In a general class of measure-partitioning or fair-division problems, the extremal case occurs when the measures are proportional. Applications are given to classical and recent fair-division problems, and to statistical decision theory, mathematical physics, Banach space theory, and inequalities for continuous random variables.

We test Einstein’s theory of the photoelectric effect, which predicts a linear relation between the energy of light incident on a metal surface and the energy of the emitted electrons. We determine the electron stopping voltage as a function of frequency of incident radiation by illuminating a potassium cathode and constraining the wavelength of incident radiation using several optical band-pas...

No human right to subsistence has yet been settled, due continuing debate over equality and the meanings of proportionality in survival. Across Europe, groceries energy costs are overtaking consumers’ resources pay for them. Economists say this crisis will increase number households subsisting poverty. In light statement significance, overall objective research is discover a critical exegesis o...