We propose a general technique related to the polytopal Sperner lemma for proving old and new multilabeled versions of Sperner’s lemma. A notable application of this technique yields a cake-cutting theorem where the number of players and the number of pieces can be independently chosen. We also prove multilabeled versions of Fan’s lemma, a combinatorial analogue of the Borsuk-Ulam theorem, and ...

To the best of our knowledge, this is the first report in the literature concerning the bioactive properties of faveleira products. This work focuses on the physicochemical evaluation of faveleira oil, as well as it investigates the bioactive properties of faveleira seeds, faveleira oil and the press cake obtained during the oilseed processing. The seeds were cold pressed and the following test...

Palm oil mill effluent (POME) poses a great threat to the environment. However, it contains valuable resources such as energy, water and nutrients that could be recovered for sustainable development. Currently, anaerobic digester has been employed to recover the energy potential in POME. However, the presence of suspended solids in the digestate hinders the downstream nutrients recovery process...

From 24.06. to 29.06.2007, the Dagstuhl Seminar 07261 Fair Division was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put to...

On a two-dimensional cake, there are m pairwise-disjoint toppings. It is required to cut the cake to m + b pieces, such that each topping is entirely contained in a unique piece, and the total number of empty pieces (b, ”blanks”) is minimized. The minimal number of blanks naturally depends on the geometric constraints of the cake and its pieces. I present tight bounds on the number of blanks wh...

Sandwich panel with central core honeycomb aluminum as one of the main shielding structures because of their high strength-to-weight ratio and improved energy absorption capacity, has been attracted the attention of many researchers and practitioners in recent years. This paper initiates and presents a new type of central core honeycomb formed by hydroforming process. The study is augmented by ...

Sandwich panel with central core honeycomb aluminum as one of the main shielding structures because of their high strength-to-weight ratio and improved energy absorption capacity, has been attracted the attention of many researchers and practitioners in recent years. This paper initiates and presents a new type of central core honeycomb formed by hydroforming process. The study is augmented by ...

To begin, we first rigorously define the model. The cake itself is represented by the real interval [0, 1] and a piece of this cake is a finite union of disjoint intervals X ⊆ [0, 1]. Furthermore, each agent i has a valuation function Vi that represents his/her assessment of pieces of the cake. That is, Vi(X) = x states that the piece X has value x to i. We will assume such Vi have the followin...