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We derived an analytic formula for T violation by using the perturbation theory for small quantities, $\Delta m_{21}^2L/2E$ and $\delta a(x)L/2E$, where $\delta a(x)$ represents symmetric and asymmetric matter fluctuations, i.e., deviations from the average density. We analyzed the effect of matter fluctuations to T violation, by assuming PREM profile of earth matter density. We found that matter fluctuations do not give any viable contribution for $L<$6000km, while the fluctuation effect becomes large due to resonances for $L>$7000km. For 7000km$$8000km, the contribution from matter fluctuations becomes large but contributes constructively., Comment: 27 pages, 10 figures

We analyzed T-violation in neutrino oscillation by using perturbation methods with respect to $\Delta m_{21}^2L/2E$ and $\delta a(x)L/2E$, where $\delta a(x)$ represents the matter density fluctuation from its average value. We found that the matter contribution to T-violation arises from interferences between $\Delta m_{21}^2L/2E$ and $\delta a(x) L/2E$. In the 2nd order, the symmetric and asymmetric matter density fluctuations give effects to the $\sin \delta$ (intrinsic) and the $\cos \delta$ (fake) parts of T-violation. We give their analytic forms and analyze the matter contribution to the $\sin \delta$ and $\cos \delta$ terms. We found that, for L=3000km, both the symmetric and asymmetric matter density fluctuations give negligible contributions to T-violation, and that thus the constant (average) matter density gives a good approximation. On the other hand, we argue that, for L=7000km or longer length, T-violation turns out to become very small due to cancellation between the 1st and the 2nd order terms. This shows that the constant (average) matter approximation is not valid., Comment: Latex, 30 pages, 6 figures

We investigate the quantum effects for the democratic-type neutrino mass matrix given at the right-handed neutrino mass scale $m_R$ in order to see (i) whether $\theta_{23}=-\pi/4$ predicted by the model is stable to explain the atmospheric neutrino anomaly, (ii) how $\theta_{12}$ and $\theta_{13}$ behave, and (iii) whether the predicted Dirac CP phase $\delta$ keeps maximal size, at the weak scale $m_Z$. We find that, for the (inversely) hierarchical mass spectrum with $m_1\sim m_2$, $\theta_{23}$ and $\theta_{13}$ are stable, while $\theta_{12}$ is not so, which leads to the possibility that the solar neutrino mixing angle can become large at $m_Z$ even if it is taken small at $m_R$. We also show that $\delta$ keeps almost maximal for the above mass spectrum, and our model can give the large CP violation effect in the future neutrino oscillation experiments if the solar neutrino puzzle is explained by the large mixing angle MSW solution., Comment: LaTeX, 21 pages, 2 figures, some mistakes corrected

In our previous paper, we proposed the democratic-type neutrino mass matrix which gives interesting predictions, $\theta_{23}=-\frac{\pi}4$, $|\tan \theta_{12}|=\sqrt{2-3\sin^2 \theta_{13}}$ and $\delta=\frac {\pi}2$, where $\theta_{ij}$ is the mixing angle between mass eigenstates $\nu_i$ and $\nu_j$, and $\delta$ is the CP violation angle in the standard parameterization of mixing matrix. In this paper, we examined how predictions behave at $m_Z$ by assuming that they are given at the right-handed neutrino mass scale, $M_R$., Comment: LaTeX file,22 pages, 2 postscript figures

We consider the democratic-type neutrino mass matrix and show that this matrix predicts the atmospheric neutrino mixing to be almost maximal, $\sin^2 2\theta_{atm}>0.999$ as well as the large CP violation (the CP violation phase in the standard form is maximal $\delta=\pi/2$). We construct the $Z_3$ symmetric dimension five effective Lagrangian with two up-type Higgs doublets and show that this Lagrangian leads to the democratic neutrino mass matrix. Furthermore, we consider the restricted model with one up-type Higgs doublet and obtain the prediction, $0.87<\sin^2 2\theta_{sol}<8/9$., Comment: LaTeX, 7 pages; Talk given at Workshop on Neutrino Oscillations and their Origin, Fuji-Yoshida, Japan, 11-13 Feb 2000

We present neutrino mass matrices which predict the atmospheric neutrino mixing to be almost maximal, $\sin^2 2\theta_{atm}>0.999$, as well as the large solar neutrino mixing, $8/9>\sin^2 2\theta_{sol}>0.87$, and the large CP violation (the CP violation phase in the standard form is maximal $\delta=\pi/2$), based on the $Z_3$ symmetry., Comment: LaTeX, 17 pages; minor corrections and some comments added

We propose a democratic-type neutrino mass matrix based on $Z_3$ symmetry. This mass matrix predicts the CP violation phase, $\delta=\pi/2$, and the mixing angle between the mass eigenstates $\nu_2$ and $\nu_3$, $\sin^2 \theta_{23}= \cos^2 \theta_{23}=1/2$ which is essential for the large atmospheric neutrino mixing, between $\nu_\mu$ and $\nu_\tau$. In this model, the large CP violation effect may be expected., Comment: LaTeX, 22pages, corrected some terminologies, reference added

We discussed neutrino masses and mixings in SUSY SO(10) model where quarks and leptons have Yukawa couplings to at least two 10 and one $\bar{126}$ Higgs scalars. In this model, the Dirac and the right-handed Majorana mass terms are expressed by linear combinations of quark and charged lepton mass matrices, which then determine the neutrino mass matrix by the see-saw mechanism. We show that there are various solutions to reproduce a large mixing angle for $\nu_\mu-\nu_\tau$ and a small mixing angle for $\nu_e-\nu_\mu$, as well as the hierarchical mass spectrum of neutrinos., Comment: LaTeX, 32 pages including 15 eps figures

We examined the question that what is a general form of quark mass matrices which is achieved by the transformation that leaves the left-handed gauge interaction invariant. In particular, we analyzed in detail the Fritzsch-type and the Branco-Silva-Marcos-type parametrization. Both parametrizations contain ten parameters and can be expressed by the experimental data. We explicitly reconstructed quark mass matrices in terms of quark masses and CKM parameters for the Fritzsch-type parametrization., Comment: 17 pages and 4 figures