9,137 research outputs found
Multiplicity of solutions for a class of quasilinear equations involving critical Orlicz-Sobolev nonlinear term
In this work, we study the existence and multiplicity of solutions for a
class of problems involving the -Laplacian operator in a bounded domain,
where the nonlinearity has a critical growth. The main tool used is the
variational method combined with the genus theory for even functionals
The Value Iteration Algorithm is Not Strongly Polynomial for Discounted Dynamic Programming
This note provides a simple example demonstrating that, if exact computations
are allowed, the number of iterations required for the value iteration
algorithm to find an optimal policy for discounted dynamic programming problems
may grow arbitrarily quickly with the size of the problem. In particular, the
number of iterations can be exponential in the number of actions. Thus, unlike
policy iterations, the value iteration algorithm is not strongly polynomial for
discounted dynamic programming
On the Reduction of Total-Cost and Average-Cost MDPs to Discounted MDPs
This paper provides conditions under which total-cost and average-cost Markov
decision processes (MDPs) can be reduced to discounted ones. Results are given
for transient total-cost MDPs with tran- sition rates whose values may be
greater than one, as well as for average-cost MDPs with transition
probabilities satisfying the condition that there is a state such that the
expected time to reach it is uniformly bounded for all initial states and
stationary policies. In particular, these reductions imply sufficient
conditions for the validity of optimality equations and the existence of
stationary optimal poli- cies for MDPs with undiscounted total cost and
average-cost criteria. When the state and action sets are finite, these
reductions lead to linear programming formulations and complexity estimates for
MDPs under the aforementioned criteria
Monodromy of Inhomogeneous Picard-Fuchs Equations
We study low-degree curves on one-parameter Calabi-Yau hypersurfaces, and
their contribution to the space-time superpotential in a superstring
compactification with D-branes. We identify all lines that are invariant under
at least one permutation of the homogeneous variables, and calculate the
inhomogeneous Picard-Fuchs equation. The irrational large volume expansions
satisfy the recently discovered algebraic integrality. The bulk of our work is
a careful study of the topological integrality of monodromy under navigation
around the complex structure moduli space. This is a powerful method to recover
the single undetermined integration constant that is itself also of arithmetic
significance. The examples feature a variety of residue fields, both abelian
and non-abelian extensions of the rationals, thereby providing a glimpse of the
arithmetic D-brane landscape.Comment: 35 page
Reduction of total-cost and average-cost MDPs with weakly continuous transition probabilities to discounted MDPs
This note describes sufficient conditions under which total-cost and
average-cost Markov decision processes (MDPs) with general state and action
spaces, and with weakly continuous transition probabilities, can be reduced to
discounted MDPs. For undiscounted problems, these reductions imply the validity
of optimality equations and the existence of stationary optimal policies. The
reductions also provide methods for computing optimal policies. The results are
applied to a capacitated inventory control problem with fixed costs and lost
sales
The Spin of the Proton
The twenty years since the announcement of the proton spin crisis by the
European Muon Collaboration has seen tremendous progress in our knowledge of
the distribution of spin within the proton. The problem is reviewed, beginning
with the original data and the suggestion that polarized gluons may play a
crucial role in resolving the problem through the U(1) axial anomaly. The
discussion continues to the present day where not only have strong limits have
been placed on the amount of polarized glue in the proton but the experimental
determination of the spin content has become much more precise. It is now clear
that the origin of the discrepancy between experiment and the naive expectation
of the fraction of spin carried by the quarks and anti-quarks in the proton
lies in the non-perturabtive structure of the proton. We explain how the
features expected in a modern, relativistic and chirally symmetric description
of nucleon structure naturally explain the current data.Comment: Invited lecture presented at Erice: International School of Nuclear
Physics, Course 29, Quarks in Hadrons and Nuclei (September 16-24, 2007
On a nonlocal multivalued problem in an Orlicz-Sobolev space via Krasnoselskii's genus
This paper is concerned with the multiplicity of nontrivial solutions in an
Orlicz-Sobolev space for a nonlocal problem involving N-functions and theory of
locally Lispchitz continuous functionals.Comment: arXiv admin note: substantial text overlap with arXiv:1411.375
Multivalued Elliptic Equation with exponential critical growth in
In this work we study the existence of nontrivial solution for the following
class of multivalued elliptic problems -\Delta u+V(x)u-\epsilon h(x)\in
\partial_t F(x,u) \quad \text{in} \quad \mathbb{R}^2, \eqno{(P)} where
, is a continuous function verifying some conditions, and is a generalized gradient
of with respect to and . Assuming
that has an exponential critical growth and a discontinuity point, we have
applied Variational Methods for locally Lipschitz functional to get two
solutions for when is small enough
Existence of least energy nodal solution with two nodal domains for a generalized Kirchhoff problem in an Orlicz Sobolev space
We show the existence of a nodal solution with two nodal domains for a
generalized Kirchhoff equation of the type -M\left(\displaystyle\int_\Omega
\Phi(|\nabla u|)dx\right)\Delta_\Phi u = f(u) \ \ \mbox{in} \ \ \Omega, \ \ u=0
\ \ \mbox{on} \ \ \partial\Omega, where is a bounded domain in
, is a general class function, is a superlinear
class function with subcritical growth, is defined for by setting , is the
operator . The proof is based on
a minimization argument and a quantitative deformation lemma
Gep/Gmp for bound protons: first results for 16O with the recoil polarization technique
The first (e,e'p) polarization transfer measurements on a nucleus heavier
than deuterium have been carried out at Jefferson Laboratory. Transverse and
longitudinal components of the polarization of protons ejected in the reaction
16O(e,e'p) were measured in quasielastic perpendicular kinematics at a Q^2 of
0.8 (GeV/c)^2. The data are in good agreement with state of the art
calculations, but do not exclude possible changes in the ratio of the electric
to magnetic form factors of the nucleon in the nuclear medium at the level of
recent theoretical predictions.Comment: 5 pages, 2 figures, uses revtex.st
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