Pasting and Reversing Approach to Matrix Theory

The aim of this paper is to study some aspects of matrix theory through Pasting and Reversing. We start giving a summary of previous results concerning to Pasting and Reversing over vectors and matrices, after we rewrite such properties of Pasting and Reversing in matrix theory using linear mappings to finish with new properties and new sets in matrix theory involving Pasting and Reversing. In particular we introduce new linear mappings: Palindromicing and Antipalindromicing mappings, which allow us to obtain palindromic and antipalindromic vectors and matrices.Comment: 19 page

Multi-scale structure, pasting and digestibility of adlay (Coixlachryma-jobi L.) seed starch

peer-reviewedThe hierarchical structure, pasting and digestibility of adlay seed starch (ASS) were investigated compared with maize starch (MS) and potato starch (PS). ASS exhibited round or polyglonal morphology with apparent pores/channels on the surface. It had a lower amylose content, a looser and more heterogeneous C-type crystalline structure, a higher crystallinity, and a thinner crystalline lamellae. Accordingly, ASS showed a higher slowly digestible starch content combined with less resistant starch fractions, and a decreased pasting temperature, a weakened tendency to retrogradation and an increased pasting stability compared with those of MS and PS. The ASS structure-functionality relationship indicated that the amylose content, double helical orders, crystalline lamellar structure, and surface pinholes should be responsible for ASS specific functionalities including pasting behaviors and in vitro digestibility. ASS showed potential applications in health-promoting foods which required low rearrangement during storage and sustainable energy-providing starch fractions

Making the Cut: Lattice Kirigami Rules

In this paper we explore and develop a simple set of rules that apply to cutting, pasting, and folding honeycomb lattices. We consider origami-like structures that are extinsically flat away from zero-dimensional sources of Gaussian curvature and one-dimensional sources of mean curvature, and our cutting and pasting rules maintain the intrinsic bond lengths on both the lattice and its dual lattice. We find that a small set of rules is allowed providing a framework for exploring and building kirigami -- folding, cutting, and pasting the edges of paper.Comment: 5 pages, 5 figure

On Deformations of Pasting Diagrams

We adapt the work of Power to describe general, not-necessarily composable, not-necessarily commutative 2-categorical pasting diagrams and their composable and commutative parts. We provide a deformation theory for pasting diagrams valued in $k$-linear categories, paralleling that provided for diagrams of algebras by Gerstenhaber and Schack, proving the standard results. Along the way, the construction gives rise to a bicategorical analog of the homotopy G-algebras of Gerstenhaber and Voronov.Comment: 31 page