The Dunford-Pettis Property for some Function Algebras in Several Complex Variables

The Dunford-Pettis property is shown to hold for the uniformalgebra A() and its dual for some standard domains , includingstrongly pseudoconvex bounded domains in Cⁿ, pseudoconvex boundeddomains of finite type in C², and bounded domains in C. Previouslythe result was known for the unit ball and unit polydisc inCⁿ. Techniques used involve Bourgain algebras, Hankel operators,properties of the Bergman kernel, quasi-metrics on the boundary,and -theory.     

Aspects of nucleon Compton scattering

We consider the spin-averaged nucleon forward Compton scattering amplitude in heavy baryon chiral perturbation theory including all terms to order . The chiral prediction for the spin-averaged forward Compton scattering amplitude is in good agreement with the data for photon energies110 MeV. We also evaluate the nucleon electric and magnetic Compton polarizabilities to this order and discuss the uncertainties of the various counter terms entering the chiral expansion of these quantities.     

Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model

For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t ^–(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1.     

On laplace integrals and transfer operators in large dimension: Examples in the nonconvex case

This Letter gives detailed proofs concerning the analysis of the pair correlations for a nonconvex model. Using the transfer matrix approach, the problem is reduced to the analysis of the spectral properties of this transfer operator. Although the problem is similar to the semiclassical study of the Kac operator presented in a paper with M. Brunaud, which was devoted to the study of exp-(v/2) exp h ² exp-(v/2) for h small, new features appear for the model exp-(v/2h) exp h exp-(v/2h). Our principal results concern the splitting of this operator between the two largest eigenvalues. We give an upper and a lower bound for this splitting in the semi-classical regime. As a corollary, we get good control of the decay of the pair correlation. Some of the results were announced in a previous paper. Related WKB constructions will be developed in a later paper.Inspired by papers by M. Kac [15, 16].     

Synthesis, Conformational Studies, X-ray Structures, and Complexation Properties of Semirigid Macrocyclic Phosphonamides

The semirigid phosphonamide ligands 1-5 have been synthesized from the macrocyclic precursors 6-9 by reaction with 1,3-propanediol ditosylate or 1,2-dichloroethane. For the thiophosphoryl compounds 1 and 2, and the phosphoryl derivative 5, the reactions were carried out in biphasic aqueous NaOH solutions. The phosphoryl derivatives 3 and 4 were better obtained from NaH in anhydrous tetrahydrofuran. The conformations of the hosts in solution were deduced from low-temperature NMR and NOE difference experiments. Conformational equilibria between exo and endo forms are observed for the 18-membered macrocycles 1 and 3. The exo conformer predominates in solution for the 21-membered macrocycle 2, whereas 4 exists as rapidly exchanging conformers. The X-ray crystal structures of macrocycles 1, 2, and 5 have been determined as well as the complexes 1.Hg(SCN)(2) and 5.LiNO(3). In the Hg(2+) complex the metal ion is located out of the macrocyclic cavity and is coordinated to the thiophosphoryl unit. In 5.LiNO(3)()()the Li(+) cation is located inside the macrocyclic cavity and is coordinated to a tetrahedral array of oxygen donors. Free energies of complexation (DeltaG degrees ) of the phosphorylated ligands 3-5 with alkali metal and ammonium cations were determined in CHCl(3) saturated with H(2)O by picrate extraction experiments. The -DeltaG degrees values are greatest for 4 complexing K(+) and NH(4)(+) (7.3 and 8.0 kcal/mol, respectively). The relationships between structure and binding are discussed.     

Properties of compact complex manifolds carrying closed positive currents

We show that a compact complex manifold is Moishezon if and only if it carries a strictly positive, integral (1, 1)-current. We then study holomorphic line bundles carrying singular hermitian metrics with semi-positive curvature currents, and we give some cases in which these line bundles are big. We use these cases to provide sufficient conditions for a compact complex manifold to be Moishezon in terms of the existence of certain semi-positive, integral (1,1)-currents. We also show that the intersection number of two closed semi-positive currents of complementary degrees on a compact complex manifold is positive when the intersection of their singular supports is contained in a Stein domain. The first author was partially supported by National Science Foundation Grant Nos. DMS-8922760 and DMS-9204273. The second author was partially supported by National Science Foundation Grant Nos. DMS-9001365 and DMS-9204037.