Sur l'équation φ (x+k)=φ (x). II

The Effective Action for Local Composite Operators Φ(x) and Φ(x)

The generating functionals for the local composite operators, Φ2(x) and Φ4(x), are used to study excitations in the scalar quantum field theory with λΦ4 interaction. The effective action for the composite operators is obtained as a series in the Planck constant h̄, and the twoand four-particle propagators are derived. The numerical results are studied in the space-time of one dimension, when the...

Recherche sur l'immunisations anticlaveleuse. II. Sur un nouvea vaccjn tissulaire formule

The number of solutions of φ ( x ) =

An old conjecture of Sierpiński asserts that for every integer k > 2, there is a number m for which the equation φ(x) = m has exactly k solutions. Here φ is Euler’s totient function. In 1961, Schinzel deduced this conjecture from his Hypothesis H. The purpose of this paper is to present an unconditional proof of Sierpiński’s conjecture. The proof uses many results from sieve theory, in particul...

Sur la courbe modulaire X E (7)

φ φ φ φ φ φ k From Max - SAT to Min - UNSAT : Insights and Applications

This report describes a strong connection between maximum satisfiability and minimally-unsatisfiable subfor-mulas of any constraint system, as well as techniques for exploiting it. Focusing on CNF formulas, we explore this relationship and present novel algorithms for extracting minimally-unsatisfiable subformulas, including one that finds all such subformulas. We present experimental results s...