Considering operators defined using Structural Operational Semantics (SOS), commutativity axioms are intuitive properties that hold for many of them. Proving this intuition is usually a laborious task, requiring several pages of boring and standard proof. To save this effort, we propose a syntactic SOS format which guarantees commutativity for a set of composition operators.

We consider scalar field theory with space and space-time-dependent non-commutativity. In perturbation theory, we find that the structure of the UV/IR mixing is quite different from cases with constant non-commutativity. In particular, UV/IR mixing becomes intertwined in an interesting way with violations of momentum conservation. email: [email protected] email: [email protected]

Second-price auctions are designed to induce people to reveal their private preferences for a good. Laboratory evidence suggests that while these auctions do a reasonable job on aggregate, they fall short at the individual level, especially for bidders who are off-margin of the market-clearing price. Herein we introduce and explore whether a random nth-price auction can engage all bidders to bi...

Stronger light intensity fluctuations are pursued by related applications such as optical resolution, image enhancement, and beam positioning. In this paper, an Nth-order fluctuation amplifier is proposed, which was demonstrated a four-wave mixing process with different statistical distribution coupling lights. Firstly, its amplification mechanism revealed both theoretically experimentally. The...