We study Weyl-Heisenberg (=Gabor) expansions for either L 2 (IR d) or a subspace of it. These are expansions in terms of the spanning set where K and L are some discrete lattices in IR d , L 2 (IR d) is nite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the \basis" properties of WH systems (e.g. being a frame or a Riesz ba...

The basic operations for combining real values in the frame of decision analysis are the Weighted Mean (WM) and the Ordered Weighted Averaging operator (OWA). The weighted mean allows the system to compute an aggregate value from the ones coming from several sources, taking into account the reliability of each information source. Alternatively, the OWA operator allows the user to weight the val...

The Schrödinger operators on the Newtonian space-time are defined in a way which make them independent on the class of inertial observers. In this picture the Schrödinger operators act not on functions on the space-time but on sections of certain one-dimensional complex vector bundle – the Schrödinger line bundle. This line bundle has trivializations indexed by inertial observers and is associa...

We consider basic algebraic constructions associated with an abstract pre-operad C (Sec. 2), such as a ⌣-algebra (Sec. 3), total composition • (Sec. 4), pre-coboundary operator δ (Sec. 5) and tribraces {·, ·, ·} (Sec. 6). Main result of the present paper is the Main Theorem (Sec. 6). By defining (see degree notations in Sec. 2) a derivation deviation (Definition 6.2) of the pre-coboundary opera...

Preprint No. 1239, Department of Mathematics, University of Utrecht, May 2002. Submitted to SIAM J. Numer. Anal. In “Adaptive Wavelet Methods II Beyond the Elliptic case” of Cohen, Dahmen and DeVore ([CDD00]), an adaptive method has been developed for solving general operator equations. Using a Riesz basis of wavelet type for the energy space, the operator equation is transformed into an equiva...

Volume Visualization of Multicolor Laser Confocal Microscope data Anshuman Razdan, Kamal Patel, Gerald E. Farin and David G. Capco Abstract: The objective of this work is to give biologists the ability to visualize Multicolor Laser Confocal Microscope (MLCM) data sets. We present the application of volume ray casting techniques to create fast and accurate visualization of the spatial structures...

The theory of frames is fundamental to timefrequency (TF or time-scale signal expansions like Gabor ysis of frames via two “TF frame representations” called the Weyl symbol and Wigner distribution of a frame. The T F analysis shows how a frame’s properties depend on the signal’s T F location and on certain frame parameters. 1 I N T R O D U C T I O N Linear time-frequency (TF) or time-scale sign...

abstract. certain facts about frames and generalized frames (g- frames) are extended for the g-frames for hilbert c*-modules. it is shown that g-frames for hilbert c*-modules share several useful properties with those for hilbert spaces. the paper also character- izes the operators which preserve the class of g-frames for hilbert c*-modules. moreover, a necessary and suffcient condition is ob- ...

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition, while ...