I) Given a segment-cuttable polygon P drawn on a planar piece of material Q, we show how to cut P out of Q by a (short) segment saw with a total length of the cuts no more than 2.5 times the optimal. We revise the algorithm of Demaine et al. (2001) so as to achieve this ratio. (II) We prove that any collection R of n disjoint1 axis-parallel rectangles drawn on a planar piece of material Q is cu...

This paper proposes a cake-cutting protocol using cryptography when the cake is a heterogeneous good that is represented by an interval on a real line. Although the Dubins-Spanier moving-knife protocol with one knife achieves simple fairness, all players must execute the protocol synchronously. Thus, the protocol cannot be executed on asynchronous networks such as the Internet. We show that the...

the aim of this study was to determine the optimal cutting cycle in an uneven-aged beech forest in the north of iran. first of all, a logistic growth model was determined for an uneven aged forest. then, the stumpage price was predicted via an autoregressive model. the average stumpage price of beech was derived from actual timber, round wood, fire and pulpwood prices at road side minus the var...

We analyze a class of proportional cake-cutting algorithms that use a minimal number of cuts (n − 1 if there are n players) to divide a cake that the players value along one dimension. While these algorithms may not produce an envy-free or efficient allocation—as these terms are used in the fair-division literature—one, divide-and-conquer (D&C), minimizes the maximum number of players that any ...

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...

The aim of this study was to determine the optimal cutting cycle in an uneven-aged beech forest in the North of Iran. First of all, a logistic growth model was determined for an uneven aged forest. Then, the stumpage price was predicted via an autoregressive model. The average stumpage price of beech was derived from actual timber, round wood, fire and pulpwood prices at road side minus the var...

An unceasing problem of our prevailing society is the fair division of goods. The problem of fair cake cutting is dividing a heterogeneous and divisible resource, the cake, among n players who value pieces according to their own measure function. The goal is to assign each player a not necessarily connected part of the cake that the player evaluates at least as much as her proportional share. I...

The aim of this study was to quantify the impact two cutting severities on dynamics aerial and perennial (root plus crown) biomass lucerne (Medicago sativa L.) plants cultivars contrasting fall dormancy rating during establishment phase. We worked at Unidad Integrada Balcarce with (non-winter dormant: FD10; semi-winter FD6) (40 100 mm) defining four treatments (FD6-40 mm, FD6-100 FD10-40 mm FD1...

We construct canonical heights of subvarieties for dynamical systems of several morphisms associated with line bundles defined over a number field, and study some of their properties. We also construct invariant currents for such systems over C. Introduction Let X be a projective variety over a field K and fi : X → X (i = 1, · · · , k) morphisms over K. Let L be a line bundle on X, and d > k a ...