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 $\phi$-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 R2\mathbb{R}^2

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 $\epsilon>0$, $V$ is a continuous function verifying some conditions, $h \in (H^{1}(\mathbb{R}^{2}))^{*}$ and $\partial_t F(x,u)$ is a generalized gradient of $F(x,t)$ with respect to $t$ and $F(x,t)=\int_{0}^{t}f(x,s)\,ds$. Assuming that $f$ has an exponential critical growth and a discontinuity point, we have applied Variational Methods for locally Lipschitz functional to get two solutions for $(P)$ when $\epsilon$ 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 $\Omega$ is a bounded domain in $\mathbf{R}^N$, $M$ is a general $C^{1}$ class function, $f$ is a superlinear $C^{1}$ class function with subcritical growth, $\Phi$ is defined for $t\in \mathbf{R}$ by setting $\Phi(t)=\int_0^{|t|}\phi(s)sds$, $\Delta_\Phi$ is the operator $\Delta_\Phi u:=div(\phi(|\nabla u|)\nabla u)$. 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