MSW Effects in Vacuum Oscillations

We point out that for solar neutrino oscillations with the mass-squared difference of Delta m^2 ~ 10^-10 - 10^-9 eV^2, traditionally known as ``vacuum oscillation'' range, the solar matter effects are non-negligible, particularly for the low energy pp neutrinos. One consequence of this is that the values of the mixing angle theta and pi/2-theta are not equivalent, leading to the need to consider the entire physical range of the mixing angle 0<=theta<=pi/2 when determining the allowed values of the neutrino oscillation parameters.Comment: 4 pages, 5 figures. The calculation of the level crossing probability is now performed numerically using the BP2000 solar density profile. Conclusions unchange

The Collatz-Wielandt quotient for pairs of nonnegative operators

In this paper we consider two versions of the Collatz-Wielandt quotient for a pair of nonnegative operators A,B that map a given pointed generating cone in the first space into a given pointed generating cone in the second space. If the two spaces and two cones are identical, and B is the identity operator then one version of this quotient is the spectral radius of A. In some applications, as commodity pricing, power control in wireless networks and quantum information theory, one needs to deal with the Collatz-Wielandt quotient for two nonnegative operators. In this paper we treat the two important cases: a pair of rectangular nonnegative matrices and a pair completely positive operators. We give a characterization of minimal optimal solutions and polynomially computable bounds on the Collatz-Wielandt quotient.Comment: 24 pages. To appear in Applications of Mathematics, ISSN 0862-794

FPRAS for computing a lower bound for weighted matching polynomial of graphs

We give a fully polynomial randomized approximation scheme to compute a lower bound for the matching polynomial of any weighted graph at a positive argument. For the matching polynomial of complete bipartite graphs with bounded weights these lower bounds are asymptotically optimal.Comment: 16 page

Equality in Wielandt's eigenvalue inequality

In this paper we give necessary and sufficient conditions for the equality case in Wielandt's eigenvalue inequality.Comment: 6 pages, few typos are correcte

Ideation and Appropriation: Wittgenstein on Intellectual Property

This paper provides a critique of the contemporary notion of intellectual property based on the consequences of Wittgenstein's “private language argument”. The reticence commonly felt toward recent applications of patent law, e.g., sports moves, is held to expose erroneous metaphysical assumptions inherent in the spirit of current IP legislation. It is argued that the modern conception of intellectual property as a kind of natural right, stems from the mistaken internalist or Augustinian picture of language that Wittgenstein attempted to diffuse. This view becomes persuasive once it is shown that a complete understanding of the argument against private language must include Wittgenstein's investigation of the role of the will in the creative process. It is argued that original thought is not born by decree of the will, but engendered by a public context of meaning and value. What marks a person as a genius is, therefore, according to Wittgenstein, not some sovereign capacity of conceptual world-making, but merely a propitious dose of intellectual courage