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.

Abftract: A polyhedral image is a segmentation of the image plane into connected regions, called faces, joined by vertices and edges. The segmentation is represented by a planar network of nodes (vertices, edges, faces) linked by adjacency links. The labeling constraints at a node are all local labelings of the node consistent with itself and all its adjacent neighbors. The local labelings are ...

In this paper, Dirac’s equation in anisotropic Bianchi-type-I background spacetimes is treated with respect to orthonormal frames. By specializing the massless spinor case and metrics power-law scale factors planar symmetry, an analytical expression of approximate time evolution operator (TEO) derived. use operator, all solutions can be generated. construction, these agree asymptotically at ear...

In this study, impacts of residual stress and shear deformation are investigated on 2D steel frames using a new fiber plastic hinge method. Geometry material nonlinearities, stress, deformation, imperfections considered simultaneously in the nonlinear analysis. The proposed method is efficient computational efforts since one-element modeling used for analysis by employing stability functions ca...

Frames play significant role in various areas of science and engineering. Motivated by the work of Chander Shekhar, S. K. Kaushik and Abas Askarizadeh, Mohammad Ali Dehghan, we introduce the concepts of $K$-frames for $B(mathcal{H, K})$ and  we establish some result. Also, we consider the relationships between $K$-Frames and $K$-Operator Frames for $B(mathcal{H})$.

Considering the network structure is one of the new approaches in studying stochastic PERT networks (SPN). In this paper, planar networks are studied as a special class of networks. Two structural reducible mechanisms titled arc contraction and deletion are developed to convert any planar network to a series-parallel network structure.&#10In series-parallel SPN, the completion time distribution...

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...

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- ...

considering the network structure is one of the new approaches in studying stochastic pert networks (spn). in this paper, planar networks are studied as a special class of networks. two structural reducible mechanisms titled arc contraction and deletion are developed to convert any planar network to a series-parallel network structure. in series-parallel spn, the completion time distribution fu...

In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a ...