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This paper presents a numerical method of verifying existence and local uniqueness of a solution for an initial-boundary value problem of semi-linear parabolic equations. The main theorem of this paper gives a sufficient condition for enclosing the solution in a neighborhood of a numerical solution. In the formulation of this paper, the initial-boundary… (More)

Three-dimensional analysis of the aurora which is an atmospheric phenomenon is significant because the shape of aurora reflects the electromagnetic relationship between the Earth and the Sun, which can influence electric equipments such as satellites. To analyze a number of auroras, our research group set two fish-eye cameras in Poker Flat Research Range… (More)

We explore a mechanism of radiative B − L symmetry breaking in analogous to the radiative electroweak symmetry breaking. The breaking scale of B − L symmetry is related to the neutrino masses through the seesaw mechanism. Once we incorporate the U(1) B−L gauge symmetry in SUSY models, the U(1) B−L gaugino, ˜ Z B−L appears, and it can mediate the SUSY… (More)

This paper presents a method of numerical verification for existence of a global-in-time solution to a class of semilinear parabolic equations. Such a method is based on two main theorems in this paper. One theorem gives a sufficient condition for proving existence of a solution to the semilinear parabolic equations with the initial point t = t ′ ≥ 0. If… (More)

In this paper, we will find the numerical solution of partial differential equations by using the finite element method with Riesz bases that are elevated from ortho normal bases. Especially for the two-dimensional cases, we also propose another way to solve a matrix-valued equation (Lyapunov equation). Moreover, we give the precise inverse formula for… (More)

—In this article, a numerical method is presented for computer assisted proofs to the existence and uniqueness of solutions to Dirichlet boundary value problems in a certain class of nonlinear elliptic equations. In a weak formulation of the problem, a weak solution is described as a zero point of a certain nonlinear map. Based on Newton-Kantorovich… (More)

It is demonstrated that the light Higgs boson scenario, which the lightest Higgs mass is less than the LEP bound, m h > 114.4 GeV, is consistent with the SUSY seesaw model. With the assumptions of the universal right-handed neutrino mass and the hierarchical mass spectrum of the ordinary neutrinos, the bounds for the right-handed neu-trino mass is… (More)

Anomaly mediated supersymmetry breaking implemented in the minimal super-symmetric standard model (MSSM) is known to suffer from the tachyonic slepton problem leading to breakdown of electric charge conservation. We show however that when MSSM is extended to explain small neutrino masses by gauging the B-L symmetry , the slepton masses can be positive due… (More)

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