Dynamical lower bounds for 1D Dirac operators

Quantum dynamical lower bounds for continuous and discrete one-dimensional Dirac operators are established in terms of transfer matrices. Then such results are applied to various models, including the Bernoulli–Dirac one and, in contrast to the discrete case, critical energies are also found for the continuous Dirac case with positive mass. R. A. Prado was supported by FAPESP (Brazil). C. R. de Oliveira was partially supported by CNPq (Brazil).     

Degenerate resonances and branching of periodic orbits

In this paper we establish results on the existence of Lyapunov families of periodic orbits of reversible systems in around an equilibrium that presents a 0:1:1-resonance. The main proofs are based on a combined use of normal form theory, Lyapunov–Schmidt reduction and elements of symbolic computation. This work was supported by France–Brazil cooperation.     

The Bipolaron in the Strong Coupling Limit

The bipolaron are two electrons coupled to the elastic deformations of an ionic crystal. We study this system in the Fr?hlich approximation. If the Coulomb repulsion dominates, the lowest energy states are two well separated polarons. Otherwise the electrons form a bound pair. We prove the validity of the Pekar–Tomasevich energy functional in the strong coupling limit, yielding estimates on the coupling parameters for which the binding energy is strictly positive. Under the condition of a strictly positive binding energy we prove the existence of a ground state at fixed total momentum P, provided P is not too large. Tadahiro Miyao: This work was supported by Japan Society for the Promotion of Science (JSPS). Permanent address: The graduate school of natural science and technology, Okayama university, Okayama 700-8530, Japan. Submitted: December 14, 2006. Accepted: March 20, 2007.     

Examples of ill-behaved central paths in convex optimization

This paper presents some examples of ill-behaved central paths in convex optimization. Some contain infinitely many fixed length central segments; others manifest oscillations with infinite variation. These central paths can be encountered even for infinitely differentiable data.Mathematics Subject Classification (2000): 90C25, 90C51Research partially supported by CAPES, Brazil.Research partially supported by CAPES and CNPq, Brazil.     

Tits alternative for 3-manifold groups

Let M be an irreducible, orientable, closed 3-manifold with fundamental group G. We show that if the pro-p completion of G is infinite then G is either soluble-by-finite or contains a free subgroup of rank 2. Both authors are partially supported by “Bolsa de produtividade de pesquisa” from CNPq, Brazil. Received: 16 February 2006     

Exploring the complexity boundary between coloring and?list-coloring

Many classes of graphs where the vertex coloring problem is polynomially solvable are known, the most prominent being the class of perfect graphs. However, the list-coloring problem is NP-complete for many subclasses of perfect graphs. In this work we explore the complexity boundary between vertex coloring and list-coloring on such subclasses of perfect graphs where the former admits polynomial-time algorithms but the latter is NP-complete. Our goal is to analyze the computational complexity of coloring problems lying “between” (from a computational complexity viewpoint) these two problems: precoloring extension, μ-coloring, and (γ,μ)-coloring. Flavia Bonomo partially supported by UBACyT Grants X606 and X069 (Argentina), and CNPq under PROSUL project Proc. 490333/2004-4 (Brazil). Guillermo Durán partially supported by FONDECyT Grant 1080286 and Millennium Science Institute “Complex Engineering Systems” (Chile), and CNPq under PROSUL project Proc. 490333/2004-4 (Brazil). Javier Marenco partially supported by UBACyT Grant X069 (Argentina), and CNPq under PROSUL project Proc. 490333/2004-4 (Brazil).     

The Schur Transformation for Generalized Nevanlinna Functions: Interpolation and Self-Adjoint Operator Realizations

The Schur transformation for generalized Nevanlinna functions has been defined and applied in [2]. In this paper we discuss its relation to a basic interpolation problem and study its effect on the minimal self-adjoint operator (or relation) realization of a generalized Nevanlinna function. D. Alpay acknowledges with thanks the Earl Katz family for endowing the chair which supported this research and the Netherlands Organization for Scientific Research, NWO (grant B 61-524). The research of A. Dijksma and H. Langer was partly supported by the Center for Advanced Studies in Mathematics, CASM, of the Department of Mathematics of Ben-Gurion University, that of H. Langer also by the Austrian Science Fund, Project P15540-N05. Received: September 25, 2006. Accepted: October 11, 2006.     

Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh [Ka]. The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author was supported by NSERC and FQRNT. Received: April 2006 Revision: October 2006 Accepted: October 2006     

A nonlinear programming algorithm based on non-coercive penalty functions

 We consider first the differentiable nonlinear programming problem and study the asymptotic behavior of methods based on a family of penalty functions that approximate asymptotically the usual exact penalty function. We associate two parameters to these functions: one is used to control the slope and the other controls the deviation from the exact penalty. We propose a method that does not change the slope for feasible iterates and show that for problems satisfying the Mangasarian-Fromovitz constraint qualification all iterates will remain feasible after a finite number of iterations. The same results are obtained for non-smooth convex problems under a Slater qualification condition. Received: September 2000 / Accepted: June 2002 Published online: March 21, 2003 Research partially supported by CAPES, Brazil Research partially supported by CNPq, Brazil, and CONICIT, Venezuela. Mathematics Subject Classification (1991): 20E28, 20G40, 20C20     

Invariant surfaces of the Heisenberg groups

Summary We fix a left-invariant metric g in the eisenberg group,H ₃, and give a complete classification of the constant mean curvature surfaces (including minimal) which are invariant with respect to 1-dimensional closed subgroups of the connected component of the isometry group of (H ₃, g). In addition to finding new examples, we organize in a common framework results that have appeared in various forms in the literature, by the systematic use of Riemannian transformation groups. Using the existence of a family of spherical surfaces for all values of nonzero mean curvature, we show that there are no complete graphs of constant mean curvature. We extend some of these results to the higher dimensional Heisenberg groupsH _2n+1. Entrata in Redazione il 2 aprile 1998. The first author was supported by Fapesp (Brazil), the second was partially supported by Fapesp and CNPq (Brazil), and the third was partially supported by Fapesp.     

Prime ideals and radicals of centred extensions and tensor products

In this paper, we study prime ideals and radicals of centred extensions of rings. Obtained results are applied to tensor products of algebras over commutative rings. This research was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. The second-named author was also supported by KBN grant 2 P301 035 06.     

Families of vector measures of uniformly bounded variation

We characterize families of vector measures of uniformly bounded variation and semivariation in terms of additivity properties. A classical theorem of Rickart and a simplified proof of Nikodym’s boundedness theorem follow. Received: 3 January 2006; Revised: 31 March 2006 The second named author was supported by Estonian Science Foundation Grant 5704.     

Lower Bounds on the Lowest Spectral Gap of Singular Potential Hamiltonians

We analyze Schr?dinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient space. Under the assumption that the operator has at least two eigenvalues below its essential spectrum we derive estimates on the lowest spectral gap. In the case where the sub-manifold is a finite curve in two dimensional Euclidean space the size of the gap depends only on the following parameters: the length, diameter and maximal curvature of the curve, a certain parameter measuring the injectivity of the curve embedding, and a compact sub-interval of the open, negative energy half-axis which contains the two lowest eigenvalues. Dedicated to Krešimir Veselić on the occasion of his 65^th birthday. Submitted: February 20, 2006; Accepted: May 8, 2006     

The minimal entropy conjecture for nonuniform rank one lattices

The Besson–Courtois–Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices. This research was partially supported by an NSF Postdoctoral Fellowship. Received: June 2004; Revision: January 2006; Accepted: March 2006     

Limiting profile of blow-up solutions for the Gross-Pitaevskii equation

This paper is concerned with the blow-up solutions of the Gross-Pitaevskii equation. Using the concentration compact principle and the variational characterization of the corresponding ground state, we obtain the limiting profile of blow-up solutions with critical mass in the corresponding weighted energy space. Moreover, we extend this result to small super-critical mass case by the variational methods and scaling technique. This work was supported by National Natural Science Foundation of China (Grant No. 10771151) and Scientific Research Fund of Sichuan Provincial Education Department (Grant No. 2006A068)     

Concavity of the conditional mean sojourn time in the <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/1 processor-sharing queue with batch arrivals

Avrachenkov et al. (Queueing Syst. 50:459–480, [2005]) conjectured that in an M/G/1 processor-sharing queue with batch arrivals, the conditional mean sojourn time is concave. In this paper, we show that this conjecture is generally not true. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-312-C00470).     

Ads Manifolds With Particles and Earthquakes on Singular Surfaces

We prove two related results. The first is an “earthquake theorem” for closed hyperbolic surfaces with cone singularities where the total angle is less than π: any two such metrics in are connected by a unique left earthquake. The second result is that the space of “globally hyperbolic” AdS manifolds with “particles” – cone singularities (of given angle) along time-like lines – is parametrized by the product of two copies of the Teichmüller space with some marked points (corresponding to the cone singularities). The two statements are proved together. F.B. was partially supported by the A.N.R. project GEODYCOS. J.-M.S. was partially supported by the A.N.R. programs RepSurf, 2006-09, ANR-06-BLAN-0311, GeomEinstein, 2006-09, 06-BLAN-0154, and FOG, 2007-10, ANR-07-BLAN-0251-01.     

A version of Rolle's theorem and applications

This paper deals with global injectivity of vector fields defined on euclidean spaces. Our main result establishes a version of Rolle's Theorem under generalized Palais-Smale conditions. As a consequence of this, we prove global injectivity for a class of vector fields defined on n-dimensional spaces.Research partially supported by CNPq/Brazil under grant # 307014/89-4Research partially supported by CNPq/Brazil under grant # 301251/78-9     

A note on cones associated to Schauder bases

We study the existence of infima of subsets in Banach spaces ordered by normal cones associated to shrinking Schauder bases. Under these conditions we prove the existence of infima for a class of subsets verifying a weakly compactness property. Moreover we prove that a normal cone associated to a Schauder basis in a reflexive Banach space is strongly minihedral extending the known result for unconditional Schauder bases. Several examples are also discussed. Miguel Sama: The work of this author is partially supported by Ministerio de Educación y Ciencia (Spain), project MTM2006-02629 and Ingenio Mathematica (i-MATH) CSD2006-00032 (ConsoliderIngenio 2010).     

Islands at infinity on manifolds of asymptotically nonnegative curvature

We introduce an invariant which measures the R-eccentricity of a point in a complete Riemannian manifold M and show that it goes to zero when the point goes to infinity, if M has asymptotically nonnegative curvature. As a consequence we show that the isometry group is compact if M has asymptotically nonnegative curvature and a point with positive sectional curvature. Both authors were partially supported by CNPq of Brazil and the second author was also partially supported by FAPERJ of Brazil.