Weighted inequalities for commutators of Schr\"odinger-Riesz transforms

In this work we obtain weighted $L^p$, $1<p<\infty$, and weak $L\log L$ estimates for the commutator of the Riesz transforms associated to a Schr\"odinger operator -\lap+V, where $V$ satisfies some reverse H\"older inequality. The classes of weights as well as the classes of symbols are larger than $A_p$ and $BMO$ corresponding to the classical Riesz transforms

Replica-symmetric solutions of a dilute Ising ferromagnet in a random field

We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the replica-symmetric context, the problem is reduced to the analysis of the solutions of a nonlinear integral equation. At zero temperature, and under some restrictions on the form of the random fields, we are able to perform a detailed analysis of stability of the replica-symmetric solutions. In contrast to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a uniform field, the paramagnetic solution is fully stable in a sufficiently large random field

The fluctuation-dissipation theorem and the linear Glauber model

We obtain exact expressions for the two-time autocorrelation and response functions of the $d$-dimensional linear Glauber model. Although this linear model does not obey detailed balance in dimensions $d\geq 2$, we show that the usual form of the fluctuation-dissipation ratio still holds in the stationary regime. In the transient regime, we show the occurence of aging, with a special limit of the fluctuation-dissipation ratio, $X_{\infty}=1/2$, for a quench at the critical point.Comment: Accepted for publication (Physical Review E

Weighted inequalities for negative powers of Schrödinger operators

AbstractIn this article we obtain boundedness of the operator (−Δ+V)−α/2 from Lp,∞(w) into weighted bounded mean oscillation type spaces BMOLβ(w) under appropriate conditions on the weight w. We also show that these weighted spaces also have a point-wise description for 0<β<1. Finally, we study the behaviour of the operator (−Δ+V)−α/2 when acting on BMOLβ(w)

Relations between weighted Orlicz and BMOϕBMO_\phi spaces through fractional integrals

summary:We characterize the class of weights, invariant under dilations, for which a modified fractional integral operator $I_\alpha$ maps weak weighted Orlicz$-\phi$ spaces into appropriate weighted versions of the spaces $BMO_\psi$, where $\psi (t)=t^{\alpha /n}\phi ^{-1}(1/t)$. This generalizes known results about boundedness of $I_\alpha$ from weak $L^p$ into Lipschitz spaces for $p>n/\alpha$ and from weak $L^{n/\alpha }$ into $BMO$. It turns out that the class of weights corresponding to $I_\alpha$ acting on weak$-L_\phi$ for $\phi$ of lower type equal or greater than $n/\alpha$, is the same as the one solving the problem for weak$-L^p$ with $p$ the lower index of Orlicz-Maligranda of $\phi$, namely $\omega ^{p'}$ belongs to the $A_1$ class of Muckenhoupt

Compressible Sherrington-Kirkpatrick spin-glass model

We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressure-temperature phase diagram, and obtain expressions for the critical boundaries between the disordered and the ordered (spin-glass and ferromagnetic) phases. The second-order para-ferromagnetic border ends at a tricritical point, beyond which the transition becomes discontinuous. We use these results to make contact with the temperature-concentration phase diagrams of mixtures of hydrogen-bonded crystals.Comment: 8 pages, 2 figures; added references, added conten

Desarrollo estratégico: cómo abrir la 'caja negra' del planeamiento estratégico

The strategy-making process, for Henry Mintzberg and others, is seen as an impenetrable 'black box' for planners, around which they work, providing some of its inputs, programming its outputs as well as encouraging strategic thinking in general. The challenge is how to open this 'black box' to generate creative and doable strategies, to evaluate them and choose the most favorable for the company.   The Strategic Decisions Group (SDG) process allows to generate alternative strategies; which are evaluated given the relevant information and the c/early established decision criteria to determine the potential value and risk associated with each strategy. This process is efficient and well balanced; it does not waste time and resources in issues that are not crucial to the decisions that define the strategy, concluded in a timing manner and tend to 100% of quality on the content of the decision, and assure a commitment for its implementation. The success of this systematic process, with intermediate reviews, hinges on two main factors: having the right people involved and ensuring deliverables associated with the elements of the decision quality at the end of each step.El proceso de desarrollo de estrategias, para Henry Mintzberg y muchos otros, es vista como una 'caja negra' impenetrable para los planificadores, alrededor de la cual trabajan, brindando algunos de sus inputs, programando sus outputs así como promoviendo el pensamiento estratégico en general. El desafío es cómo abrir esta 'caja negra' para generar estrategias creativas y viables, para luego evaluarlas y escoger la más favorable para la empresa. El proceso de Strategic Decisions Group (SDG) permite generar estrategias alternativas; y a la luz de la información relevante y de los criterios de decisión claramente establecidos, las evalúa para determinar el valor potencial y el riesgo asociados a cada estrategia. Este proceso es eficiente y bien balanceado, no desperdicia tiempo ni recursos en asuntos que no son cruciales a las decisiones que conforman las estrategias, concluye de manera oportuna y tiende sistemáticamente hacia el 100% de calidad en el contenido de la decisión, y asegura que se logre el compromiso organizacional para su implementación. El éxito de este proceso sistemático, con revisiones intermedias, se basa en dos factores fundamentales: involucrar a las personas correctas y producir, en cada paso, resultados concretos asociados a los elementos de calidad decisional