Multiple Solutions for a Nonlinear Schrödinger Equation with Magnetic Fields

We study a nonlinear Schrödinger equation in presence of a magnetic field and relate the number of solutions with the topology of the set where the potential attains its minimum value. In the proofs we apply variational methods, penalization techniques and Ljusternik–Schnirelmann theory.     

Enhancing computations of nondominated solutions in MOLFP via reference points

In previous work, Costa and Alves (J Math Sci 161:(6)820–831, 2009; 2011) have presented Branch & Bound and Branch & Cut techniques that allow for the effective computation of nondominated solutions, associated with reference points, of multi-objective linear fractional programming (MOLFP) problems of medium dimensions (ten objective functions, hundreds of variables and constraints). In this paper we present some results that enhance those computations. Firstly, it is proved that the use of a special kind of achievement scalarizing function guarantees that the computation error does not depend on the dimension of the problem. Secondly, a new cut for the Branch & Cut technique is presented. The proof that this new cut is better than the one in Costa and Alves (2011) is presented, guaranteeing that it reduces the region to explore. Some computational tests to assess the impact of the new cut on the performance of the Branch & Cut technique are presented.     

Kernels of Asymmetric Toeplitz Operators and Applications to Almost Periodic Factorization

Necessary and sufficient factorability conditions are established for some new classes of almost periodic matrix functions, and explicit factorization formulas are given whenever the factorization exists. The results are based on the connection between factorability and properties of solutions to a related homogeneous Riemann–Hilbert problem. These solutions, in their turn, are described completely, for the cases at hand, via introduction and consideration of certain asymmetric Toeplitz operators.     

Desenvolvimento de uma ferramenta computacional para a análise de elementos de membrana em concreto estrutural

Reinforced concrete elements subjected to membrane forces, i.e., elements subjected to in-plane shear and axial stresses are very common for modeling complex structures such as aircraft hangars, nuclear power plants, offshore oil platforms and long-span bridges. While the design of reinforcement for membrane elements is well adressed the same can not be said regarding the analysis of performance of these elements. Into this context, the present paper aims at providing a numerical tool developed in the Matlab platform, taking into account the “Modified Compression Field Theory”. In order to certificate the performance of the proposed tool, extensive numerical results were compared with experimental results available in the literature. The obtained results revealed that the proposed tool is very confident for the analysis of reinforced concrete membrane elements.     

Geometry of expanding absolutely continuous invariant measures and the liftability problem

We show that for a large class of maps on manifolds of arbitrary finite dimension, the existence of a Gibbs–Markov–Young structure (with Lebesgue as the reference measure) is a necessary as well as sufficient condition for the existence of an invariant probability measure which is absolutely continuous measure (with respect to Lebesgue) and for which all Lyapunov exponents are positive.     

Integral Representations and the Behavior of Krasner Analytic Functions Around Singular Points

Given a prime number p and K a compact subset of ? _p , the topological completion of the algebraic closure of the field of p-adic numbers, we are interested in integral representations for a class of Krasner analytic functions defined on ${\mathbb{P}}^1({\mathbb{C}}_p)\setminus K$ with values in ${\mathbb{P}}^1({\mathbb{C}}_p)$ . We apply these results to study the behavior of Krasner analytic functions around singular points.     

On the Zeros of Krasner Analytic Functions

Given a prime number p and a compact subset X of the topological completion ? _p of the algebraic closure of the field of p-adic numbers, we study the set of zeros of Krasner analytic functions defined on ?¹(? _p ) \ X with values in ? _p .     

Processing of high resolution magic angle spinning spectra of breast cancer cells by the filter diagonalization method

Proton nuclear magnetic resonance ((1)H NMR) spectroscopy for detection of biochemical changes in biological samples is a successful technique. However, the achieved NMR resolution is not sufficiently high when the analysis is performed with intact cells. To improve spectral resolution, high resolution magic angle spinning (HR-MAS) is used and the broad signals are separated by a T(2) filter based on the CPMG pulse sequence. Additionally, HR-MAS experiments with a T(2) filter are preceded by a water suppression procedure. The goal of this work is to demonstrate that the experimental procedures of water suppression and T(2) or diffusing filters are unnecessary steps when the filter diagonalization method (FDM) is used to process the time domain HR-MAS signals. Manipulation of the FDM results, represented as a tabular list of peak positions, widths, amplitudes and phases, allows the removal of water signals without the disturbing overlapping or nearby signals. Additionally, the FDM can also be used for phase correction and noise suppression, and to discriminate between sharp and broad lines. Results demonstrate the applicability of the FDM post-acquisition processing to obtain high quality HR-MAS spectra of heterogeneous biological materials.