In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective ...

If (fn) is a sequence of elements of an infinite dimensional Hilbert space H and (en) is an orthonormal basis for H , we define the preframe operator T : H → H by: Ten = fn. It follows that for any f ∈ H , T ∗f = ∑ n〈f, fn〉en. Hence, (fn) is a frame if and only if T ∗ is an isomorphism (called the frame transform) and in this case S = TT ∗ is an invertible operator on H called the frame operato...

This paper is concerned with the determination of optimal sensor locations for structural modal identification in a strap-braced cold formed steel frame based on an improved genetic algorithm (IGA). Six different optimal sensor placement performance indices have been taken as the fitness functions two based on modal assurance criterion (MAC), two based on maximization of the determinant of a Fi...

We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...

Stephan Dahlke a, Massimo Fornasier b and Thorsten Raasch a a Philipps-Universität Marburg, FB 12 Mathematik und Informatik, Hans-Meerwein Straße, Lahnberge, 35032 Marburg, Germany E-mail: {dahlke;raasch}@mathematik.uni-marburg.de b Università “La Sapienza” in Roma, Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Via Antonio Scarpa, 16/B, 00161 Roma, Italy E-mail: mfornasi...

In structural design of steel frames, in order to achieve proper safety, the effect uncertainties and loading parameters structure must be considered. This approach is obtained by defining a reliability index. this study, Modified Dolphin Monitoring (MDM) operator was used evaluate index three well-known frame structures based on Hasofer-Lind method. The evaluated using EVPS VPS algorithms with...

The g-frame operator for g-frame in Hilbert space is introduced. The results of g-frame operator are presented. A sequence of operators Λ̄j∈J(where Λ̄ = ΛSg −1 ) is a g-frame for the Hilbert space H with frame bounds 1 B and 1 A . Frame identities for g-normalized tight frames are established. Results on direct sum of gframe operators on direct sum of Hilbert spaces are presented. Mathematics Sub...

Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected in the efficiency of the inversion of the fusion frame operator SW , which in turn is heavily dependent on the sparsity of SW . We will show that sparsity of ...