Global structures in a composite system of two scale-free discs with a coplanar magnetic field

We investigate a theoretical MHD disc problem involving a composite disc system of gravitationally coupled stellar and gaseous discs with a coplanar magnetic field in the presence of an axisymmetric dark matter halo. The two discs are expediently approximated as razor-thin, a ring-like magnetic field, and a power-law rotation curve in radius . By imposing the scale-free condition, we construct analytically stationary global MHD perturbation configurations for both aligned and logarithmic spiral patterns. MHD perturbation configurations in a composite system of partial discs in the presence of an axisymmetric dark matter halo are also considered. We derive analytically the stationary MHD dispersion relations for both aligned and unaligned perturbation structures and analyze the corresponding phase relationships between surface mass densities and the magnetic field. Compared with earlier results, we obtain three solution branches corresponding to super fast MHD density waves, fast MHD density waves and slow MHD density waves, respectively. By evaluating the unaligned $m=0$ case, we determine the marginal stability curves where the two unstable regimes corresponding to Jeans collapse instability and ring fragmentation instability are identified. We find that the aligned $m=0$ case is simply the limit of the unaligned $m=0$ case with the radial wavenumber $\xi\to0$. We further show that a composite system of partial discs behaves much differently from a composite system of full discs in certain aspects. Our formalism provides a useful theoretical framework in the study of stationary global perturbation configurations for MHD disc galaxies with bars, spirals and barred spirals.Comment: 35 pages, 24 figures, Accepted for publication in MNRA

Retinal image enhancement via a multiscale morphological approach with OCCO filter.

Retinal images are widely used for diagnosis and eye disease detection. However, due to the acquisition process, retinal images often have problems such as low contrast, blurry details or artifacts. These problems may severely affect the diagnosis. Therefore, it is very impor tant to enhance the visual quality of such images. Contrast enhancement is a pre-processing applied to images to improve their visual quality. This technique betters the identification of retinal structures in degraded reti nal images. In this work, a novel algorithm based on multi-scale mathe matical morphology is presented. First, the original image is blurred us ing the Open-Close Close-Open (OCCO) filter to reduce any artifacts in the image. Next, multiple bright and dark features are extracted from the filtered image by the Top-Hat transform. Finally, the maximum bright values are added to the original image and the maximum dark values are subtracted from the original image, previously adjusted by a weight. The algorithm was tested on 397 retinal images from the public STARE database. The proposed algorithm was compared with state of the art al gorithms and results show that the proposal is more efficient in improving contrast, maintaining similarity with the original image and introducing less distortion than the other algorithms. According to ophthalmologists, the algorithm, by improving retinal images, provides greater clarity in the blood vessels of the retina and would facilitate the identification of pathologies.CONACYT - Consejo Nacional de Ciencia y TecnologíaPROCIENCI

The CAPM strikes back? An equilibrium model with disasters

Embedding disasters into a general equilibrium model with heterogeneous firms induces strong nonlinearity in the pricing kernel, helping explain the empirical failure of the (consumption) CAPM. Our single-factor model reproduces the failure of the CAPM in explaining the value premium in finite samples without disasters and its relative success in samples with disasters. Due to beta measurement errors, the estimated beta-return relation is flat, consistent with the beta “anomaly,” even though the true beta-return relation is strongly positive. Finally, the consumption CAPM fails in simulations, even though a nonlinear model with the true pricing kernel holds exactly by construction

The topological AC effect on noncommutative phase space

The Aharonov-Casher (AC) effect in non-commutative(NC) quantum mechanics is studied. Instead of using the star product method, we use a generalization of Bopp's shift method. After solving the Dirac equations both on noncommutative space and noncommutative phase space by the new method, we obtain the corrections to AC phase on NC space and NC phase space respectively.Comment: 8 pages, Latex fil

Applying spatial reasoning to topographical data with a grounded geographical ontology

Grounding an ontology upon geographical data has been pro- posed as a method of handling the vagueness in the domain more effectively. In order to do this, we require methods of reasoning about the spatial relations between the regions within the data. This stage can be computationally expensive, as we require information on the location of points in relation to each other. This paper illustrates how using knowledge about regions allows us to reduce the computation required in an efficient and easy to understand manner. Further, we show how this system can be implemented in co-ordination with segmented data to reason abou

Determination of astrophysical 12N(p,g)13O reaction rate from the 2H(12N, 13O)n reaction and its astrophysical implications

The evolution of massive stars with very low-metallicities depends critically on the amount of CNO nuclides which they produce. The $^{12}$N($p$,\,$\gamma$)$^{13}$O reaction is an important branching point in the rap-processes, which are believed to be alternative paths to the slow 3$\alpha$ process for producing CNO seed nuclei and thus could change the fate of massive stars. In the present work, the angular distribution of the $^2$H($^{12}$N,\,$^{13}$O)$n$ proton transfer reaction at $E_{\mathrm{c.m.}}$ = 8.4 MeV has been measured for the first time. Based on the Johnson-Soper approach, the square of the asymptotic normalization coefficient (ANC) for the virtual decay of $^{13}$O$_\mathrm{g.s.}$ $\rightarrow$ $^{12}$N + $p$ was extracted to be 3.92 $\pm$ 1.47 fm$^{-1}$ from the measured angular distribution and utilized to compute the direct component in the $^{12}$N($p$,\,$\gamma$)$^{13}$O reaction. The direct astrophysical S-factor at zero energy was then found to be 0.39 $\pm$ 0.15 keV b. By considering the direct capture into the ground state of $^{13}$O, the resonant capture via the first excited state of $^{13}$O and their interference, we determined the total astrophysical S-factors and rates of the $^{12}$N($p$,\,$\gamma$)$^{13}$O reaction. The new rate is two orders of magnitude slower than that from the REACLIB compilation. Our reaction network calculations with the present rate imply that $^{12}$N($p,\,\gamma$)$^{13}$O will only compete successfully with the $\beta^+$ decay of $^{12}$N at higher ($\sim$two orders of magnitude) densities than initially predicted.Comment: 8 figures, 2 tables, Submitted to Physical Review

The 13N(d,n)14O Reaction and the Astrophysical 13N(p,g)14O Reaction Rate

$^{13}$N($p,\gamma$)$^{14}$O is one of the key reactions in the hot CNO cycle which occurs at stellar temperatures around $T_9$ $\geq$ 0.1. Up to now, some uncertainties still exist for the direct capture component in this reaction, thus an independent measurement is of importance. In present work, the angular distribution of the $^{13}$N($d,n$)$^{14}$O reaction at $E_{\rm{c.m.}}$ = 8.9 MeV has been measured in inverse kinematics, for the first time. Based on the distorted wave Born approximation (DWBA) analysis, the nuclear asymptotic normalization coefficient (ANC), $C^{^{14}O}_{1,1/2}$, for the ground state of $^{14}$O $\to$ $^{13}$N + $p$ is derived to be $5.42 \pm 0.48$ fm$^{-1/2}$. The $^{13}$N($p,\gamma$)$^{14}$O reaction is analyzed with the R-matrix approach, its astrophysical S-factors and reaction rates at energies of astrophysical relevance are then determined with the ANC. The implications of the present reaction rates on the evolution of novae are then discussed with the reaction network calculations.Comment: 17 pages and 8 figure

The Gaussian approximation for multi-color generalized Friedman's urn model

The Friedman's urn model is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we prove that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman's urn model with non-homogeneous generating matrices. The Gaussian process is a solution of a stochastic differential equation. This Gaussian approximation together with the properties of the Gaussian process is important for the understanding of the behavior of the urn process and is also useful for statistical inferences. As an application, we obtain the asymptotic properties including the asymptotic normality and the law of the iterated logarithm for a multi-color generalized Friedman's urn model as well as the randomized-play-the-winner rule as a special case