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 $B(mathcal{H})$.

Bumblebees tend to face their nest over a limited range of compass directions when learning the nest's location on departure and finding it on their approach after foraging. They thus obtain similar views of the nest and its surroundings on their learning and return flights. How do bees coordinate their flights relative to nest-based and compass-based reference frames to get such similar views?...

In this paper we present a new microscopy configuration based upon temporal tracking of a secondary reflected speckle by imaging the speckle through properly defocused optics. The configuration is used to monitor three-dimensional (3-D) spontaneous contraction of rat cardiac muscle cells while achieving nanometer tracking accuracy at a rate of 30 frames per second (fps) without using interferom...

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- ...

The past few years have witnessed great success in applying deep learning to enhance the quality of compressed image/video. The existing approaches mainly focus on enhancing the quality of a single frame, ignoring the similarity between consecutive frames. In this paper, we investigate that heavy quality fluctuation exists across compressed video frames, and thus low quality frames can be enhan...

A coordinate frame in an n-dimensional space is defined by n mutually orthogonal unit vectors. In particular, for a two-dimensional (2D) space, i.e., n = 2, a coordinate frame is defined by an X axis and a Y axis with these two axes being orthogonal to each other. The intersection between the X axis and the Y axis is the origin of the coordinate frame. For a three-dimensional (3D) space, i.e., ...

‎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 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...