Papers by Bernhard Parodi
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Astronomy and Astrophysics, May 28, 2002
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The Astrophysical Journal, Sep 10, 2000
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RePEc: Research Papers in Economics, Dec 13, 2014
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RePEc: Research Papers in Economics, Mar 15, 2013
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yCat, Mar 1, 2002
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Astronomy & Astrophysics, 2003
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arXiv (Cornell University), Apr 19, 2020
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ORiON, Oct 1, 2013
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ORiON, Oct 1, 2013
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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...
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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...
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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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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...
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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...
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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