An approach is proposed to represent functionally defined multidimensional shapes as multimedia objects. A multimedia object can be described using 2D/3D world coordinates, visual, audio, haptic and other "multimedia coordinates". We introduce a space mapping between geometric coordinates and multimedia coordinates. The approach is supported by the interactive modeling system which integrates h...

We consider fast oscillating perturbations of dynamical systems in regions where one can introduce action-angle type coordinates. In an appropriate time scale, a diffusion approximation the first-integrals evolution is described under assumption that set resonance tori small enough. If coordinates be introduced just piece-wise , limiting process should considered on open book space. Such by dif...

Although simple and based on physical realizable color primaries, the RGB color space cannot allow the direct definition of a topology-preserving, perceptually-compatible inter-color distance. The classical normalized inter-color distances are rather complex to implement and tune and do not account for the natural incertitude and confusion regarding both the numerical color values and the color...

Certain topological and geometrical properties of data driven local coordinates (DDLC) for state-space systems as introduced in (Wolodkin et al., 1997) and (McKelvey and Helmersson, 1999) are derived. First the special case of SISO systems with McMillan degree n 1 is discussed in order to provide some insights into the geometry of the DDLC construction. Then for the MIMO case with general n it ...

We write down a general action principle for spinning strings in 2 + 1 dimensional space-time without introducing Grassmann variables. The action is written solely in terms of coordinates taking values in the 2 + 1 Poincaré group, and it has the usual string symmetries, i.e. it is invariant under a) diffeomorphisms of the world sheet and b) Poincaré transformations. The system can be generalize...