Maximal And Minimal Weak Solutions For Elliptic Problems With Nonlinearity On The Boundary

This paper deals with the existence of weak solutions for semilinear elliptic equation with nonlinearity on the boundary. We establish the existence of a maximal and a minimal weak solution between an ordered pair of sub- and supersolution for both monotone and nonmonotone nonlinearities. We use iteration argument when the nonlinearity is monotone. For the nonmonotone case, we utilize the surjectivity of a pseudomonotone and coercive operator, Zorn\u27s lemma and a version of Kato\u27s inequality

The Nuclear and Circum-nuclear Stellar Population in Seyfert 2 Galaxies: Implications for the Starburst-AGN Connection

We report the results of a spectroscopic investigation of a sample of 20 of the brightest type 2 Seyfert nuclei. Our goal is to search for the direct spectroscopic signature of massive stars, and thereby probe the role of circumnuclear starbursts in the Seyfert phenomenon. The method used is based on the detection of the higher order Balmer lines and HeI lines in absorption and the Wolf-Rayet feature at $\sim$4680 \AA in emission. These lines are strong indicators of the presence of young (a few Myrs) and intermediate-age (a few 100 Myrs) stellar populations. In over half the sample, we have detected HeI and/or strong stellar absorption features in the high-order (near-UV) Balmer series together with relatively weak lines from an old stellar population. In three others we detect a broad emission feature near 4680 \AA that is most plausibly ascribed to a population of Wolf-Rayet stars (the evolved descendants of the most massive stars). We therefore conclude that the blue and near-UV light of over half of the sample is dominated by young and/or intermediate age stars. The ``young'' Seyfert 2's have have larger far-IR luminosities, cooler mid/far-IR colors, and smaller [OIII]/H$\beta$ flux ratios than the ``old'' ones. These differences are consistent with a starburst playing a significant energetic role in the former class. We consider the possibility that there may be two distinct sub-classes of Seyfert 2 nuclei (``starbursts'' and ``hidden BLR''). However, the fact that hidden BLRs have been found in three of the ``young'' nuclei argues against this, and suggests that nuclear starbursts may be a more general part of the Seyfert phenomenon.Comment: To be published in ApJ, 546, Jan 10, 200

Probability distribution of arrival times in quantum mechanics

In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)] we introduced a self-adjoint operator $\hat {{\cal T}}(X)$ whose eigenstates can be used to define consistently a probability distribution of the time of arrival at a given spatial point. In the present work we show that the probability distribution previously proposed can be well understood on classical grounds in the sense that it is given by the expectation value of a certain positive definite operator $\hat J^{(+)}(X)$ which is nothing but a straightforward quantum version of the modulus of the classical current. For quantum states highly localized in momentum space about a certain momentum $p_0 \neq 0$, the expectation value of $\hat J^{(+)}(X)$ becomes indistinguishable from the quantum probability current. This fact may provide a justification for the common practice of using the latter quantity as a probability distribution of arrival times.Comment: 21 pages, LaTeX, no figures; A Note added; To be published in Phys. Rev.

Photoionization models of the CALIFA HII regions. I. Hybrid models

Photoionization models of HII regions require as input a description of the ionizing SED and of the gas distribution, in terms of ionization parameter U and chemical abundances (e.g. O/H and N/O). A strong degeneracy exists between the hardness of the SED and U, which in turn leads to high uncertainties in the determination of the other parameters, including abundances. One way to resolve the degeneracy is to fix one of the parameters using additional information. For each of the ~ 20000 sources of the CALIFA HII regions catalog, a grid of photoionization models is computed assuming the ionizing SED being described by the underlying stellar population obtained from spectral synthesis modeling. The ionizing SED is then defined as the sum of various stellar bursts of different ages and metallicities. This solves the degeneracy between the shape of the ionizing SED and U. The nebular metallicity (associated to O/H) is defined using the classical strong line method O3N2 (which gives to our models the status of "hybrids"). The remaining free parameters are the abundance ratio N/O and the ionization parameter U, which are determined by looking for the model fitting [NII]/Ha and [OIII]/Hb. The models are also selected to fit [OII]/Hb. This process leads to a set of ~ 3200 models that reproduce simultaneously the three observations. We find that the regions associated to young stellar bursts suffer leaking of the ionizing photons, the proportion of escaping photons having a median of 80\%. The set of photoionization models satisfactorily reproduces the electron temperature derived from the [OIII]4363/5007 line ratio. We determine new relations between the ionization parameter U and the [OII]/[OIII] or [SII]/[SIII] line ratios. New relations between N/O and O/H and between U and O/H are also determined. All the models are publicly available on the 3MdB database.Comment: Accepted for publication in A&

Divergences in Kaluza-Klein Models and their String Regularization

Effective field theories with (large) extra dimensions are studied within a physical regularization scheme provided by string theory. Explicit string calculations then allow us to consistently analyze the ultraviolet sensitivity of Kaluza--Klein theories in the presence or absence of low energy supersymmetry.Comment: 50 pages, LaTe

Quantum Measurements and Gates by Code Deformation

The usual scenario in fault tolerant quantum computation involves certain amount of qubits encoded in each code block, transversal operations between them and destructive measurements of ancillary code blocks. We introduce a new approach in which a single code layer is used for the entire computation, in particular a surface code. Qubits can be created, manipulated and non-destructively measured by code deformations that amount to `cut and paste' operations in the surface. All the interactions between qubits remain purely local in a two-dimensional setting.Comment: Revtex4, 6 figure

Quantum probability distribution of arrival times and probability current density

This paper compares the proposal made in previous papers for a quantum probability distribution of the time of arrival at a certain point with the corresponding proposal based on the probability current density. Quantitative differences between the two formulations are examined analytically and numerically with the aim of establishing conditions under which the proposals might be tested by experiment. It is found that quantum regime conditions produce the biggest differences between the formulations which are otherwise near indistinguishable. These results indicate that in order to discriminate conclusively among the different alternatives, the corresponding experimental test should be performed in the quantum regime and with sufficiently high resolution so as to resolve small quantum efects.Comment: 21 pages, 7 figures, LaTeX; Revised version to appear in Phys. Rev. A (many small changes

Analysis of Public Bus Transportation of a Brazilian City Based on the Theory of Complex Networks Using the P-Space

The city of Curitiba, located at Southern Brazil, is recognized by its urban planning structured on three pillars: land use, collective transportation, and traffic. With 3.8 million people in its metropolitan area, the public transport system deals with approximately 2.5 million passengers daily. The structure and properties of such a transportation system have substantial implications for the urban planning and public politics for sustainable development of Curitiba. Therefore, this paper analyzes the structure of the public transportation system of Curitiba through the theory of complex networks in a static approach of network topology and presents a comparative analysis of the results from Curitiba, three cities from China (Shanghai, Beijing, and Guangzhou), and three cities from Poland (GOP, Warszawa, and Łódź). The transportation network was modeled as a complex network with exact geographical coordinates of its bus stops. In all bus lines, the method used was the P-Space. The results show that this bus network has characteristics of both small-world and scale-free networks

A Lorentz Invariant Pairing Mechanism: Relativistic Cooper Pairs

We study a Lorentz invariant pairing mechanism that arises when two relativistic spin-1/2 fermions are subjected to a Dirac string coupling. In the weak coupling regime, we find remarkable analogies between this relativistic bound system and the well known superconducting Cooper pair. As the coupling strength is raised, quenched phonons become unfrozen and dynamically contribute to the gluing mechanism, which translates into novel features of this relativistic superconducting pair.Comment: Revtex4 file, color figures with less resolution to comply with arxiv restriction