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...

an efficient and green method for the synthesis of pyrano[3,2-c]chromene or pyrano[4,3-b]pyrone derivatives is described by using a three-component condensation process of malononitrile, aldehyde, and 4-hydroxycoumarine or 4-hydroxypyrone in [bmim]bf4-licl as an ionic liquid.

Abstract-A novel and efficient method has been developed for the synthesis of pyrano[3,2-c]quinoline-2,5-dione derivatives by the convenient ultrasound-mediated condensation of 4-hydroxyquinolin-2-one with Meldrum’s acid and aldehydes in the presence of a catalytic amount of [HMIm]HSO4 as a green, efficient and reusable acidic ionic liquid medium. The stability of the ionic liquid during the re...

The acid dyes are one of the most widely used commercial dyes used in the textile industries. This work investigates the ability of magnetite nanoparticles functionalized with imidazolium based ionic liquid as an efficient sorbent for removal of the Acid Blue 113 from wastewater. Fourier Transform Infrared Spectroscopy FT-IR, X-ray diffraction XRD and Transmission Electron Microscopy TEM were u...

abstract-a novel and efficient method has been developed for the synthesis of pyrano[3,2-c]quinoline-2,5-dione derivatives by the convenient ultrasound-mediated condensation of 4-hydroxyquinolin-2-one with meldrum’s acid and aldehydes in the presence of a catalytic amount of [hmim]hso4 as a green, efficient and reusable acidic ionic liquid medium. the stability of the ionic liquid during the re...