1,315 research outputs found
Positive solutions of Schr\"odinger equations and fine regularity of boundary points
Given a Lipschitz domain in and a nonnegative
potential in such that is bounded
in we study the fine regularity of boundary points with respect to
the Schr\"odinger operator in . Using potential
theoretic methods, several conditions equivalent to the fine regularity of are established. The main result is a simple (explicit if
is smooth) necessary and sufficient condition involving the size of
for to be finely regular. An essential intermediate result consists in
a majorization of for
positive harmonic in and . Conditions for
almost everywhere regularity in a subset of are also
given as well as an extension of the main results to a notion of fine
-regularity, if , being two potentials, with and a second order elliptic operator.Comment: version 1. 23 pages version 3. 28 pages. Mainly a typo in Theorem 1.1
is correcte
Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas
In recent work we have shown how it is possible to define very precise type
systems for object-oriented languages by abstractly compiling a program into a
Horn formula f. Then type inference amounts to resolving a certain goal w.r.t.
the coinductive (that is, the greatest) Herbrand model of f.
Type systems defined in this way are idealized, since in the most interesting
instantiations both the terms of the coinductive Herbrand universe and goal
derivations cannot be finitely represented. However, sound and quite expressive
approximations can be implemented by considering only regular terms and
derivations. In doing so, it is essential to introduce a proper subtyping
relation formalizing the notion of approximation between types.
In this paper we study a subtyping relation on coinductive terms built on
union and object type constructors. We define an interpretation of types as set
of values induced by a quite intuitive relation of membership of values to
types, and prove that the definition of subtyping is sound w.r.t. subset
inclusion between type interpretations. The proof of soundness has allowed us
to simplify the notion of contractive derivation and to discover that the
previously given definition of subtyping did not cover all possible
representations of the empty type
Os arquivos fotograficos e a agenda da Uniao Europeia : entrevista ao diretor dos Arquivos Nacionais de Malta durante a presidência maltesa da Uniao Europeia
The European Union (EU) has a system of six-month rotation whereby each Member State holds the Presidency of the Council of Ministers, which is the main governing body of the EU. Malta is leading its first term in such a role spanning from 1 January to 30 June 2017. Such an opportunity often stimulates the various sectors and this is the case with the archives domain in Malta during the Presidency. The National Archives of Malta is responsible to organise four high level meetings and support three others. Heading the organisation team is Dr. Charles J. Farrugia, Malta’s national archivist. He is not a new face to the sector and has worked in archives for the last twenty-eight years, eighteen of which leading the national archives. He also has the organisational experience of the highly successful CITRA conference held in 2009. That event welcomed in Malta 251 archivists from 91 countries. But the Presidency is different. It spans over six months and includes a high dose of policy formulation. We decided to interview Dr. Farrugia on what is the relevance of all this activity to the Maltese archives sector, in particular photographic holdings and services.peer-reviewe
A locally quadratic Glimm functional and sharp convergence rate of the Glimm scheme for nonlinear hyperbolic systems
Consider the Cauchy problem for a strictly hyperbolic,
quasilinear system in one space dimension u_t+A(u) u_x=0,\qquad u(0,x)=\bar
u(x), \eqno (1) where is a smooth matrix-valued map, and
the initial data is assumed to have small total variation. We
investigate the rate of convergence of approximate solutions of (1) constructed
by the Glimm scheme, under the assumption that, letting ,
denote the -th eigenvalue and a corresponding eigenvector of
, respectively, for each -th characteristic family the linearly
degenerate manifold is either the whole space, or it is empty, or it consists of
a finite number of smooth, -dimensional, connected, manifolds that are
transversal to the characteristic vector field . We introduce a Glimm type
functional which is the sum of the cubic interaction potential defined in
\cite{sie}, and of a quadratic term that takes into account interactions of
waves of the same family with strength smaller than some fixed threshold
parameter. Relying on an adapted wave tracing method, and on the decrease
amount of such a functional, we obtain the same type of error estimates valid
for Glimm approximate solutions of hyperbolic systems satisfying the classical
Lax assumptions of genuine nonlinearity or linear degeneracy of the
characteristic families.Comment: To appear on Archive for Rational Mechanics and Analysi
Dynamic rotor mode in antiferromagnetic nanoparticles
We present experimental, numerical, and theoretical evidence for a new mode
of antiferromagnetic dynamics in nanoparticles. Elastic neutron scattering
experiments on 8 nm particles of hematite display a loss of diffraction
intensity with temperature, the intensity vanishing around 150 K. However, the
signal from inelastic neutron scattering remains above that temperature,
indicating a magnetic system in constant motion. In addition, the precession
frequency of the inelastic magnetic signal shows an increase above 100 K.
Numerical Langevin simulations of spin dynamics reproduce all measured neutron
data and reveal that thermally activated spin canting gives rise to a new type
of coherent magnetic precession mode. This "rotor" mode can be seen as a
high-temperature version of superparamagnetism and is driven by exchange
interactions between the two magnetic sublattices. The frequency of the rotor
mode behaves in fair agreement with a simple analytical model, based on a high
temperature approximation of the generally accepted Hamiltonian of the system.
The extracted model parameters, as the magnetic interaction and the axial
anisotropy, are in excellent agreement with results from Mossbauer
spectroscopy
Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions
We study the Cauchy problem for general, nonlinear, strictly hyperbolic
systems of partial differential equations in one space variable. First, we
re-visit the construction of the solution to the Riemann problem and introduce
the notion of a nondegenerate (ND) system. This is the optimal condition
guaranteeing, as we show it, that the Riemann problem can be solved with
finitely many waves, only; we establish that the ND condition is generic in the
sense of Baire (for the Whitney topology), so that any system can be approached
by a ND system. Second, we introduce the concept of inner speed variation and
we derive new interaction estimates on wave speeds. Third, we design a wave
front tracking scheme and establish its strong convergence to the entropy
solution of the Cauchy problem; this provides a new existence proof as well as
an approximation algorithm. As an application, we investigate the
time-regularity of the graph solutions introduced by the second author,
and propose a geometric version of our scheme; in turn, the spatial component
of a graph solution can be chosen to be continuous in both time and space,
while its component is continuous in space and has bounded variation in
time.Comment: 74 page
Proof Relevant Corecursive Resolution
Resolution lies at the foundation of both logic programming and type class
context reduction in functional languages. Terminating derivations by
resolution have well-defined inductive meaning, whereas some non-terminating
derivations can be understood coinductively. Cycle detection is a popular
method to capture a small subset of such derivations. We show that in fact
cycle detection is a restricted form of coinductive proof, in which the atomic
formula forming the cycle plays the role of coinductive hypothesis.
This paper introduces a heuristic method for obtaining richer coinductive
hypotheses in the form of Horn formulas. Our approach subsumes cycle detection
and gives coinductive meaning to a larger class of derivations. For this
purpose we extend resolution with Horn formula resolvents and corecursive
evidence generation. We illustrate our method on non-terminating type class
resolution problems.Comment: 23 pages, with appendices in FLOPS 201
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