Related papers: Congruence frames of frames and $\kappa$-frames
Madden has shown that in contrast to the situation with frames, the smallest dense quotient of a $\kappa$-frame need not be Boolean. We characterise these so-called d-reduced $\kappa$-frames as those which may be embedded as a generating…
We introduce a pointfree theory of convergence on lattices and coframes. A convergence lattice is a lattice $L$ with a monotonic map $\lim_L$ from the lattice of filters on $L$ to $L$, meant to be an abstract version of the map sending…
Strictly zero-dimensional biframes were introduced by Banaschewski and Br\"{u}mmer as a class of strongly zero-dimensional biframes including the congruence biframes. We consider the category of strictly zero-dimensional biframes and show…
Complex tight frames can be canonically viewed as elements of a complex Stiefel manifold. We present a class of spaces of such frames which are simply connected relative to the subspace topology. To this class belongs the space of finite…
The context of this work is that of partial frames; these are meet-semilattices where not all subsets need have joins. A selection function, S, specifies, for all meet-semilattices, certain subsets under consideration, which we call the…
An interesting question about the perturbed sequences is: when do they inherit the properties of the original one? An elegant relation between frames (fusion frames) and their perturbations is the relation of their redundancies. In this…
For a congruence subgroup $\Gamma$, we define the notion of $\Gamma$-equivalence on binary quadratic forms which is the same as proper equivalence if $\Gamma = \mathrm{SL}_2(\mathbb Z)$. We develop a theory on $\Gamma$-equivalence such as…
We review various aspects of a fermionic gauge symmetry, known as the $\kappa$--symmetry, which plays an important role in formulations of superstrings, supermembranes and higher dimensional extended objects. We also review some aspects of…
Loosely speaking, a semi-frame is a generalized frame for which one of the frame bounds is absent. More precisely, given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower)…
K\"unzi and Ferrario have shown that a $T_0$ space is sober if and only if it is bicomplete in the well-monotone quasi-uniformity. We prove a pointfree version of this result: a strictly zero-dimensional biframe is a congruence biframe if…
In this paper we study prime, maximal and two--class congruences from the point of view of the relationships between them in various kinds of universal algebras, as well as their direct and inverse images through morphisms. This research…
In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…
We study the theory of convergence for CAT$(0)$-lattices (that is groups $\Gamma$ acting geometrically on proper, geodesically complete CAT$(0)$-spaces) and their quotients (CAT$(0)$-orbispaces). We describe some splitting and collapsing…
Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…
A common criterion in the design of finite Hilbert space frames is minimal coherence, as this leads to error reduction in various signal processing applications. Frames that achieve minimal coherence relative to all unit-norm frames are…
Recently, frame multipliers, pair frames, and controlled frames have been investigated to improve the numerical efficiency of iterative algorithms for inverting the frame operator and other applications of frames. In this paper, the concept…
In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…
We consider a sub-class of the $f$-divergences satisfying a stronger convexity property, which we refer to as strongly convex, or $\kappa$-convex divergences. We derive new and old relationships, based on convexity arguments, between…
One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a frame and its local components leads to the…
We develop the theory of frames and Parseval frames for finite-dimensional vector spaces over the binary numbers. This includes characterizations which are similar to frames and Parseval frames for real or complex Hilbert spaces, and the…