We prove an optimal relative integral convergence rate for two expanding gradient Ricci solitons coming out of the same cone. As a consequence, we obtain unique continuation result at infinity and that entropy such self-similar solutions to flow is well-defined. © 2022 Wiley Periodicals LLC.

The first part of this writeup gives Riemann’s argument that the completion of zeta, Z(s) = π−s/2Γ(s/2)ζ(s), Re(s) > 1 has a meromorphic continuation to the full s-plane, analytic except for simple poles at s = 0 and s = 1, and the continuation satisfies the functional equation Z(s) = Z(1− s), s ∈ C. The continuation is no longer defined by the sum. Instead, it is defined by a wellbehaved integ...

Computing the Jordan form of a matrix or the Kronecker structure of a pencil is a well-known ill-posed problem. We propose that knowledge of the closure relations, i.e., the stratiication, of the orbits and bundles of the various forms may be applied in the staircase algorithm. Here we discuss and complete the mathematical theory of these relationships and show how they may be applied to the st...

Abstract. In this paper, we revisit the reverse-time imaging procedure. We discuss an inverse scattering transform derived from reverse-time migration (RTM), and establish its relation with generalized Radon transform inversion. In the process, the explicit evaluation of the so-called normal operator is avoided, at the cost of introducing other pseudodifferential operator factors. Using techniq...

The first part of this writeup gives Riemann’s argument that the completion of zeta, Z(s) = π−s/2Γ(s/2)ζ(s), Re(s) > 1 has a meromorphic continuation to the full s-plane, analytic except for simple poles at s = 0 and s = 1, and the continuation satisfies the functional equation Z(s) = Z(1− s), s ∈ C. The continuation is no longer defined by the sum. Instead, it is defined by a wellbehaved integ...

The first part of this writeup gives Riemann’s argument that the completion of zeta, Z(s) = π−s/2Γ(s/2)ζ(s), Re(s) > 1 has a meromorphic continuation to the full s-plane, analytic except for simple poles at s = 0 and s = 1, and the continuation satisfies the functional equation Z(s) = Z(1− s), s ∈ C. The continuation is no longer defined by the sum. Instead, it is defined by a wellbehaved integ...

Common-azimuth migration (CAM) is an attractive solution for 3-D prestack imaging. It reduces the full 5-D phase-shift operator to 4-D through the stationary-phase approximation, lowering the computational cost. However, this assumption yields constraints in the downward-continuation process that can limit accuracy. Those errors are estimated in this paper by comparison to other wave-equation m...

This is continuation of experimental work at U.C. Irvine on fan flow deflection (FFD) [1]. The working principle of FFD is reduction of the convective Mach number of turbulent eddies that generate intense downward and sideward sound radiation. In a coaxial separate-flow turbofan engine this is achieved by tilting in the general downward direction, by a few degrees, the bypass (secondary) plume ...