We show that if the Boolean hierarchy collapses to level k, then the polynomial hierarchy collapses to BH3(k), where BH3(k) is the k th level of the Boolean hierarchy over Σ2 . This is an improvement over the known results [3], which show that the polynomial hierarchy would collapse to P [O(log . This result is significant in two ways. First, the theorem says that a deeper collapse of the Boole...

this study presents an overview of the different strategies that persian learners of english employ to deal with initial clusters. while vowel epenthesis appears to be the most widespread repair strategy to conform such clusters to persian phonotactics, the location of the epenthetic vowel varies. in this paper, we investigate two approaches that seek to explain the epenthetic site. the first o...

We show that if SAT does not have small circuits, then there must exist a small number of formulas such that every small circuit fails to compute satisfiability correctly on at least one of these formulas. We use this result to show that ifPNP[1℄ = PNP[2℄, then the polynomial-time hierarchy collapses to Sp2 p2 \ p2. Even showing that the hierarchy collapsed to p2 remained open prior to this paper.

In [1], Airault, McKean and Moser observed that the motion of poles of a rational solution to the K-dV or Boussinesq equation obeys the Calogero-Moser dynamical system [2, 3, 4] with an extra condition on the configuration of poles. In [8], Krichever observed that the motion of poles of a solution to the KP equation which is rational in t1 obeys the Calogero-Moser dynamical system. In this note...

Today’s writing instruction performance is greatly aided by oral and nonverbal communication. This study intends to contextualize the lecturer’s visual modes regarding paralinguistic features in class. Data were gathered from PSETs’ self-rated questionnaire that durably video recorded. analysed using IBM SPSS version 20 for descriptive factor analysis, as well ELAN’s software non-verbal linguis...