In [13] frames of subspaces extended to continuous version namely c-frame of subspaces. In this article we consider to the relations between cframes of subspaces and local c-frames. Also in this article we give some important relation about duality and parseval c-frames of subspaces.

The structure of binary coproducts in the category of frames is analyzed, and the results are then applied widely in the study of compactness, local compactness (continuous frames), separatedness, pushouts and closed frame homomorphisms.

Recall that a continuous function $fcolon Xto Y$ between Tychonoff spaces is proper if and only if the Stone extension $f^{beta}colon beta Xtobeta Y$ takes remainder to remainder, in the sense that $f^{beta}[beta X-X]subseteq beta Y-Y$. We introduce the notion of ``taking remainder to remainder" to frames, and, using it, we define a frame homomorphism $hcolon Lto M$ to be $beta$-proper, $lambd...

in this paper, the problem of simultaneous shape and size optimization of single-layer barrel vault frames which contains both of discrete and continuous variables is addressed. in this method, the improved magnetic charged system search (imcss) is utilized as the optimization algorithm and the open application programming interface (oapi) plays the role of interfacing analysis software with th...

These notes have a dual goal. On the one hand we shall give an overview of the recently introduced class of scalable frames. These are (finite) frames with the property that each frame vector can be rescaled in such a way that the resulting frames are tight. This process can be viewed as a preconditioning method for finite frames. In particular, we shall: (1) describe the class of scalable fram...

A discrete version of the Zak transform is defined and used to analyze discrete Weyl–Heisenberg frames, which are nonorthogonal systems in the space of square-summable sequences that, although not necessarily bases, provide representations of square-summable sequences as sums of the frame elements. While the general theory is essentially similar to the continuous case, major differences occur w...