We extend the classic cake-cutting problem to a situation in which the ”cake” is divided among families. Each piece of cake is owned and used simultaneously by all members of the family. A typical example of such a cake is land. We examine three ways to assess the fairness of such a division, based on the classic no-envy criterion: (a) Average envy-freeness means that for each family, the avera...

Cryofixation, freeze-etch techniques were used to study the structure of cake batters made from a lean cake formulation before heating and after heating to temperatures up to l00-l02 °C. Batters were prepared without added emulsifiers and with saturated and unsaturated monoglycerides replacing 5 and l 0% of the oil. Unsaturated monoglyceri des were more effective than saturated monoglycerides i...

We consider the problem of fairly dividing a heterogeneous cake between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare standpoint. Here, we show that in some cases, discarding some of the cake and fairly dividing only the remainder may be socially preferable to any fair division of th...

We consider the classic cake-divison problem when the cake is a heterogeneous good represented by an interval in the real line. We provide a mechanism to implement, in an anonymous way, an envy-free and e¢cient allocation when agents have private information on their preferences. The mechanism is a multistep sequential game form in which each agent at each step receives a morsel of the cake tha...

Stochastic sequential bargaining games (Merlo and Wilson (1995, 1998)) have found wide applications in various …elds including political economy and macroeconomics due to their ‡exibility in explaining delays in reaching an agreement. In this paper, we present new results in nonparametric identi…cation of such models under di¤erent scenarios of data availability. First, we give conditions for a...

Five new mathematical triple fouling models were developed to explore the flux decline behavior during the microfiltration. The first model was developed by the assumption of the successive effects of standard mechanism, intermediate pore blockage and cake formation by using the standard blocking flux expression in the model calculations. The second and third models also obtained by the success...

A fixed bed pyrolysis has been designed and fabricated for obtaining liquid fuel from mustard de-oiled cake. Thermal pyrolysis of mustard deoiled cake were carried out in a semi batch reactor made up of stainless steel at temperature range from 450 0 C to 600 0 C and at a rate of 150C /min to produce bio-fuel. The maximum yield of oil was 51% on wt. % basis for mustard de-oiled cake, it was obt...

We consider discrete protocols for the classical Steinhaus cake cutting problem. Under mild technical conditions, we show that any deterministic strategy-proof protocol for two agents in the standard Robertson-Webb query model is dictatorial, that is, there is a fixed agent to which the protocol allocates the entire cake. For n > 2 agents, a similar impossibility holds, namely there always exis...

Cake is a hybrid system which provides reasoning facilities for the Programmer's Apprentice. This paper describes the architecture of Cake, which is divided into eight layers, each with associated representations and reasoning procedures. The operation of Cake is illustrated by a complete trace of the solution of an example reasoning problem. We also argue that a hybrid system in general is cha...

We consider the problem of fairly dividing a heterogeneous cake between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare standpoint. Here, we show that in some cases, discarding some of the cake and fairly dividing only the remainder may be socially preferable to any fair division of th...