We investigate the values of the Remak height, which is a weighted product of the conjugates of an algebraic number. We prove
that the ratio of logarithms of the Remak height and of the Mahler measure for units αof degree d is everywhere dense in the maximal interval [d/2(d-1),1] allowed for this ratio. To do this, a “large” set of totally positive Pisot units is constructed. We also give a lower
bound on the Remak height for non-cyclotomic algebraic numbers in terms of their degrees. In passing, we prove some results
about some algebraic numbers which are a product of two conjugates of a reciprocal algebraic number.
1 Introduction The representation of vowel height, as Pulleyblank (2011) points out, is not trivial: in a five-vowel system (say, Greek), i would typically be categorised as high, e as mid, a as low. A seven-vowel system (Brazilian
A description of phase transitions as recorded by differential scanning calorimetry (DSC) is given. A new numberN is defined asN=h′/h, whereh is the height of a transition peak for a mass of samplem and a heating rate †p andh′ is the height of the same peak for a mass2m or a heating rate2†p.N is theoretically derived in the case of isothermal and nonisothermal first order phase transitions and of a second order phase transition. The equivalence of mass and heating rate is proved. An example of the possible use ofN is given.