The trumping relation and the structure of the bipartite entangled states

The majorization relation has been shown to be useful in classifying which transformations of jointly held quantum states are possible using local operations and classical communication. In some cases, a direct transformation between two states is not possible, but it becomes possible in the presence of another state (known as a catalyst); this situation is described mathematically by the trumping relation, an extension of majorization. The structure of the trumping relation is not nearly as well understood as that of majorization. We give an introduction to this subject and derive some new results. Most notably, we show that the dimension of the required catalyst is in general unbounded; there is no integer $k$ such that it suffices to consider catalysts of dimension $k$ or less in determining which states can be catalyzed into a given state. We also show that almost all bipartite entangled states are potentially useful as catalysts.Comment: 7 pages, RevTe

Fermion and Higgs Masses and the AGUT Model

We present two rather differently based predictions for the quark and lepton spectrum: One provides a rather successful fit to the mass suppressions---the well known fermion mass hierarchy---interpreted as due to most mass terms needing to violate approximately conserved quantum numbers corresponding to the AGUT group $SMG^3\times U(1)_f$. This is actually, under certain conditions, the maximal group transforming the known 45 Weyl components of the quark and leptons into each other. From the fit to the fermion spectrum, we get a picture of the series of Higgs fields causing the breakdown (presumably at the Planck scale) of this AGUT to the Standard Model and, thus, providing the small masses of all quarks and leptons except for the top quark. We separately predict the top quark mass to be $173 \pm 5$ GeV and the Higgs mass to be $135 \pm 9$ GeV, from the assumption that there be two degenerate minima in the effective potential for the Weinberg Salam Higgs field with the second one at the Planck field strength.Comment: 6 page LaTeX file plus 1 postscript figure and aipproc style file, uses epsfig.sty; to appear in the Proceedings of Beyond the Standard Model V, Balholm, Norway, 29 April - 4 May 199

Moth Species New to Michigan

This is a compilation of moth species previously unrecorded from Michigan. Moore\u27s (1955) publication has been critically examined necessitating some specific changes. All questionable material has been determined by present day specialists in their particular fields. The McDunnough (1938) checklist is followed in the arrangement of the new data together with most of the recent changes in nomenclature as presented by Forbes (1948, 1954, 1960), Hardwick (1970), Hodges (1971), and Covell (1970, 1971). With the advent of more sophisticated collecting equipment and the easier access to Michigan\u27s Upper Peninsula a total of 154 species has been added. Many institutional and private collections have been examined including the large collection at Michigan State University which was not considered in the Moore publication

Tunguska Dark Matter Ball

It is suggested that the Tunguska event in June 1908 cm-large was due to a cm-large ball of a condensate of bound states of 6 top and 6 anti-top quarks containing highly compressed ordinary matter. Such balls are supposed to make up the dark matter as we earlier proposed. The expected rate of impact of this kind of dark matter ball with the earth seems to crudely match a time scale of 200 years between the impacts. The main explosion of the Tunguska event is explained in our picture as material coming out from deep within the earth, where it has been heated and compressed by the ball penetrating to a depth of several thousand km. Thus the effect has some similarity with volcanic activity as suggested by Kundt. We discuss the possible identification of kimberlite pipes with earlier Tunguska-like events. A discussion of how the dark matter balls may have formed in the early universe is also given.Comment: In second version some typos and smaller miscalculations were change

Remarkable coincidence for the top Yukawa coupling and an approximately massless bound state

We calculate, with several corrections, the non-relativistic binding by Higgs exchange and gluon exchange between six top and six anti-top quarks (actually replaced by left-handed b quarks from time to time). The remarkable result is that, within our calculational accuracy of the order of 14% in the top quark Yukawa coupling g_t, the experimental running top-quark Yukawa coupling g_t = 0.935 happens to have just that value which gives a perfect cancellation of the unbound mass = 12 top-quark masses by this binding energy. In other words the bound state is massless to the accuracy of our calculation. Our calculation is in disagreement with a similar calculation by Kuchiev et al., but this deviation may be explained by a phase transition. We and Kuchiev et al. compute on different sides of this phase transition.Comment: 68 pages, 3 figures; published version, including a discussion of the results of Ref. (5) and the new Appendix