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The procedure to find gauge invariant variables for two-parameter nonlinear perturbations in general relativity is considered. Up to third order perturbations, it is shown that appropriate combinations of nonlinear metric perturbations and lower order one are transformed as the gauge transformation of linear order metric perturbations. This implies that… (More)

some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the second order gauge invariant perturbation theory on arbitrary background spacetime to derive these formulae. These perturbative curvatures do have the same form as the definitions of gauge invariant variables for arbitrary perturbative fields which… (More)

Following the general framework of the gauge invariant perturbation theory developed in, we formulate second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe. We consider perturbations both in the universe dominated by a single perfect fluid and in that dominated by a single scalar field. We derive… (More)

- K Nakamura, U Tokyo, Kek, S T Petcov
- 2010

The experiments with solar, atmospheric, reactor and accelerator neutrinos have provided compelling evidences for oscillations of neutrinos caused by nonzero neutrino masses and neutrino mixing. The data imply the existence of 3-neutrino mixing in vacuum. We review the theory of neutrino oscillations, the phenomenology of neutrino mixing, the problem of the… (More)

- K Suematsu, K Nakamura, J Takeda
- Yakugaku zasshi : Journal of the Pharmaceutical…
- 1983

- K.-I. Nakamura, H. Okamoto
- 2002

We consider a model equation for 3D vorticity dynamics of incompressible vis-cous fluid proposed by K. Ohkitani and the second author of the present paper. We prove that a solution blows up in finite time if the L 1-norm of the initial vorticity is greater than the viscosity. Running title: blow-up in the vorticity dynamics with linear strain

- K Nakamura
- Nihon rinsho. Japanese journal of clinical…
- 1977

- H SHIBATA, K NAKAMURA
- Iryo
- 1962

Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723], some formulae for the perturbative curvatures of each order are derived. We follow the general framework of the second-order gauge invariant perturbation theory on an arbitrary background spacetime to derive these formulae. It is found… (More)

- KEI NAKAMURA, K. NAKAMURA
- 2013

Let M be an orientable closed connected 3-manifold. We introduce the notion of amalgamated Heegaard genus of M with respect to a closed separating 2-manifold F , and use it to show that the following two statements are equivalent: (i) a compact connected 3-manifold Y can be embedded in M so that the exterior of the image of Y is a union of handlebodies; and… (More)