In this paper we get some results and applications for duals and approximate duals of g-frames in Hilbert spaces. In particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of Hilbert spaces. We also obtain some results for perturbations of approximate duals.

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...

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 ...

In this paper, g-dual function-valued frames in L2(0;1) are in- troduced. We can achieve more reconstruction formulas to ob- tain signals in L2(0;1) by applying g-dual function-valued frames in L2(0;1).

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Automatic completion of frame-to-frame (F2F) relations in the FrameNet (FN) hierarchy has received little attention, although they incorporate meta-level commonsense knowledge and are used in downstream approaches. We address the problem of sparsely annotated F2F relations. First, we examine whether the manually defined F2F relations emerge from text by learning text-based frame embeddings. Our...

In this paper, we focus on techniques for incremen-tal constraint-based connguration with discrete and continuous variables. We show how to formalize constraint knowledge using compatibility and activity constraints (Mittal 1990) and how this knowledge is used for reasoning within an intelligent CAD system. Most technical as opposed to spatial constraint connguration systems use algorithms for ...