The investigations of the bolometric light curve of SN1987A are briefly reviewed. We suggest that the accretion luminosity produced by an assumed neutron star in the center of SN1987A is important for the evolution of the bolometric light curve at a later stage. We emphasize the marked difference of our model with previous accretion models, where the backfall of material mainly occurs within th...

We consider the inverse problem to recover a part Γc of the boundary of a simply connected planar domain D from a pair of Cauchy data of a harmonic function u in D on the remaining part ∂D \ Γc when u satisfies a homogeneous impedance boundary condition on Γc. Our approach extends a method that has been suggested by Kress and Rundell [17] for recovering the interior boundary curve of a doubly c...

The truncation of stellar discs is not abrupt but characterized by a continuous distancing from the exponential profile. There exists a truncation curve, t(r), ending at a truncation radius, r t. We present here a theoretical model in which it is assumed that the magnetic hypothesis explaining the flat rotation curve also explains the truncation. Once stars are born, the centripetal magnetic fo...

The sketch-based shape modeling is one of the most challenging and active problems in computer graphics. In this paper, we present an interactive modeling system for generating free-form surfaces using a 2D sketch interface. Since inferring 3D shape from 2D sketches is an one to many function with no unique solution, we propose to interpret the given 2D curve to be the projection of the 3D curv...

This paper illustrates the use of the envelope theorem for the geometric design of a cycloidal speed reducer. Specifically, it proposes two designs for a mathematical model with tooth differences: a pin wheel epitrochoid meshing which is a cycloidal wheel (internal rotor) profile equidistant to an epitrochoid (or extended epicycloid) curve and a cycloida! wheel is generated by a pin wheel (exte...

Kirsch’s factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. The mathematical basis of this method is given by the far-field equation, which is a Fredholm integral equation of the first kind in which the data function is a known analytic function and the integral kernel is the measured (and therefore noisy) fa...

We describe a data reduction procedure to assign statistically accurate estimates of unknown hormone concentrations, with associated uncertainties, based on experimental uncertainties in sample replicates and the fitted calibration curve. Three mathematical calibration curve functions are considered. The one providing optimal statistical characterization of reference calibrators is chosen for u...

Assessing the discriminative power of rating systems is an important question to banks and to regulators. In this article we analyze the Cumulative Accuracy Profile (CAP) and the Receiver Operating Characteristic (ROC) which are both commonly used in practice. We give a test-theoretic interpretation for the concavity of the CAP and the ROC curve and demonstrate how this observation can be used ...