Papers by Bernhard Parodi
Astronomy and Astrophysics, May 28, 2002
We present B and R band surface photometry of 25 Southern field dwarf galaxies within a distance ... more We present B and R band surface photometry of 25 Southern field dwarf galaxies within a distance of 10 Mpc. For each galaxy we give the essential model-free photometric parameters and, by fitting exponentials to the surface brightness profiles, the central extrapolated surface brightness and the exponential scale length, in both colour bands. Surface brightness and colour profiles are shown. One of the objects, a very faint dwarf elliptical in the vicinity of NGC 2784, has been discovered in the course of this work. Drawing on the data from this and all previous papers of this series, we construct a complete sample of 72 late-type ("irregular") dwarf galaxies in nearby groups and the field within the 10 Mpc volume, to study the exponentialdisk parameter relations of these galaxies with respect to galaxy environment. We confirm our previous finding of statistically lower scale lengths/higher central surface brightnesses for field and group galaxies as compared to cluster galaxies. However, using a clear-cut definition of "group" versus "field" environment, we find no significant difference in the photometric structure of group and field irregulars. A difference in the star formation history may partly account for this structure-environment relation: for a given luminosity cluster dwarfs are on average redder than field and group galaxies. We also report evidence for the colour gradients of dwarf irregulars being roughly inversely proportional to the disk scale lengths. Supplementing our photometric data with kinematic data from the literature, we study possible relations with kinematic properties of the inner disk. Applying the dark matter scaling relations for a Burkert halo we show that for field and group galaxies of a given luminosity faster-than-mean disk rotational velocities at a radius of about two scale lengths are correlated with larger-than-mean disk scale lengths.
The Astrophysical Journal, Sep 10, 2000
A sample of 35 SNe Ia with good to excellent photometry in B and V, minimum internal absorption, ... more A sample of 35 SNe Ia with good to excellent photometry in B and V, minimum internal absorption, and 1200 < v < ∼ 30 000 km s −1 is compiled from the literature. As far as their spectra are known they are all Branch-normal. For 29 of the SNe Ia also peak magnitudes in I are known. The SNe Ia have uniform colors at maximum, i.e. <B-V >=−0 m. 012 (σ=0.051) and <V-I>=−0 m. 276 (σ=0.078). In the Hubble diagram they define a Hubble line with a scatter of σ M =0 m. 21-0 m. 16, decreasing with wavelength. The scatter is further reduced if the SNe Ia are corrected for differences in decline rate ∆m 15 or color (B−V). A combined correction reduces the scatter to σ < ∼ 0 m. 13. After the correction no significant dependence remains on Hubble type or galactocentric distance. The Hubble line suggests some curvature which can be differently interpreted. A consistent solution is obtained for a cosmological model with Ω M =0.3, Ω Λ =0.7, which is indicated also by much more distant SNe Ia. Absolute magnitudes are available for eight equally blue (Branch-normal) SNe Ia in spirals, whose Cepheid distances are known. If their well defined mean values of M B , M V , and M I are used to fit the Hubble line to the above sample of SNe Ia one obtains H 0 =58.3 km s −1 Mpc −1 , or, after adjusting all SNe Ia to the average values of ∆m 15 and (B−V), H 0 =60.9 km s −1 Mpc −1. Various systematic errors are discussed whose elimination tends to decrease H 0. The finally adopted value at the 90-percent level, including random and systematic errors, is H 0 =58.5±6.3 km s −1 Mpc −1. Several higher values of H 0 from SNe Ia, as suggested in the literature, are found to depend on large corrections for variations of the light curve parameter and/or on an unwarranted reduction of the Cepheid distances of the calibrating SNe Ia.
RePEc: Research Papers in Economics, Dec 13, 2014
The PGBM model for a couple of counteracting, exponentially growing capital flows is presented: t... more The PGBM model for a couple of counteracting, exponentially growing capital flows is presented: the available capital stock X(t) evolves according to a variant of inhomogeneous geometric Brownian motion (GBM) with time-dependent drift, in particular, to the stochastic differential equation dX(t) = [pX(t) + ρ 1 exp(q 1 t) + ρ 2 exp(q 2 t)]dt + σX(t)dW (t), where W (t) is a Wiener process. As a paragon, we study a continuous-time model for a nine-parameter Ponzi scheme with an exponentially growing number of investors. Investors either maintain their investment or withdraw it after some fixed investment span and quit the system. The first two moments of the process and hence a closed-form solution for the mean path are given. The capital stock exhibits a dynamic lognormal probability distribution as long as the system remains solvent. The assumed stochastic performance allows for earlier or later collaps of the investment system as compared to the deterministic analogy (σ = 0). Allowing also for negative capital values the system's default probability can be calculated at any time by numerically solving the corresponding Kolmogorov forward equation. We use the finite difference method and obtain results in accordance with those of simple Monte-Carlo simulations. Finally, a minor modification of the payout function provides a toy model for a social security system exhibiting critical behaviour. Depending on whether some parameter value violates a weak no-Ponzi game condition or not, the system represents either a non-lasting Ponzi game or a lasting no-Ponzi game in the weak sense.
RePEc: Research Papers in Economics, Mar 15, 2013
Zusammenfassung. Ein analytisches Modell mit acht Parametern zur Beschreibung idealisierter Ponzi... more Zusammenfassung. Ein analytisches Modell mit acht Parametern zur Beschreibung idealisierter Ponzi-Systeme mit asymmetrisch und progressiv wachsenden Kapitalzu-und-abflüssen wird präsentiert. Investoren bleiben optional zeitlich begrenzt oder dauerhaft investiert. Diverse Systemvarianten inklusive deren Nicht-Ponzi-Spiel-Bedingungen ergeben sich durch Modifikation der Auszahlungsfunktion. Das zugrunde liegende deterministische abc-Modell rekursiver Zeitreihen nutzt einen etablierten Ansatz zur Beschreibung einfacher wirtschaftsmathematischer Standardprozesse.
Astronomy & Astrophysics, 2003
We study the distribution of bright star-forming complexes in a homogeneous sample of 72 late-typ... more We study the distribution of bright star-forming complexes in a homogeneous sample of 72 late-type ("irregular") dwarf galaxies located within the 10 Mpc volume. Star-forming complexes are identified as bright lumps in B-band galaxy images and isolated by means of the unsharp-masking method. For the sample as a whole the radial number distribution of bright lumps largely traces the underlying exponential-disk light profiles, but peaks at a 10 percent smaller scale length. Moreover, the presence of a tail of star forming regions out to at least six optical scale lengths provides evidence against a systematic star formation truncation within that galaxy extension. Considering these findings, we apply a scale length-independent concentration index, taking into account the implied non-uniform random spread of star formation regions throughout the disk. The number profiles frequently manifest a second, minor peak at about two scale lengths. Relying on a two-dimensional stochastic self-propagating star formation model, we show these secondary peaks to be consistent with triggered star formation; for a few of the brighter galaxies a peculiar peak distribution is observed that is conceivably due to the onset of shear provided by differential rotation. On scales between 100 and 1000 pc, and by taking into account exponential-disk structure, bright lumps reveal cluster dimensions between 1.3 and 2, with a weak trend to higher dimensions for brighter galaxies. Cluster dimension weakly anticorrelates with the lumpiness index (the fraction of the total galaxy light due to the light contributed by the lumps), the latter index showing no dependence on luminosity. Lump spreading within the disk, as measured by the concentration index, and lump clustering, as given by the cluster dimension, are not linked to each other. Interpreting cluster dimension in terms of porosity of a self-similar intragalactic medium, we derive a relation between current star formation rate, scale length, and porosity.
arXiv (Cornell University), Apr 19, 2020
As a generalization of planar Fibonacci spirals that are based on the recurrence relation Fn = Fn... more As a generalization of planar Fibonacci spirals that are based on the recurrence relation Fn = Fn−1 +Fn−2, we draw assembled spirals stemming from analytic solutions of the recurrence relation Gn = a Gn−1 + b Gn−2 + c d n , with positive real initial values G0 and G1 and coefficients a, b, c, and d. The principal coordinates given in closed-form correspond to finite sums of alternating even-or alternating odd-indexed terms Gn. For rectangular spirals made of straight line segments (a.k.a. spirangles), the even-indexed and the odd-indexed directional corner points asymptotically lie on mutually orthogonal oblique lines. We calculate the points of intersection and show them in the case of inwinding spirals to coincide with the point of convergence. In the case of outwinding spirals, an n-dependent quadruple of points of intersection may form. For arched spirals, interpolation between principal coordinates is performed by means of arcs of quarter-ellipses. A three-dimensional representation is exhibited, too. The continuation of the discrete sequence {Gn} to the complex-valued function G(t) with real argument t∈R, exhibiting spiral graphs and oscillating curves in the Gaussian plane, subsumes the values Gn for t∈N as the zeros. Besides, we provide a matrix representation of Gn in terms of transformed Horadam numbers, retrieve the Shannon product difference identity as applied to Gn, and suggest a substitution method for finding a variety of other identities and summations related to Gn.
As a generalization of planar Fibonacci spirals that are based on the recurrence relation F_n=F_n... more As a generalization of planar Fibonacci spirals that are based on the recurrence relation F_n=F_n-1+F_n-2, we draw assembled spirals stemming from analytic solutions of the recurrence relation G_n=a G_n-1+b G_n-2+c d ^n, with positive real initial values G_0 and G_1 and coefficients a, b, c, and d. The principal coordinates given in closed-form correspond to finite sums of alternating even- or alternating odd-indexed terms G_n. For rectangular spirals made of straight line segments (a.k.a. spirangles), the even-indexed and the odd-indexed directional corner points asymptotically lie on mutually orthogonal oblique lines. We calculate the points of intersection and show them in the case of inwinding spirals to coincide with the point of convergence. In the case of outwinding spirals, an n-dependent quadruple of points of intersection may form. For arched spirals, interpolation between principal coordinates is performed by means of arcs of quarter-ellipses. A three-dimensional represen...
The PGBM model for a couple of counteracting, exponentially growing capital flows is presented: t... more The PGBM model for a couple of counteracting, exponentially growing capital flows is presented: the available capital stock $X(t)$ evolves according to a variant of inhomogeneous geometric Brownian motion (GBM) with time-dependent drift, in particular, to the stochastic differential equation $dX(t)=[pX(t)+\rho_1\exp(q_1 t)+\rho_2\exp(q_2 t)]dt+\sigma X(t) dW(t)$, where $W(t)$ is a Wiener process. As a paragon, we study a continuous-time model for a nine-parameter Ponzi scheme with an exponentially growing number of investors. Investors either maintain their investment or withdraw it after some fixed investment span and quit the system. The first two moments of the process and hence a closed-form solution for the mean path are given. The capital stock exhibits a dynamic lognormal probability distribution as long as the system remains solvent. The assumed stochastic performance allows for earlier or later collaps of the investment system as compared to the deterministic analogy ($\sig...
Ein analytisches Modell mit acht Parametern zur Beschreibung idealisierter Ponzi-Systeme mit asym... more Ein analytisches Modell mit acht Parametern zur Beschreibung idealisierter Ponzi-Systeme mit asymmetrisch und progressiv wachsenden Kapitalzu- und -abflussen wird prasentiert. Investoren bleiben optional zeitlich begrenzt oder dauerhaft investiert. Diverse Systemvarianten inklusive deren Nicht-Ponzi-Spiel-Bedingungen ergeben sich durch Modifikation der Auszahlungsfunktion. Das zugrunde liegende deterministische abc-Modell rekursiver Zeitreihen nutzt einen etablierten Ansatz zur Beschreibung einfacher wirtschaftsmathematischer Standardprozesse.
arXiv: Astrophysics of Galaxies, 2018
Scaling relations among structural and kinematical features of 79 late-type spiral and dwarf irre... more Scaling relations among structural and kinematical features of 79 late-type spiral and dwarf irregular galaxies of the SPARC sample are revisited or newly established. The mean central surface brightness = 19.63 $\pm$ 0.11 mag arcsec$^{-2}$ allows for a clear-cut distinction between low and high surface brightness galaxies irrespective of luminosity. The geometry of rotation curves is characterized by the relation $dv(R_d)/dr \approx v_{max}/R_{max}$. For the rotation curve decompositions we apply dark matter halos of Burkert and of pseudo-isothermal type. The disk mass-to-light ratios exhibit an asymmetric bimodal distribution with the dominant peak located at 0.2. The baryonic mass fraction at intermediate radii is included to address both an adjusted baryonic Tully-Fisher relation and the significance of deviations from the mean radial acceleration relation. The mean radial decrease of the baryonic mass fraction within galaxies is quantified. The Burkert halo parameters obey $\rh...
As a generalization of planar Fibonacci spirals that are based on the recurrence relation $F_n=F_... more As a generalization of planar Fibonacci spirals that are based on the recurrence relation $F_n=F_{n-1}+F_{n-2}$, we draw assembled spirals stemming from analytic solutions of the recurrence relation $G_n=a\, G_{n-1}+b\, G_{n-2}+c\, d\,^n$, with positive real initial values $G_0$ and $G_1$ and coefficients $a$, $b$, $c$, and $d$. The principal coordinates given in closed-form correspond to finite sums of alternating even- or alternating odd-indexed terms $G_{n}$. For rectangular spirals made of straight line segments (a.k.a. spirangles), the even-indexed and the odd-indexed directional corner points asymptotically lie on mutually orthogonal oblique lines. We calculate the points of intersection and show them in the case of inwinding spirals to coincide with the point of convergence. In the case of outwinding spirals, an $n$-dependent quadruple of points of intersection may form. For arched spirals, interpolation between principal coordinates is performed by means of arcs of quarter-e...
Ein analytisches Modell mit acht Parametern zur Beschreibung idealisierter Ponzi-Systeme mit asym... more Ein analytisches Modell mit acht Parametern zur Beschreibung idealisierter Ponzi-Systeme mit asymmetrisch und progressiv wachsenden Kapitalzu- und -abflussen wird prasentiert. Investoren bleiben optional zeitlich begrenzt oder dauerhaft investiert. Diverse Systemvarianten inklusive deren Nicht-Ponzi-Spiel-Bedingungen ergeben sich durch Modifikation der Auszahlungsfunktion. Das zugrunde liegende deterministische abc-Modell rekursiver Zeitreihen nutzt einen etablierten Ansatz zur Beschreibung einfacher wirtschaftsmathematischer Standardprozesse.
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Papers by Bernhard Parodi