This article discusses the basic categorical algebra for categories of partial frames. Categories of partial frames are labelled by subset selectors that indicate which joins exist. Constructions for limits, colimits, and free functors connecting various categories of partial frames are given. Examples of partial frame categories are given. Subset selectors which preserve surjections are virtua...

in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

in this paper, g-dual function-valued frames in l2(0;1) are in-troduced. we can achieve more reconstruction formulas to ob-tain signals in l2(0;1) by applying g-dual function-valued framesin l2(0;1).

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...

To improve the safety performance of important rooms, such as operating rooms and disaster command centers, during an earthquake, a novel partial seismic isolation system suitable for new existing frame structures is proposed, optimization analysis carried out. Using finite element numerical simulation method, models ordinary structure isolated were established. Considering response room, desig...

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

This paper addresses the natural question: “How should frames be compared?” We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept of a frame measure function: a function which maps each frame to a continuous function. The comparison of these functions induces an equivalence and partial order that allows for a meaningful compa...

Temporal integration of equations possessing continuous symmetries (e.g. systems with translational invariance associated with traveling solutions and scale invariance associated with self-similar solutions) in a “co-evolving” frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with the evolving solution) leads to improved accuracy because of the smaller time derivative in ...