In pointfree topology, a continuous real function on a frame L is a map L(R) → L from the frame of reals into L. The discussion of continuous real functions with possibly infinite values can be easily brought to pointfree topology by replacing the frame L(R) with the frame of extended reals L ( R ) (i.e. the pointfree counterpart of the extended real line R = R ∪ {±∞}). One can even deal with a...

Title of dissertation: FRAME MULTIPLICATION THEORY FOR VECTOR-VALUED HARMONIC ANALYSIS Travis D. Andrews, Doctor of Philosophy, 2014 Dissertation directed by: Professor John J. Benedetto Department of Mathematics A tight frame Φ is a sequence in a separable Hilbert space H satisfying the frame inequality with equal upper and lower bounds and possessing a simple reconstruction formula. We define...

We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity their dilation approach. We prove several results for operator-valued frames concerning duality, disjointeness, complementar...

We give the quantum subset construction of orthomodular lattice-valued finite automata, then we show the equivalence between orthomodular lattice-valued finite automata, orthomodular lattice-valued deterministic finite automata and orthomodular lattice-valued finite automata with empty string-moves. Based on these equivalences, we study the algebraic operations on orthomodular lattice-valued re...

every digital transmission system requires frame alignment. it is necessary to identify the varius signal componets and to bring receiver into phase with respect to the transmission format so that the digits can be properly assembled for demultiplexing. fast and reliable frame alignmant is important, and therefore has been a subject for study. this paper a comprehensive analysis of frame alignm...

The aim of the paper is to obtain a new version Serret-Frenet formulae for quaternionic curve in R4 by using method given Bharathi and Nagaraj. Then, we define helices H named as right left X-helix with help unit vector field X. Since quaternion product not commutative, authors ([4], [7]) have used one-sided multiplication find space related previous studies. Firstly, expressions quaternions. g...

Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying \x is true" and satisfying the \dequotation schema" ' Tr(') for all sentences '? This problem is investigated in the frame of Lukasiewicz innnitely valued logic.

A frame $L$ is called {it coz-dense} if $Sigma_{coz(alpha)}=emptyset$ implies $alpha=mathbf 0$. Let $mathcal RL$ be the ring of real-valued continuous functions on a coz-dense and completely regular frame $L$. We present a description of the socle of the ring $mathcal RL$ based on minimal ideals of $mathcal RL$ and zero sets in pointfree topology. We show that socle of $mathcal RL$ is an essent...

Modal logics for reasoning about the power of coalitions capture the notion of effectivity functions associated with game forms. The main goal of coalition logics is to provide formal tools for modelling the dynamics of a game frame whose states may correspond to different game forms. The two classes of effectivity functions studied are the families of playable and truly playable effectivity fu...