Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the …rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The conditi...

For the multi-peg Tower of Hanoi problem with k ≥ 4 pegs, so far the best solution is obtained by the Stewart’s algorithm [15] based on the the following recurrence relation: Sk(n) = min 1≤t≤n � 2 · Sk(n− t) + Sk−1(t) � , S3(n) = 2 − 1. In this paper, we generalize this recurrence relation to Gk(n) = min 1≤t≤n � pk · Gk(n− t) + qk · Gk−1(t) � , G3(n) = p3 · G3(n− 1) + q3, for two sequences of a...

every digital transmission system requires frame alignment. it is necessary to identify the varius signal componets and to bring receiver into phase with respect to the transmission format so that the digits can be properly assembled for demultiplexing. fast and reliable frame alignmant is important, and therefore has been a subject for study. this paper a comprehensive analysis of frame alignm...

A generalized continuous frame is a family of operators on a Hilbert space H which allows reproductions of arbitrary elements of H by continuous superpositions. Generalized continuous frames are natural generalization of continuous and discrete frames in Hilbert spaces which include many recent generalization of frames. In this article,we associate to a generalized continuous frame suitable Ban...

G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first generalize the concept of g-frames to Hilbert modules over pro-C*-algebras. Then, we introduce the g-frame operators in such spaces and show that they sha...

Video frame interpolation aims at synthesizing intermediate frames from nearby source while maintaining spatial and temporal consistencies. The existing deep-learning-based video methods can be roughly divided into two categories: flow-based kernel-based methods. performance of is often jeopardized by the inaccuracy flow map estimation due to oversimplified motion models, that tends constrained...

For a polyatomic molecule at zero total angular momentum, this paper shows that an internal motion with nonzero internal angular momentum within a (generalized) Eckart frame will produce a net rotation of the (generalized) Eckart frame in the center-of-mass frame. For a polyatomic molecule at nonzero total angular momentum, an internal motion within a generalized Eckart frame with nonzero orbit...