Gravity and CP violation

The non-conservation of CP symmetry in the decay of neutralK mesons was discovered almost three decades ago. The origin of this unique phenomenon is still not well understood. There have been attempts to link it with energy splitting of theK and in the earth's gravitational field. In this essay we examine these attempts critically. A more natural way in which a gravitational field can couple asymmetrically to the system is through torsion, which coupling to isospin can, in addition to parity violation, also give rise to a C violation. The magnitude of this effect is estimated in the vicinity of a kaon and found to give a CP-violating parameter of the right value. Moreover, it is predicted that the CP violating parameter for the new system is much smaller 10^–6. Implications for baryogenesis in the early universe is also studied. In this paper we work not with the Newtonian gravitational constantG but with a torsion coupling constant, which is energy-dependent and can be related to the Fermi weak interaction constant.     

The dilution of silica in a NiZnCo spinel ferrite matrix

Silica may dissolve up to about 0.05 wt% in an iron excess NiZnCo spinel matrix, affecting noticeably the magnetic properties at low and high values of the applied field. The initial permeability is reduced by about 50% with the addition of only 0.1 % SiO₂, while the coercivity almost triples, without noticeable changes in porosity or grain distribution. The vacancy and Fe²⁺ content of the sintered material also show a considerable change. The energy associated to the transformation Fe³⁺ Fe²⁺ for the samples without SiO₂ was found to be 0.41–0.42 eV, while for the samples with SiO₂ additions it decreased to 0.26 eV. The changes in magnetic properties are thought to be caused, more than because of the mentioned changes in ion distribution, by the stresses and defects created in the lattice due to the very small size of the Si⁴⁺ ion, which substitutes Fe³⁺ ions in tetrahedral sites. The transition Fe³⁺ Fe²⁺ seems to take place exclusively in the octahedral sites.     

Theq-calculus for genericq andq a root of unity

Theq-calculus for genericq is developed and related to the deformed oscillator of parameterq ^1/2. By passing with care to the limit in whichq is a root of unity, one uncovers the full algebraic structure ofZ _n -graded fractional supersymmetry and its natural representation.Presented at the 5th International Colloquium on Quantum Groups: Quantum Groups and Integrable Systems, Prague, 20–22 June 1996.This paper describes research supported in part by E.P.S.R.C and P.P.A.R.C. (UK) and by the C.I.C.Y.T (Spain). J.C.P.B. wishes to acknowledge an FPI grant from the CSIC and the Spanish Ministry of Education and Science.     

Codes Based on Complete Graphs

We consider the problem of embedding the even graphical code based on the complete graph onn vertices into a shortening of a Hamming code of length 2^m-1, wherem = h(n) should be as small as possible. As it turns out, this problem is equivalent to the existence problem for optimal codes with minimum distance 5, and optimal embeddings can always be realized as graphical codes based onK _n. As a consequence, we are able to determineh(n) exactly for alln of the form 2 ^k + 1 and to narrow down the possibilities in general to two or three conceivable values.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe research for this note was done while the first author was visiting the University of Waterloo and the University of Rome, respectively. He thanks his colleagues there for their hospitality and also acknowledges the financial support of the Consiglio Nazionale delle Ricerche (Italy). The third author acknowledges the support of the National Science and Engineering Research Council of Canada given under grant #0GP0009258.