Original models for direction relations ignored the restriction of topology and distance relations to direction representation. To improve the representation of direction relations model by pondering about the influence of topology and distance relations on direction relations, we categorize direction reference frame into topological reference and coarse directions reference and present a new d...

this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as well as about a reference frame in which this geometry is studied. We consider the evolution of a physical object (the Universe) in “physical” subspace of ex...

This article gives a procedure to convert a frame which is not a tight frame into a Parseval frame for the same space, with the requirement that each element in the resulting Parseval frame can be explicitly written as a linear combination of the elements in the original frame. Several examples are considered, such as a Fourier frame on a spiral. The procedure can be applied to the construction...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

We give a characterization of all (quasi) aane frames in L 2 (R n) which have a (quasi) aane dual in terms of the two simple equations in the Fourier transform domain. In particular, if the dual frame is the same as the original system, i.e. it is a tight frame, we obtain the well known characterization of wavelets. Although these equations have already been proven under some special conditions...

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...

Motivation Online video lectures are a very effective way to revisit the material after having watching live, or to have access to the lecture when impossible to attend it. A very common occurrence, both live and in video, is that the lecturer will stand in front of the whiteboard when trying to explain a concept (Figure 1). There is little that one can do being live in the audience, except may...

18 Frames are conceptual structures that provide context for elements of in19 terpretation; their primary role in an account of text understanding is to 20 explain how our text interpretations can leap far beyond what the text lit21 erally says. The present article explores the role of frames in providing a 22 principled account of the openness and richness of word-meanings, distin23 guishing a...