A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envyfree, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are satisfied, however many cuts are made. It turns out that two of the three properties can be satisfied by ...

Fair Division, unlike most research on fairness in the social sciences and mathematics, is devoted solely to the analysis of constructive procedures for actually dividing things up and resolving disputes, including...

In data envelopment analysis, the relative efficiency of a decision making unit (DMU) is defined as the ratio of the sum of its weighted outputs to the sum of its weighted inputs allowing the DMUs to freely allocate weights to their inputs/outputs. However, this measure may not reflect a the true efficiency of a DMU because some of its inputs/outputs may not contribute reasonably in computing t...

The performance of the units is defined as the ratio of the weighted sum of outputs to the weighted sum of inputs. These weights can be determined by data envelopment analysis (DEA) models. The inputs and outputs of the related (Decision Making Unit) DMU are assessed by a set of the weights obtained via DEA for each DMU. In addition, the weights are not generally common, but rather, they are ve...

A novel domino synthesis of 1,3,5-trisubstituted hydantoin derivatives has been developed in low melting L-(+)-tartaric acid-DMU melt mixtures. The functionalized hydantoins are obtained in good yields from β,γ-unsaturated ketoacids and urea under environmentally benign and simple reaction conditions.

Examining the impacts of data modification is considered as sensitivity analysis. A lot of studies have considered the data modification of inputs and outputs in DEA. The issues which has not heretofore been considered in DEA sensitivity analysis is modification in the number of inputs and (or) outputs and determining the impacts of this modification in the status of efficiency of DMUs. This pa...

examining the impacts of data modification is considered as sensitivity analysis. a lot of studies have considered the data modification of inputs and outputs in dea. the issues which has not heretofore been considered in dea sensitivity analysis is modification in the number of inputs and (or) outputs and determining the impacts of this modification in the status of efficiency of dmus. this pa...