We give a natural way to identify between two scales, potentially arbitrarily far apart, in non-compact Ricci-flat manifold with Euclidean volume growth when tangent cone at infinity has smooth cross section. The identification map is given as the gradient flow of solution an elliptic equation.

Non-modal linear stability analysis results are presented for hypersonic flow over an elliptic cone with aspect ratio of two at zero angle attack, completing earlier modal instability around the same geometry. The theoretical framework to perform transient growth compressible flows on a generalized two-dimensional frame reference is developed first time and then applied solve initial-value prob...

We study the existence and nonexistence of positive (super-) solutions to a singular semilinear elliptic equation −∇ · (|x|∇u)−B|x|u = C|x|u in cone–like domains of R (N ≥ 2), for the full range of parameters A,B, σ, p ∈ R and C > 0. We provide a complete characterization of the set of (p, σ) ∈ R such that the equation has no positive (super-) solutions, depending on the values of A,B and the p...

We describe an affine transformation on the (CIE) color matching functions and map the spectral locus as a circle. We then homogenize the right circular cylinder erected by the circle, with respect to a normalizing plane and develop an analytical equation to the chromaticity cone, for the spectral colors. In the interior of the (CIE) chromaticity diagram, by homogenizing elliptic cylinders with...

It is suggested recently that most of halo coronal mass ejections (CMEs) may be formed by an ice cream cone-like shell of dense CME electrons. We improve our cone model (Zhao, Plunkett and Liu, 2002) to include the contribution of the top surface of the ice cream part as well as the cone part to the shape of the halo CMEs. It is found that for an ice cream cone with a half sphere sitting on the...