On the mean-field Ising model in a random external field

We use a method developed by van Hemmen to obtain the free energy of the mean-field Ising model in a random external magnetic field. Some results of previous mean-field calculations are confirmed and generalized. The tricritical point in the global phase diagram is discussed in detail. We also consider different probability distributions of the random fields and provide some proofs regarding the conditions for the existence of a tricritical point.     

A Look at BMOϕ(ω) through Carleson Measures

As Fefferman and Stein showed, there is a tight connection between Carleson measures and BMO functions. In this work we extend this type of results to the more general scope of the BMO_ϕ(ω) spaces. As a byproduct a weighted version of the Triebel-Lizorkin space is introduced, which turns out to be isomorphic to BMO(ω) as in the unweighted case.     

Limit cycles and update digraphs in Boolean networks

Boolean networks have been used as models of gene regulation and other biological networks, as well as for other kinds of distributed dynamical systems. One key element in these models is the update schedule, which indicates the order in which states have to be updated. In Salinas (2008) [22] and Aracena et al. (2009) [1], equivalence classes of deterministic update schedules according to the labeled digraph associated to a Boolean network (update digraph) were defined and it was proved that two schedules in the same class yield the same dynamical behavior. In this paper, we study the relations between the update digraphs and the preservation of limit cycles of Boolean networks iterated under non-equivalent update schedules. We show that the related problems lie in the class of NP-hard problems and we prove that the information provided by the update digraphs is not sufficient to determine whether two Boolean networks share limit cycles or not. Besides, we exhibit a polynomial algorithm that works as a necessary condition for two Boolean networks to share limit cycles. Finally, we construct some update schedule classes whose elements share a given limit cycle under certain conditions on the frozen nodes of it.     

Wavelet expansions forBMOρ (w)‐functions

We give necessary and sufficient conditions on the wavelet coefficients of a function for being a member of some BMO_φ (w) space. We achieve this characterization for a wide variety of wavelet systems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Commutators of singular integrals on spaces of homogeneous type

In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on L ^p (w) when w belongs to the Muckenhoupt’s class A _p , p > 1. In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature.     

First highly regio- and diastereoselective [3+2] cycloaddition of chiral nonracemic Fischer carbene complexes with azomethine ylides: an enantioselective synthesis of (+)-rolipram

A new procedure for the synthesis of 1,3,4-trisubstituted and 1,4-disubstituted pyrrolidin-2-one derivatives in an enantioselective fashion is reported. The 1,3-dipolar cycloaddition of (+/-)-menthol and (-)-8-phenylmenthol derived Fischer alkoxy alkenyl carbene complexes with in situ generated functionalized azomethine ylides gives the corresponding cycloadducts as chelated tetracarbonyl Fischer carbene complexes. Only one regioisomer is detected in all cases, and the diastereoselectivity of the reaction is very high when (-)-8-phenylmenthol derived carbenes are employed. Oxidation and further transformation of the cycloadducts provide an easy access to pyrrolidin-2-ones. The anti-inflammatory and antidepressant drug (+)-Rolipram is readily prepared in four steps in a 20% overall yield by taking advantage of this newly developed methodology.