Viewing the language of modal logic as a language for describing directed graphs, a natural type of directed graph to study modally is one where the nodes are sets and the edge relation is the subset or superset relation. A well-known example from the literature on intuitionistic logic is the class of Medvedev frames hW,Ri where W is the set of nonempty subsets of some nonempty finite set S, an...

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In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ wi...

Inertial frames are frames related by a constant velocity along any axis. An object is at rest in an inertial frame when its position in space does not change with time. We consider two inertial frames: the 26-100 (S) frame in which we are at rest and the Space Shuttle frame (S ′) which moves relative to S with a velocity u along the x axis and in which the Shuttle is at rest. Newton postulated...

The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $varphi_U: U to Y$ on each member $U$ of an open cover ${mathfrak C}$ of $X$ such that $varphi_Umid U cap V = varphi_V mid U cap V$ for all $U,V in {mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar cla...

In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames  are given.  A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is ...

MapC(A,X) = MorC(A⊗∆, X), where we take the morphisms on each component of the cosimplicial objectA⊗∆• to get a simplicial set of morphisms associated to the pair A,X ∈ C. We have a dual approach involving simplicial function objects X 7→ X∆ instead of cosimplicial objects A 7→ A ⊗ ∆•, but in a simplicial model category, we have an adjunction relation between these functors, so that both constr...

UWGSP4 is configured with a parallel architecture for image processing and a pipelined architecture for computer graphics. The system's peak performance is 1,280 MFLOPS for image processing and over 200,000 Gouraud shaded 3-D polygons per second for graphics. The simulated sustained performance is about 50% of the peak performance in general image processing. Most of the 2-D image processing fu...

Three sets of 20 trinucleotides are preferentially associated with the reading frames and their 2 shifted frames of both eukaryotic and prokaryotic genes. These 3 sets are circular codes. They allow retrieval of any frame in genes (containing these circular code words), locally anywhere in the 3 frames and in particular without start codons in the reading frame, and automatically with the readi...