The Bulletin—June 19, 2013

19 April 2013 − − François

19 April 2013 − −

19 August 2013.dvi

The amalgamation property (AP) is of particular interest in the study of residuated lattices due to its relationship with various syntactic interpolation properties of substructural logics. There are no examples to date of non-commutative varieties of residuated lattices that satisfy the AP. The variety SemRL of semilinear residuated lattices is a natural candidate for enjoying this property, s...

Package ‘ Zelig ’ February 19 , 2013

Description Zelig is an easy-to-use program that can estimate, and help interpret the results of, an enormous range of statistical models. It literally is ‘‘everyone’s statistical software’’because Zelig’s simple unified framework incorporates everyone else’s (R) code. We also hope it will become ‘‘everyone’s statistical software’’ for applications and teaching, and so have designed Zelig so th...

18.783 Elliptic Curves Spring 2013 Lecture #12 03/19/2013

Theorem 12.2. Let p and q be prime divisors of N , and let `p and `q be the largest prime divisors of p− 1 and q− 1, respectively. If `p ≤ B and `p < `q then Algorithm 12.1 succeeds with probability at least 1− 1 `q . Proof. If a ≡ 0 mod p then the algorithm succeeds in step 2, so we may assume a ⊥ p. When the algorithm reaches ` = `p in step 3 we have b = a m, where m = ∏ `≤`p ` e is a multipl...