An extrapolation procedure to obtain the total fringe number from Gouy fringe pattern data

A rapid new procedure is described for getting the total number of fringes J from Gouy fringe pattern data. This PQ method is exact and the results excellent (within 0.01–0.03 fringe) for ideal systems (_j=0 for all j, Q₀=0). Such systems include most binaries; for these, the diffusion coefficient is either constant or a polynomial function of concentration with small concentration differences. For multicomponent systems and some binaries, Q₀ can be significantly different from 0. In these cases, the PQ method unambiguously gives the integer number of fringes. If in addition Q₀/Q₁ is larger than 2.0, then J obtained from a second extrapolation procedure is also good.     

Sacks forcing,Laver forcing,and Martin's axiom

Summary In this paper we study the question assuming MA+CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalent to the question of what is the additivity of Marczewski's ideals ⁰. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals.Research partially supported by NSF grant 8801139