabolic chemotaxis model \[ u_t=\Delta u - \chi
\nabla\cdot(\frac uv \nabla v), \qquad\qquad v_t=\Delta v - v + u\] in a
smooth, bounded, convex two-dimensional domain and show global existence and
boundedness of solutions for $\chi\in(0,\chi_0)$ for some $\chi_0>1$, thereby
proving that the value $\chi=1$ is not critical in this regard. Our main tool
is consideration of the energy functional \[ \mathcal{F}_{a,b}(u,v)=\int_\Omega
u\ln u - a \int_\Omega u\ln v + b \int_\Omega |\nabla \sqrt{v}|^2 \] for $a>0$,
$b\geq 0$, where using nonzero values of $b$ appears to be new in this context.Comment: 11 page
Advances in mosquito dynamics modeling

It is preliminarily known that Aedes mosquitoes are very close to humans and
their dwellings, also give rises to a broad spectrum of diseases: dengue,
yellow fever, chikungunya. In this paper, we explore a multi-age-class model
for mosquito population secondarily classified into indoor-outdoor dynamics. We
accentuate a novel design for the model in which periodicity of the affecting
time-varying environmental condition is taken into account. Application of the
optimal control with collocated measure as apposed to the widely-used
prototypic smooth time-continuous measure is also considered. Using two
approaches: least-square and maximum likelihood, we estimate several involving
undetermined parameters. We analyze the model enforceability to biological
point of view such as existence, uniqueness, positivity and boundedness of
solution trajectory, also existence and stability of (non)trivial periodic
solution(s) by means of the basic mosquito offspring number. Some numerical
tests are brought along at the rest of the paper as a compact realistic
visualization of the model
A conformal mapping algorithm for the Bernoulli free boundary value problem

International audienceWe propose a new numerical method for the solution of Bernoulli's free boundary valueproblem for harmonic functions in a doubly connected domain $D$ in $\real^2$ where an  unknown free boundary $\Gamma_0$ is determined by prescribed Cauchy data on $\Gamma_0$  in addition to a  Dirichlet condition  on the known boundary $\Gamma_1$.Our main idea is to involve the conformal mapping methodas proposed and analyzed by Akduman, Haddar and Kress~\cite{AkKr,HaKr05}for the solution of a related inverse boundary value problem. For this we  interpret  the free boundary $\Gamma_0$as the unknown boundary in the inverse problem  to construct $\Gamma_0$  from the Dirichlet condition on $\Gamma_0$ and  Cauchy data on the known boundary $\Gamma_1$. Our method for the Bernoulli problem iterates  on the missing normal derivative on $\Gamma_1$by alternating between the application of the conformal mapping method for the inverse problemand solving a mixed Dirichlet--Neumann boundary value  problem in $D$. We present the mathematicalfoundations of our algorithm and prove a convergence result. Some numerical examples will serve as proof of concept of our approach
Well-posedness and exact controllability of the mass balance equations
  for an extrusion process

In this paper, we study the well-posedness and exact controllability of a
physical model for a food extrusion process in the isothermal case. The model
expresses the mass balance in the extruder chamber and consists of a hyperbolic
Partial Differential Equation (PDE) and a nonlinear Ordinary Differential
Equation (ODE) whose dynamics describes the evolution of a moving interface. By
suitable change of coordinates and fixed point arguments, we prove the
existence, uniqueness and regularity of the solution, and finally the exact
controllability of the coupled system.Comment: 19pages, 3figures. arXiv admin note: substantial text overlap with
  arXiv:1404.337
(p,q)-Generalization of Szasz-Mirakyan Operators

In this paper, we introduce new modifications of Szasz-Mirakyan operators
based on (p,q)-integers. We first give a recurrence relation for the moments of
new operators and present explicit formula for the moments and central moments
up to order 4. Some approximation properties of new operators are explored: the
uniform convergence over bounded and unbounded intervals is established, direct
approximation properties of the operators in terms of the moduli of smoothness
is obtained and Voronovskaya theorem is presented. For the particular case p=1,
the previous results for q-Szasz-Mirakyan operators are captured
Monogenic functions in the biharmonic boundary value problem

We consider a commutative algebra $\mathbb{B}$ over the field of complex
numbers with a basis $\{e_1,e_2\}$ satisfying the conditions
$(e_1^2+e_2^2)^2=0$, $e_1^2+e_2^2\ne 0$. Let $D$ be a bounded domain in the
Cartesian plane $xOy$ and $D_{\zeta}=\{xe_1+ye_2 : (x,y)\in D\}$. Components of
every monogenic function $\Phi(xe_1+ye_2)=U_{1}(x,y)\,e_1+U_{2}(x,y)\,ie_1+
U_{3}(x,y)\,e_2+U_{4}(x,y)\,ie_2$ having the classic derivative in $D_{\zeta}$
are biharmonic functions in $D$, i.e. $\Delta^{2}U_{j}(x,y)=0$ for $j=1,2,3,4$.
We consider a Schwarz-type boundary value problem for monogenic functions in a
simply connected domain $D_{\zeta}$. This problem is associated with the
following biharmonic problem: to find a biharmonic function $V(x,y)$ in the
domain $D$ when boundary values of its partial derivatives $\partial V/\partial
x$, $\partial V/\partial y$ are given on the boundary $\partial D$. Using a
hypercomplex analog of the Cauchy type integral, we reduce the mentioned
Schwarz-type boundary value problem to a system of integral equations on the
real axes and establish sufficient conditions under which this system has the
Fredholm property.Comment: 30 page