### A Method of Characteristics Solving the Initial-Boundary Value Problem of a Hyperbolic Differential Equation of Second Order.

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The aim of this article is to propose a new method for the grey-level image classification problem. We first present the classical variational approach without and with a regularization term in order to smooth the contours of the classified image. Then we present the general topological asymptotic analysis, and we finally introduce its application to the grey-level image classification problem.

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems...

Object oriented design has proven itself as a powerful tool in the field of scientific computing. Several software packages, libraries and toolkits exist, in particular in the FEM arena that follow this design methodology providing extensible, reusable, and flexible software while staying competitive to traditionally designed point tools in terms of efficiency. However, the common approach to identify classes is to turn data structures and algorithms of traditional implementations into classes such...

Object oriented design has proven itself as a powerful tool in the field of scientific computing. Several software packages, libraries and toolkits exist, in particular in the FEM arena that follow this design methodology providing extensible, reusable, and flexible software while staying competitive to traditionally designed point tools in terms of efficiency. However, the common approach to identify classes is to turn data structures and algorithms of traditional implementations into ...

In der vorliegenden Arbeit wird für lineare Mehrschrittblock verfahren zur numerischen Lösung von Anfangswertaufgaben eine explizite Konstruktionsmöglichkeit angegeben. Sie ermöglicht es, zu einem gegebenen Stabilitätspolynom ohne Lösung eines linearen Gleichungssystems die Koefizienten des zugehörigen Blockverfahrens zu berechnen.

The current powerful graphics cards, providing stunning real-time visual effects for computer-based entertainment, have to accommodate powerful hardware components that are able to deliver the photo-realistic simulation to the end-user. Given the vast computing power of the graphics hardware, its producers very often offer a programming interface that makes it possible to use the computational resources of the graphics processors (GPU) to more general purposes. This step gave birth to the so-called...