We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality  for some kinds of g-frames. Finally, we illustrate an example which provides a  suitable translation from discrete frames to Sun's g-frames.

yielding elements (ye) are among those devices that not only help control structural damages, but make better seismic behavior by concentrating the frames in some removable part of the structures. ye are located at the intersection of concentric braced frame (cbf) in a rectangular shape. in this paper, seismic behavior of the frames with ye will be investigated. for this reason, 5 braced steel ...

Quality requirements, like security requirements, are difficult to elicit, especially if they cross multiple domains. Understanding these domains is an important issue in the requirements engineering process for the corresponding systems. Well-known requirements engineering approaches, such as goal-oriented techniques provide a good starting point in capturing security requirements in the form ...

Finite tight frames have many applications and some interesting physical interpretations. One of the important subjects in this area is the ways for constructing such frames. In this article we give a concrete method for constructing finite normalized frames using Platonic solids.

We develop an algebraic procedure to rotate a general NewmanPenrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars Ψ1 and Ψ3 equal to zero, assuming that initially all the Weyl scalars are non vanishing. The new frame highlights the physical properties of the spacetime. In particular, in a Petrov Type I spacetime, setting Ψ1 and Ψ3 to zero makes apparent the superposition of...

response modification factor (r-factor) is one of the seismic design parameters to consider nonlinear performance of building structures during strong earthquake. relying on this, many seismic design codes led to reduce earthquake loads imposed to the structure. the present paper tries to evaluate the r-factors of conventional concentric braced frames (cbfs) and special moment frames (mrfs) in ...

We establish a close and previously unknown relation between quantales and groupoids, in terms of which the notion of étale groupoid is subsumed in a natural way by that of quantale. In particular, to each étale groupoid, either localic or topological, there is associated a unital involutive quantale. We obtain a bijective correspondence between localic étale groupoids and their quantales, whic...

This paper describes a novel sensor system to estimate the motion of a stereo camera. Local invariant image features are matched between pairs of frames and linked into image trajectories at video rate, providing the so-called visual odometry, i.e., motion estimates from visual input alone. Our proposal conducts two matching sessions: the first one between sets of features associated to the ima...

Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...