We wish to consider the following type of cake division problem: There are p individuals. Each individual has available a measure that he or she uses to evaluate the sizes of pieces of cake. We wish to partition our cake into q pieces in such a way that the various evaluations that the individuals make of the sizes of the pieces satisfy certain pre-assigned equalities and inequalities. Our main...

Enzymatic hydrolysis ofxylan, and isolation ofhydrolysis products. Cotton-seed cake, lOOOg of air-dried matter (containing 458g of total pentose analyzed by the orcinol-HCl method),1) was soaked in 600 ml of2% NaOH solution at room temperature for 4 days, to promote the enzymatic susceptibility of xylan in the cake. The alkali-treated cake (790g of air-dried matter containing 394g of total pent...

Unconditionally secure authentication codes with arbitration (A 2-codes) protect against deceptions from the transmitter and the receiver as well as that from the opponent. In this paper, we present combinatorial lower bounds on the cheating probabilities and the sizes of keys of A 2-codes. Especially, our bounds for A 2-codes without secrecy are all tight for small size of source states.

Consider a gambling game in which we are allowed to repeatedly bet a portion of our bankroll at favorable odds. We investigate the question of how to minimize the expected number of rounds needed to increase our bankroll to a given target amount. Specifically, we disprove a 50-year old conjecture of L. Breiman [1], that there exists a threshold strategy that optimizes the expected number of rou...

objective:mold contamination of cakes and the possibility of mold growth can pose a serious health problem. bakery products include various ingredients, which regularly contain molds. these microorganisms on cakes can come from the air, contaminated packaging materials and other sources.methods: in this study, a total of 500 fungal isolates representing 36 species, were identified from cake sam...

the scope for using sunflower cake in ration formulation was tested in 6 horses employed for equine tourism. three experimental diets providing the same amount of proteins and energy as the control diet were formulated using rising doses of sunflower cake (sd3: 0.3 kg; sd6: 0.6 kg and sd10: 1.0 kg). digestibility evaluation using internal markers showed that rising sunflower cake doses reduced ...

A class of Nash implementation problems of particular economic interest is that of implementing the core in games of pure allocation, or ‘cake division’. Mechanisms that have been proposed to solve this type of problem often involve off-equilibrium ‘punishments’ that lie in the interior of the feasible set; that is, in which not all the cake is allocated. They also tend to make use of extraneou...

We introduce the simultaneous model for cake cutting (the fair allocation of a divisible good), in which agents simultaneously send messages containing a sketch of their preferences over the cake. We show that this model enables the computation of divisions that satisfy proportionality — a popular fairness notion — using a protocol that circumvents a standard lower bound via parallel informatio...

We propose an online form of the cake cutting problem. This models situations where players arrive and depart during the process of dividing a resource. We show that well known fair division procedures like cut-and-choose and the Dubins-Spanier moving knife procedure can be adapted to apply to such online problems. We propose some desirable properties that online cake cutting procedures might p...

The use of biological phosphorus removal by activated sludge has been shown to have adverse effects downstream in the solids handling processes of anaerobic digestion. From struvite formation problems within the digesters to increased polymer dosage and dewatered biosolids solids content. The fundamental cause is unknown however phosphorus removal prior to anaerobic digestion has been shown to ...