1 5 A ug 1 99 4 More forcing notions imply diamond

More forcing notions imply diamond

We prove that the Sacks forcing collapses the continuum onto d, answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses ω2 then it forces ♦ω1 . Research partially supported by KBN 654/2/91 Research partially supported by “Basic Research Foundation” administered by The Israel Academy of Sciences and Humanities. Publication 475.

4 A ug 1 99 9 Stokes ’ drift : a rocking ratchet

We derive the explicit analytic expression for the Stokes' drift in one dimension in the presence of a dichotomic Markov forcing. For small amplitudes of the forcing, the drift is enhanced, but the enhancement in reduced with increasing frequency of the forcing. On the other hand, a reduction of the drift or even a flux reversal can be induced at larger amplitudes, while the flux is now found t...

ar X iv : h ep - p h / 95 08 24 5 v 1 5 A ug 1 99 5 UCSD / PTH 95 - 07 June 1995 EFFECTIVE FIELD THEORIES

These lectures introduce some of the basic notions of effective field theories, as used in particle physics. The topics discussed are the ∆S = 1 and ∆S = 2 weak interactions, and chiral perturbation theory as applied to mesons, baryons, and hadrons containing heavy quarks.

ar X iv : m at h / 98 08 06 5 v 1 [ m at h . Q A ] 1 4 A ug 1 99 8 QUANTUM DETERMINANTS AND QUASIDETERMINANTS

m at h . L O ] 2 5 A ug 1 99 8 Forcing for hL , hd and Depth

We address three questions of Donald Monk. Two of them, [M2, Problems 50, 54], are related to attainment problems in equivalent definitions of hereditary density hd and hereditary Lindelöf degree hL. The third problem is [M2, Problem 14] and it is about subalgebra– Depth–relation. ∗ The second author thanks KBN (Polish Committee of Scientific Research) for partial support through grant 2 P03 A ...