It is well known that almost perfect nonlinear (APN) functions achieve the lowest possible differential uniformity for functions defined on fields with even characteristic, and hence, from this point of view, they are the most ideal choices for S-boxes in block and stream ciphers. They are also interesting as the link to many other areas, for instance topics in coding theory and combinatorics. ...

In this paper, we consider the Cauchy problem of system quadratic derivative nonlinear Schrödinger equations introduced by Colin and (2004). We determine an almost optimal Sobolev regularity where smooth flow map exists, except for scaling critical case. This result covers a gap left open in papers first second authors (2014, 2019).

Many reasoning problems in Knowledge Representation can be reduced to the satisfiability problem of propositional logic. Since Cook proved that satisfiability is NP-Complete, several classes of propositional formulas have been identified for which satisfiability is polynomially solvable. These polynomial classes form the basis of several tractable knowledge representation systems, for example, ...