We study some combinatorial principles intermediate between square and weak square. We construct models which distinguish various square principles, and show that a strengthened form of weak square holds in the Prikry model. Jensen proved that a large cardinal property slightly stronger than 1extendibility is incompatible with square; we prove this is close to optimal by showing that 1-extendib...

In this paper, a new structure of photonic crystal fibers (PCFs) with large negative dispersion is presented in order to compensate the positive at wavelength 1.55 μm. The proposed PCF has square lattice structure. basic cladding, it consists four rings, so that each ring number circular holes. final structure, two inner rings cladding are reshaped relative outer rings. first near core stellar ...

Square is a multivariate quadratic encryption scheme proposed in 2009. It is a specialization of Hidden Field Equations by using only odd characteristic elds and also X as its central map. In addition, it uses embedding to reduce the number of variables in the public key. However, the system was broken at Asiacrypt 2009 using a di erential attack. At PQCrypto 2010 Clough and Ding proposed two n...