The Arrow impossibility theorem when individual preferences are weak orders is equivalent to the HEX game theorem. Because Gale showed that the Brouwer fixed point theorem is equivalent to the HEX game theorem, this paper indirectly shows the equivalence of the Brouwer fixed point theorem and the Arrow impossibility theorem. Chichilnisky showed the equivalence of her impossibility theorem and t...

Impossible figures are striking examples of inconsistencies between global and local perceptual structures, in which the overall spatial configuration of the depicted image does not yield a coherent three-dimensional object. In order to investigate whether structural "impossibility" is an important perceptual property of depicted objects, we used a category formation task in which subjects were...

It is well known that it impossible to clone an arbitrary quantum state. However, this inability does not lead directly no-cloning of coherence. Here, we show the coherence state which a stronger statement than 'no-cloning state'. In particular, with ancillary system as machine state, states whose greater on transformations are defined. Also, characterize class for cloning will be possible give...