We study the classic problem of fairly dividing a heterogeneous resource (”cake”) among several agents with different preferences. In our setting, the resource is already divided among several ”old” agents. When ”young” agents come, the resource should be re-divided in a way that is fair both for the young and for the old agents. Motivated by land redivision and other two-dimensional division p...

Cake cutting is a common metaphor for the division of a heterogeneous divisible good. There are numerous papers that study the problem of fairly dividing a cake; a small number of them also take into account self-interested agents and consequent strategic issues, but these papers focus on fairness and consider a strikingly weak notion of truthfulness. In this paper we investigate the problem of...

For cake cutting, cuts are parallel to an axis or segment and yield rectangular pieces. As such, cutting a cake is viewed as dividing a line segment. For pie cutting, cuts are radial from the center of a disc to the circumference and yield sectors or wedge-shaped pieces. As such, cutting a pie is viewed as dividing a circle. This difference in topology is apparent in the minimal number of cuts ...

CMC polymer is used as an additive to decrease water loss and mud-cake-thickness in mud drilling. In this study, the effect of CMC and CMC nanoparticles on water loss and mud-cake-thickness in mud drilling is investigated. CMC nanoparticles are made by using of ball milling and their size is measured by Particle size analyzer. CMC and CMC nanoparticles which were prepared by Hamilton batch mixe...

Are there individual differences in children's prediction of upcoming linguistic input and what do these differences reflect? Using a variant of the preferential looking paradigm (Golinkoff, Hirsh-Pasek, Cauley, & Gordon, 1987), we found that, upon hearing a sentence like, "The boy eats a big cake," 2-year-olds fixate edible objects in a visual scene (a cake) soon after they hear the semantical...

Plant growth promoting substances are widely used in modern agriculture. Several products in the market are humic substances isolated from different sources. The filter cake, a residue of sugar production, is a rich and renewable source of organic matter and these characteristics place the filter cake as a possible source of plant growth promoting substances. Humic acids (HA) from filter cake w...

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 ...

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...

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...