Must φ is felicitous only if φ is not known

Why Is Π < 2 Φ ?

We give a combinatorial proof of the inequality in the title in terms of Fibonacci numbers and Euler numbers. The result is motivated by Sidorenko’s theorem on the number of linear extensions of the poset and its complement. We conclude with some open problems. November 5, 2016. ⋆Department of Mathematics, UCLA, LA, CA 90095. Email: {ahmorales,pak}@math.ucla.edu. Department of Mathematics, UPen...

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...

1 2 Κ ′ 2 ( Φ † Φ ′ ′ ) ( Φ ′ ′

We show how the nearly bi-maximal mixing scenario comes out naturally from gauged SO(3) F flavor symmetry via spontaneous symmetry breaking. An interesting relation between the neutrino mass-squared differences and the mixing angle, i.e., ∆m 2 µe /∆m 2 τ µ ≃ 2|U e3 | 2 is obtained. The smallness of the ratio (or |U e3 |) can also naturally be understood from an approximate permutation symmetry....

( a ) Φ ( a , B ) Φ Φ ( B , C ) ( C , D )

[Investigation of child sexual abuse: if psychoanalysis is used it must not be done in metaphor only].