Calculation of the planar supercritical flow over a NASA supercritical profile

An unsteady finite difference procedure was used to calculate the steady inviscid flow over an 11% thickness ratio NASA supercritical profile of LWP 505 at M sub infinity = 0.80 and alpha = 0. An attempt is made to include the viscous effects using a modified form of Head's entrainment method to calculate the turbulent boundary layer. The attempt to predict the viscous effects using the compressible form of Head's integral method with a modified auxiliary equation for the form factors was unsatisfactory. Though a reasonably separation bubble was established on the lower surface, a grossly exaggerated displacement effect resulted downstream of the shock on the upper surface. There clearly is substantial further effort required to evolve a satisfactory boundary layer procedure, which must then be coupled in a still unproven manner with the inviscid procedure

Steady inviscid transonic flows over planar airfoils: A search for a simplified procedure

A finite difference procedure based upon a system of unsteady equations in proper conservation form with either exact or small disturbance steady terms is used to calculate the steady flows over several classes of airfoils. The airfoil condition is fulfilled on a slab whose upstream extremity is a semi-circle overlaying the airfoil leading edge circle. The limitations of the small disturbance equations are demonstrated in an extreme example of a blunt-nosed, aft-cambered airfoil. The necessity of using the equations in proper conservation form to capture the shock properly is stressed. Ability of the steady relaxation procedures to capture the shock is briefly examined

Maximum Likelihood Estimation of the Multivariate Normal Mixture Model

The Hessian of the multivariate normal mixture model is derived, and estimators of the information matrix are obtained, thus enabling consistent estimation of all parameters and their precisions. The usefulness of the new theory is illustrated with two examples and some simulation experiments. The newly proposed estimators appear to be superior to the existing ones.Mixture model; Maximum likelihood; Information matrix

"On the estimation of a large sparse Bayesian system: the Snaer program"

The Snaer program calculates the posterior mean and variance of variables on some of which we have data (with precisions), on some we have prior information (with precisions), and on some prior indicator ratios (with precisions) are available. The variables must satisfy anumber of exact restrictions. The system is both large and sparse. Two aspects of the sta-tistical and computational development are a practical procedure to solve a linear integer system, and a stable linearization routine for ratios. We test our numerical method to solve large sparse linear least-squares estimation problems, and find that it performs well, even when the n ~k design matrix is large(nk equivalent 2^27.5).

Posterior moments and quantiles for the normal location model with Laplace prior

We derive explicit expressions for arbitrary moments and quantiles of the posterior distribution of the location parameter eta in the normal location model with Laplace prior, and use the results to approximate the posterior distribution of sums of independent copies of eta

"On some definitions in matrix algebra"

Many definitions in matrix algebra are not standardized. This notediscusses some of thepitfalls associated with undesirable orwrong definitions, anddealswith central conceptslikesymmetry, orthogonality, square root, Hermitian and quadratic forms, and matrix derivatives.