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A new generalization of the Takagi function
We consider a one-parameter family of functions on
and partial derivatives with respect to the
parameter . Each function of the class is defined by a certain pair of two
square matrices of order two. The class includes the Lebesgue singular
functions and other singular functions. Our approach to the Takagi function is
similar to Hata and Yamaguti. The class of partial derivatives
includes the original Takagi function and some
generalizations. We consider real-analytic properties of as a function of , specifically, differentiability, the Hausdorff
dimension of the graph, the asymptotic around dyadic rationals, variation, a
question of local monotonicity and a modulus of continuity. Our results are
extensions of some results for the original Takagi function and some
generalizations.Comment: 22 pages, 2 figures. The structure of paper has been changed
significantl
Effect of the smaller mass-squared difference for the long base-line neutrino experiments
Usually, neutrino oscillation experiments are analyzed within the two-flavor
framework which is governed by 1 mass-squared difference and 1 mixing angle.
But there are 6 parameters,2 mass-squared differences, 3 mixing angles, and 1
CP phase within the three-flavor framework.In this article,we estimate the
effect from the smaller mass-squared difference,the other mixing angles, and
the CP phase, which we call three-flavor effect, for the determination of the
mass-squared difference and the mixing angle from the nu_mu's survival and
transition probability with the two-flavor analysis.It is found that the
mass-squared difference from the two-flavor analysis is slightly shifted from
the larger mass-squared difference by the three-flavor effect.The order of
magnitude of the three-flavor effect for the mass-squared difference is
comparable with that of the expected error for the mass-squared difference of
the two-flavor analysis in the future long base-line neutrino oscillation
experiments.The CP phase dependence of the nu_mu to nu_etransition probability
is also shown.Comment: 13 pages, no figure new reference added, correct typos, Accepted by
Progress of Theoretical Physic
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