In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.

We consider the variational problem defined by the functional ∫ H−K K dA on immersed surfaces in Euclidean space. Using the invariance of the functional under the group of Laguerre transformations, we study the extremal surfaces by the method of moving frames.

We consider a vector bundle E → M and the principal bundle PE of frames of E. Let K be a principal connection on PE and let Λ be a linear connection on M . We classify all principal connections on W 2PE = P 2M ×M J2PE naturally given by K and Λ.

We propose a frame-based representation of k-mers for detecting sequencing errors and rare variants in next generation sequencing data obtained from populations of closely related genomes. Frames are sets of non-orthogonal basis functions, traditionally used in signal processing for noise removal. We define a frame for genomes and sequenced reads to consist of discrete spatial signals of every ...

Overlapping genes (encoded on t he same DNA locus but in different frames) are thought to be rare and, therefore, were largely neglected in t he past. In a test set of 800 viruses we found more t han 350 potent ial overlapping open reading frames of >500 bp which generate BLAST hits, indicating a possible biological fun ction . Interestingly, five overlaps with more t han 2000 bp were found, th...

A nonlinear Hammerstein model is proposed for coding speech signals. Using Tsay’s nonlinearity test, we first show that the great majority of speech frames contain nonlinearities (over 80% in our test data) when using 20-millisecond speech frames. Frame length correlates with the level of nonlinearity: the longer the frames the higher the percentage of nonlinear frames. Motivated by this result...

a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...

We show that the homogeneous approximation property and the comparison theorem hold for arbitrary coherent frames. This observation answers some questions about the density of frames that are not covered by the theory of Balan, Casazza, Heil, and Landau. The proofs are a variation of the method developed by Ramanathan and Steger. Frames provide redundant non-orthogonal expansions in Hilbert spa...

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- ...