Strict partitions and discrete dynamical systems

AbstractWe prove that the set of partitions with distinct parts of a given positive integer under dominance ordering can be considered as a configuration space of a discrete dynamical model with two transition rules and with the initial configuration being the singleton partition. This allows us to characterize its lattice structure, fixed point, and longest chains as well as their length, using Chip Firing Game theory. Finally, we study the recursive structure of infinite extension of the lattice of strict partitions

Physico-chemical properties of fourteen popular cocoa bean varieties in Dongnai-highland Vietnam

Cocoa (Theobroma cacao L.) is a major, crucial economic, global crop and has been maintained several nutritional benefits. The exporting volume of Vietnamese cocoa bean is increasing in the world cocoa trade. The beans of fourteen popular cocoa varieties that are commonly cultivated in Trang Bom (Dong Nai, Vietnam) were characterized for their physico-chemical qualifications on the background of post-fermented cocoa beans and dehydration in the region of Trang Bom-Dong Nai. The physical properties were determined based on mass ratio and bean’s dimension (lengh, width and thickness) as well as chemical (proximate) composition (total crude protein, ash, moisture, and lipid). These values were analysed using AOAC methods. The largest-size beans were found for the TD8 variety (1.5 g of mass, 25.02 mm of length, 14.28 mm of width and 7.96 mm of thickness). The moisture content of the cocoa beans was in the range between 5.64 and 6.99 (% wb) and the ash content in the range between 3.67% and 2.47% (wb). Noticeably, the fat content ratio (the most important value of cocoa bean) found in 8 varieties (TD1, TD2, TD5, TD9, TD11, TD12, TD13, TD14) was over 50%, thus these varieties are worthy chemical component especially for exported cocoa bean and industrized cultivation (extending the cultivation producing area)