The variety of Heyting algebras has a nice property that HS = SH. Heyting algebras are the algebraic dual of intuitionistic descriptive frames. The goal of this paper is to define proper dual notions so as to formulate this algebraic properties in the frame language, and to give a frame-based proof of this property and some other duality theorems.

‎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 short technical note we show how PADL – the process algebraic architectural description language of Bernardo, Ciancarini and Donatiello – can be used to specify AFrames. AFrames exist to structure the machine in a Problem Frames development, and are important in that framework as they allow architectural expertise to be captured and reused therein. Because of the close proximity of PADL...

Preframes (directed complete posets with finite meets that distribute over the directed joins) are the algebras for an infinitary essentially algebraic theory, and can be presented by generators and relations. This result is combined with a general argument concerning categories of commutative monoids to give a very short proof of the localic Tychonoff Theorem. It is also shown how frames can b...

In this paper we discuss the nature of independence of sources in the theory of evidence from an algebraic point of view. Independence in Dempster’s rule is equivalent to independence of frames IF as Boolean sub-algebras. IF , however, cannot be explained neither in terms of classical matroidal independence, nor (even if finite families of frames form geometric lattices) as a cryptomorphic form...

Sequences of unit vectors for which the Kaczmarz algorithm always converges in Hilbert space can be characterized in frame theory by tight frames with constant 1. We generalize this result to the context of frames and bases. In particular, we show that the only effective sequences which are Riesz bases are orthonormal bases. Moreover, we consider the infinite system of linear algebraic equation...

finite normalized tight frames are interesting because they provide decompositionsin applications and some physical interpretations. in this article,we give a recursive method for constructing them.