2,162 research outputs found
Recommended from our members
D-optimal designs formulti-response linear mixed models
Linear mixed models have become popular in many statistical applications duringrecent years. However design issues for multi-response linear mixed models are rarelydiscussed. Themain purpose of this paper is to investigate D-optimal designs formultiresponselinear mixed models. We provide two equivalence theorems to characterizethe optimal designs for the estimation of the fixed effects and the prediction of randomeffects, respectively. Two examples of the D-optimal designs formulti-response linearmixed models are given for illustration
Existence and stability of cylindrical transonic shock solutions under three dimensional perturbations
In this paper, we establish the existence and stability of cylindrical
transonic shock solutions under three dimensional perturbations of the incoming
flows and the exit pressure without any further restrictions on the background
transonic shock solutions. The strength and position of the perturbed transonic
shock are completely determined by the incoming flows and the exit pressure.
The optimal regularity is obtained for all physical quantities, and the
velocity, the Bernoulls's function, the entropy and the pressure share the same
regularity. The problem is reduced to solve a nonlinear free boundary value
problem for a hyperbolic-elliptic mixed system. There are two main ingredients
in our analysis. One is to use the deformation-curl decomposition to the steady
Euler system introduced by the authors in \cite{wx19,w19} to effectively
decouple the hyperbolic and elliptic modes. Another one is the reformulation of
the Rankine-Hugoniot conditions, which determines the shock front by an
algebraic equation and also gives an unusual second order differential boundary
conditions on the shock front for the deformation-curl system. After
homogenizing the curl system and introducing a potential function, the
solvability of the boundary value problem of the deformation-curl system for
the velocity field is reduced to a second order elliptic equation for the
potential function with a nonlocal term involving only the trace of the
potential function on the shock front. This simplification follows essentially
from an oblique boundary condition for the potential function on the shock
front which is obtained by solving the Poisson equation on the shock front with
the homogeneous Neumann boundary conditions on the intersection of the shock
front and the cylinder walls.Comment: 50 pages. Any comments are welcom
Smooth transonic flows with nonzero vorticity to a quasi two dimensional steady Euler flow model
This paper concerns studies on smooth transonic flows with nonzero vorticity
in De Laval nozzles for a quasi two dimensional steady Euler flow model which
is a generalization of the classical quasi one dimensional model. First, the
existence and uniqueness of smooth transonic flows to the quasi one-dimensional
model, which start from a subsonic state at the entrance and accelerate to
reach a sonic state at the throat and then become supersonic are proved by a
reduction of degeneracy of the velocity near the sonic point and the implicit
function theorem. These flows can have positive or zero acceleration at their
sonic points and the degeneracy types near the sonic point are classified
precisely. We then establish the structural stability of the smooth one
dimensional transonic flow with positive acceleration at the sonic point for
the quasi two dimensional steady Euler flow model under small perturbations of
suitable boundary conditions, which yields the existence and uniqueness of a
class of smooth transonic flows with nonzero vorticity and positive
acceleration to the quasi two dimensional model. The positive acceleration of
the one dimensional transonic solutions plays an important role in searching
for an appropriate multiplier for the linearized second order mixed type
equations. A deformation-curl decomposition for the quasi two dimensional model
is utilized to deal with the transonic flows with nonzero vorticity.Comment: 54 page
- …