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 ...

the aim of the present study was to investigate the possibility of improving egg lipids and fatty acids composition of laying hens through inclusion of olive cake plus barley malt rootlets in the diets. seventy, 54-week-old, lohman laying hens were fed for a 12 weeks laying period on 3 iso-caloric and iso-nitrogenous diets contained 0 (control), 28.5 g olive cake (oc) + 25.5 g barley malt rootl...

In petroleum production, Produced Water Re-Injection (PWRI) has earned much interest among disposal methods of the produced water. However, presence of the contaminants in the produced waters usually results in formation damage in well bores and their surrounding fracture systems. In the present study, modeling of external cake formation on a fracture in unsteady-state conditions i...

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...

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...

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...

Fair allocation of goods or resources among various agents is a central task in multiagent systems and other fields. The specific setting where just one divisible resource is to be divided fairly is commonly referred to as cake cutting, and agents are called players in this setting. Cake-cutting protocols aim at dividing a cake and assigning the resulting portions to several players in a way th...

Participants' eye movements were recorded as they inspected a semi-realistic visual scene showing a boy, a cake, and various distractor objects. Whilst viewing this scene, they heard sentences such as `the boy will move the cake' or `the boy will eat the cake'. The cake was the only edible object portrayed in the scene. In each of two experiments, the onset of saccadic eye movements to the targ...

This paper deals with controlling of a semi-batch nonlinear reactor used for chromium sludge regeneration process. The aim is to process the largest amount of chromium filter cake (chromium sludge) in the shortest possible time. The reactor has to be cooled because of strongly exothermic process. For safety reasons the temperature should not exceed 100 °C. In this study the reactor is controlle...