Woven codes with outer binary block codes and additional permutation are presented. This enables the construction of a new class of woven block codes, where the minimum distance is about twice the product of the minimum distances of the component codes.

The Woven Stories is a tool for writing stories collaboratively. In order to represent the written stories adaptively, we need to construct description about the content of the stories and the relative information between di erent stories. The formal presentation of Woven Stories is called StoryML and it can be used for adaptive content representation of the stories.

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...

Due to the presence of through-thickness reinforcement, 3D woven composites have superior fracture toughness, fatigue life, and damage tolerance compared to laminated composites. Furthermore, 3D woven composites exhibit a progressive damage behavior which is more benign than the typical catastrophic failure behavior of laminated composites. These properties lead to high specific energy absorpti...

Three dimensional (3D) woven composites have attracted the interest of academia and industry thanks to their damage tolerance characteristics and automated fabric manufacturing. Although much research has been conducted to investigate their out-of-plane “through thickness” properties, still their in-plane properties are not fully understood and rely on extensive experimentation. To date, the li...

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...