‎In this paper‎, ‎first we develop the duality concept for $g$-Bessel sequences‎ ‎and Bessel fusion sequences in Hilbert spaces‎. ‎We obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎We also expand every $g$-Bessel ‎sequence to a frame by summing some elements‎. ‎We define the restricted isometry property for ‎$g$-frames and generalize some resu...

In the study, weight efficiency of Triple Friction Pendulum Bearing (TFP) Isolators is investigated on optimal planar steel frames. For this investigation, an optimization program based Artificial Bee Colony (ABC) algorithm have been developed for study. design frames, structure should satisfy strength, inter-story drift, top-story drift and geometric requirements that are implemented from LRFD...

Understanding thin sheets, ranging from the macro to nanoscale, can allow control of mechanical properties such as deformability. Out-of-plane buckling due in-plane compression be a key feature in designing new materials. While thin-plate theory predict critical thresholds for frames and nanoribbons at very low temperatures, unifying framework describe effects thermal fluctuations on more eleva...

In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and ...

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...