The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of frames  which is important for frame applications, have been specified  completely for the c...

In this article, we consider pair frames in Banach spaces and   introduce Banach pair frames. Some various concepts in the frame theory such as frames, Schauder frames, Banach frames and atomic decompositions are considered as   special kinds of (Banach) pair frames.  Some frame-like inequalities  for (Banach)  pair frames are presented. The elements that participant  in the construction of (Ba...

Analysis of long image sequence is important for visual surveillance, mobile robotics, and areas where a dynamic scene is observed over a long period of time, which means that a compact representation is needed to efficiently process it. In this report a novel representation for motion segmentation in long image sequences is presented. This representation, the feature interval graph, measures t...

In this paper we encode some of the reasoning methods used in frame based knowledge representation languages in answer set programming (ASP). In particular, we show how “cloning” and “unification” in frame based systems can be encoded in ASP. We then show how some of the types of queries with respect to a biological knowledge base can be encoded using our methodology. We also provide insight on...

Efficient and accurate similarity searching for a large amount of time series data set is an important but non-trivial problem. Many dimensionality reduction techniques have been proposed for effective representation of time series data in order to realize such similarity searching, including Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), the Adaptive Piecewise Consta...

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...