A complete classification of bifurcation diagrams of a Dirichlet problem with concave-convex nonlinearities

We study the bifurcation diagrams of positive solutions of the two point boundary value problem

     

From a Floyd-Auslander minimal system to an odd triangular map

In 1989 A.N. Sharkovsky asked the question which of the properties characterizing continuous maps of the interval with zero topological entropy remain equivalent for triangular maps of the square. The problem is difficult and only partial results are known. However, in the case of triangular maps with nondecreasing fibres there are only few gaps in a classification (given by Z. Ko?an) of a set of 24 of these conditions. In the present paper we remove these gaps by giving an example of a triangular map in the square with the following properties:

(1)

all fibre maps are nondecreasing,

(2)

all recurrent points of the map are uniformly recurrent, and

(3)

the restriction of the map to the set of recurrent points has an uncountable scrambled set (and so is Li-Yorke chaotic).

The example is obtained by taking an appropriate Floyd-Auslander minimal system and then taking its appropriate continuous extension to a triangular map of the square.     

The norm of a symmetric elementary operator

The norm of the operator on (or on any prime C-algebra ) is computed for all and is shown to be equal to the completely bounded norm.

     

An Isometric Embedding of Moebius Band with Positive Gaussian Curvature

The main purpose of this paper is to show that there is an isometric embedding from Moebius band to R4 with positive Gaussian curvature.     

Compact optimization can outperform separation: A case study in structural proteomics

In Combinatorial Optimization, one is frequently faced with linear programming (LP) problems with exponentially many constraints, which can be solved either using separation or what we call compact optimization. The former technique relies on a separation algorithm, which, given a fractional solution, tries to produce a violated valid inequality. Compact optimization relies on describing the feasible region of the LP by a polynomial number of constraints, in a higher dimensional space. A commonly held belief is that compact optimization does not perform as well as separation in practice. In this paper, we report on an application in which compact optimization does in fact largely outperform separation. The problem arises in structural proteomics, and concerns the comparison of 3-dimensional protein folds. Our computational results show that compact optimization achieves an improvement of up to two orders of magnitude over separation. We discuss some reasons why compact optimization works in this case but not, e.g., for the LP relaxation of the TSP.Received: April 2003, Revised: January 2004, MSC classification: 65K05, 90C05, 90C90Thanks to Arie Tamir for pointing out to us many relevant references, and to Brian Walenz and Giulio Zanetti for helpful discussions. We thank two anonymous referees for their suggestions which improved this paper considerably. The second author wishes to thank Sandia National Labs, Albuquerque, NM, and the Mathematical Biosciences Institute, Columbus, OH, for their hospitality. Sandia is a multiprogram laboratory, operated by Sandia Corporation, a Lockhead Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000.     

Covering maps that are not compositions of covering maps of lesser order

In 1995 J.W. Heath asked which exactly -to-one maps are compositions of exactly -to-one maps with . This paper deals with compositions of covering maps. Exactly -to-one covering maps on locally arcwise connected continua that are not factorable into covering maps of order are constructed for all 's, and characterized in algebraic terms (fundamental groups). They are not proper compositions of exactly -to-one maps, open maps, or locally one-to-one maps.     

Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs

Given two densities on with the same total mass, the Monge transport problem is to find a Borel map rearranging the first distribution of mass onto the second, while minimizing the average distance transported. Here distance is measured by a norm with a uniformly smooth and convex unit ball. This paper gives a complete proof of the existence of optimal maps under the technical hypothesis that the distributions of mass be compactly supported. The maps are not generally unique. The approach developed here is new, and based on a geometrical change-of-variables technique offering considerably more flexibility than existing approaches.

     

Any 3-manifold 1-dominates at most finitely many 3-manifolds of -geometry

Any 3-manifold 1-dominates at most finitely many 3-manifolds supporting geometry.

     

Three-dimensional numerical simulations of susceptibility-induced magnetic field inhomogeneities in the human head

Three-dimensional numerical simulations of the static magnetic field in the human head were carried out to assess the field inhomogeneity due to magnetic susceptibility differences at tissue interfaces. We used a finite difference method and magnetic permeability distributions obtained by segmentation of computed tomography images. Computations were carried out for four models, consisting of the head and the neck; the head, neck, and shoulders; the head, neck, and thorax; and the head tilted backwards, including the neck and the shoulders. Considerable magnetic field inhomogeneities were observed in the inferior frontal lobes and inferior temporal lobes, particularly near the sphenoid sinus and the temporal bones. Air/tissue interfaces at the shoulders were found to induce substantial magnetic field inhomogeneities in the occipital lobes and the cerebellum, whereas air/tissue interfaces in the lungs appeared to have less influence on the magnetic field in the brain. Tilting the head backwards could significantly reduce the field inhomogeneities superior to the planum sphenoidale as well as in the occipital lobes and the cerebellum.     

Spectral Properties of a Piecewise Linear Intermittent Map

For a piecewise linear intermittent map, the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions of the Frobenius–Perron operator ^P are explicitly derived. The evolution of the averages are shown to be a superposition of the contributions from two simple eigenvalues 1 and _d (–1, 0), and a continuous spectrum on the unit interval [0,1] of ^P. Power-law decay of correlations are controlled by the continuous spectrum. Also the non-normalizable invariant measure in the non-stationary regime is shown to determine the strength of the power-law decay.