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Gen Nakamura

Publications and source records attributed to Gen Nakamura.

60 records · Page 4Linked to original sources
arXiv2009

Constraint on the growth factor of the cosmic structure from the damping of the baryon acoustic oscillation signature

We determine a constraint on the growth factor by measuring the damping of the baryon acoustic oscillations in the matter power spectrum using the Sloan Digital Sky Survey luminous red galaxy sample. The damping of the BAO is detected at the one sigma level. We obtain σ_8D_1(z=0.3) = 0.42^{+0.34}_{-0.28} at the 1σstatistical level, where σ_8 is the root mean square overdensity in a sphere of radius 8h^{-1}Mpc and D_1(z) is the growth factor at redshift z. The above result assumes that other parameters are fixed and the cosmology is taken to be a spatially flat cold dark matter universe with the cosmological constant.

astro-ph.CO↗
arXiv2009

Breaking the scale invariance of the primordial power spectrum in Horava-Lifshitz Cosmology

We study the spectral tilt of primordial perturbations in Horava-Lifshitz cosmology. The uniform approximation, which is a generalization of the familiar Wentzel-Kramers-Brillouin (WKB) method, is employed to compute the spectral index both numerically and analytically in a closed form. We clarify how the spectral index depends on the inflation model and parameters in the modified dispersion relation.

astro-ph.CO↗
arXiv2009

Estimate of the Fundamental Solution for Parabolic Operators with Discontinuous Coefficients

We will show that the same type of estimates known for the fundamental solutions for scalar parabolic equations with smooth enough coefficients hold for the first order derivatives of fundamental solution with respect to space variables of scalar parabolic equations of divergence form with discontinuous coefficients. The estimate is very important for many applications. For example, it is important for the inverse problem identifying inclusions inside a heat conductive medium from boundary measurements.

math.AP↗
arXiv2009

Optimal three-ball inequalities and quantitative uniqueness for the Lamé system with Lipschitz coefficients

In this paper we study the local behavior of a solution to the Lamé system with \emph{Lipschitz} coefficients in dimension $n\ge 2$. Our main result is the bound on the vanishing order of a nontrivial solution, which immediately implies the strong unique continuation property. This paper solves the open problem of the strong uniqueness continuation property for the Lamé system with Lipschitz coefficients in any dimension.

math.AP↗
arXiv2008

Quantitative uniqueness for second order elliptic operators with strongly singular coefficients

In this paper we study the local behavior of a solution to second order elliptic operators with sharp singular coefficients in lower order terms. One of the main results is the bound on the vanishing order of the solution, which is a quantitative estimate of the strong unique continuation property. Our proof relies on Carleman estimates with carefully chosen phases. A key strategy in the proof is to derive doubling inequalities via three-sphere inequalities. Our method can also be applied to certain elliptic systems with similar singular coefficients.

math.AP↗