In this paper, we set up the bi-module of the algebra A on fuzzy sphere. Based on the differential operators in moving frame, we generalize the ABS construction into fuzzy sphere case. The applications of ABS construction are investigated in various physical systems. PACS Numbers: 46.10.+z, 05.40.+j, 05.60.+w

In this work, we introduce sufficient and necessary conditions for a pair of fuzzy conjunctor and implication considered in a multi-adjoint frame under which the usual combinations of multi-adjoint sufficiency, possibility and necessity operators form either antitone or isotone Galois connections.

In the frame of the Lindblad theory of open quantum systems, the system of three uncoupled harmonic oscillators with opening operators linear in the coordinates and momenta of the considered system is analyzed. The damping of the angular momentum and of its projection is obtained.

We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel multipliers (operators that map wavelet Bessel functions to wavelet Bessel functions). In addition we obtain an asymptotically tight approximation result for wavelet frames.

We construct bivariate biorthogonal cosine wavelets on a twooverlapping rectangular grid with bell functions not necessary of tensor product type. The biorthogonal system as well as frame and Riesz basis conditions are given explicitly. Our methods are based on the properties of bivariate total folding and unfolding operators.

The new era of digital communication has brought up many challenges that network operators need to overcome. The high demand of mobile data rates require improved networks, which is a challenge for the operators in terms of maintaining the quality of experience (QoE) for their consumers. In live video transmission, there is a sheer need for live surveillance of the videos in order to maintain t...

In this paper we investigate the computational aspects of some recently proposed iterative methods for approximating the canonical tight and canonical dual window of a Gabor frame (g, a, b). The iterations start with the window g while the iteration steps comprise the window g, the k iterand γk, the frame operators S and Sk corresponding to (g, a, b) and (γk, a, b), respectively, and a number o...

We introduce a classification of locally compact Hausdorff topological spaces with respect to the behavior $$ \sigma -compact subsets and, relying on this classification, we study properties corresponding $$C^*$$ -algebras in terms frame theory and {\mathscr A} operators Hilbert -modules; some pathological examples are constructed.

A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or system, of unitary operators. We will describe the operator-interpolation approach to wavelet theory using the local commutant of a system. This is really an abstract application of the theory of operator algebras to wavelet theory. The concrete applications of this m...

Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from groupinvariant flows of non-stretching curves in constant curvature manifolds and Lie group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming ...