Quark mixing from softly broken symmetries

Quark flavor mixing may originate in the soft breaking of horizontal symmetries. Those symmetries, which in the simplest case are three family U(1) groups, are obeyed only by the dimension-4 Yukawa couplings and lead, when unbroken, to the absence of mixing. Their breaking may arise from the dimension-3 mass terms of SU(2)-singlet vector-like quarks. Those gauge-singlet mass terms break the horizontal symmetries at a scale much higher than the Fermi scale, yet softly, leading to quark mixing while the quark masses remain unsuppressed.Comment: 9 pages, plain Latex, no figure

Non-extremal Localised Branes and Vacuum Solutions in M-Theory

Non-extremal overlapping p-brane supergravity solutions localised in their relative transverse coordinates are constructed. The construction uses an algebraic method of solving the bosonic equations of motion. It is shown that these non-extremal solutions can be obtained from the extremal solutions by means of the superposition of two deformation functions defined by vacuum solutions of M-theory. Vacuum solutions of M-theory including irrational powers of harmonic functions are discussed.Comment: LaTeX, 16 pages, no figures, typos correcte

B&N Signature Edition

Barnes and Noble did a Classic Edition in 2003 that presented V.S. Vernon Jones' and Arthur Rackham's Aesop. Now here is a new effort by Barnes and Noble, nicely done. Griset's illustrations, so often dark and poorly printed, are well presented here. I have tried to pin the texts down to a known author, but I cannot find the source, and there is none acknowledged here. Of course one great advantage of this book is that it is inexpensive. Where does one find a well-bound book with a dust-jacket for $6.98? Further, the book has a good introduction and good suggestions for pursuing study of Aesop. There are notes and an AI at the end of the fables, besides a list of illustrations and a chronology at the book's beginning. Here is its biggest surprise: it refers twice to the Carlson Fable Collection! In fact, this collection gets the book's first footnote, and it comes with the book's first sentence! The note itself is on 231. Readers are also referred to the collection on 239 when Clayton discusses presentations of fables in other media.This is a hardbound book (hard cover)This book has a dust jacket (book cover)First printingIntroduction and Notes by Edward W. Clayto