The discrete (finite) Gabor scheme is generalized by incorporating multiwindows. Two approaches are presented for the analysis of the multiwindow scheme: the signal domain approach and the Zak transform domain approach. Issues related to undersampling, critical sampling, and oversampling are considered. The analysis is based on the concept of frames and on generalized (Moore-Penrose) inverses. ...

We analyze the problem of graceful exit from superinflationary pre-big bang phase of string cosmology within the context of lowest-order string effective action. The previous no go theorems are generalized for the case when higher genus terms of general form and additional matter fields are included. It is shown that the choice of the E-frame essentially simplifies the consideration. For the ex...

We consider a unit speed timelike curve α in Minkowski 4-space E41 and denote the Frenet frame of α by {T,N,B1,B2}. We say that α is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction U of E41. In this work we study those helices where the function 〈B2, U〉 is constant and we give different characterizations of such curves....

The sweeping surface, or generalized cylinder, is important in graphics, computer vision and elsewhere. A rotation minimizing frame, avoid the unnecessary twist given it by the Frenet frame. We give a quadratically convergent algorithm for computing it along a 3D trajectory curve, with an error bound. This is then used to create NURBS-approximated sweeping surfaces, to aid its incorporation int...

The availability of affordable RGB-D cameras like Microsoft Kinect can improve VSLAM applications, object 3D modeling and reconstruction of indoor environments, through the use of dense, synchronized depth and color images. The high frame rate of such devices isn’t exploited so far, since they require both fast and accurate algorithms for real-time registration. In this paper we present a techn...

given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

The solution to the problem of optical or electromagnetic-wave scattering from perfectly conducting rough surfaces modeled by a multiscale fractal function is generalized to the case of relative uniform translating motion with respect to the observer. The presence of motion can be treated by the relativistic frame hopping method by means of plane-wave simplification techniques, since the soluti...

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted Lp-spa...

In this paper, the unsteady oscillatory flows of a generalized Burgers’ fluid in a rotating frame are investigated. The constitutive equations of the generalized Burgers’ fluid are used in the mathematical formulation of the problem. The solutions are obtained by using the Laplace transform method. The graphical results are displayed and discussed for various parameters of interest. It is found...

It has been customary to define measures of information by relating information to uncertainty.But Van der Lubbe et al. [12] have followed a different approach and chosen the relation between information and certainty as a starting point.They have introduced information measures with the help of certainty measures within this frame work.This approach leads to three generalized classes of inform...