Residual Irreducibility of Compatible Systems

Irreducibility of A-hypergeometric systems

We give an elementary proof of the Gel’fand–Kapranov–Zelevinsky theorem that non-resonant Ahypergeometric systems are irreducible. We also provide a proof of a converse statement. c ⃝ 2011 Royal Netherlands Academy of Arts and Sciences. Published by Elsevier B.V. All rights reserved.

Compatible Systems and Correspondences

Bigness in Compatible Systems

Clozel, Harris and Taylor have recently proved a modularity lifting theorem of the following general form: if ρ is an l-adic representation of the absolute Galois group of a number field for which the residual representation ρ comes from a modular form then so does ρ. This theorem has numerous hypotheses; a crucial one is that the image of ρ must be “big,” a technical condition on subgroups of ...

Compatible Deductive Systems of Pulexes

Imai and Iséki [1] introduced the concept of BCK-algebra as a generalization of notions of set difference operation and propositional calculus. The notion of pseudo-BCK algebra was introduced by Georgescu and Iorgulescu [2] as generalization of BCK-algebras not assuming commutativity. Hájek [3] introduced the concept of BL-algebras as the general semantics of basic fuzzy logic (BL-logic). Iorgu...

Exponential law as a more compatible model to describe orbits of planetary systems

  According to the Titus-Bode law, orbits of planets in the solar system obey a geometric progression. Many investigations have been launched to improve this law. In this paper, we apply square and exponential models to planets of solar system, moons of planets, and some extra solar systems, and compare them with each other.