Estimation automatique de la densité
Two general solutions of the collocation problem of physical geodesy are given. Their mutual equivalency and equivalency of them to the classical solution in the regular case are proved. The regularity means the non-singularity of the covariance matrix of those random variables by outcomes of which the measured values of the gravitational field are generated.
A Markov process converging to a random state of the 6-vertex model is constructed. It is used to show that a droplet of c-vertices is created in the antiferromagnetic phase and that the shape of this droplet has four cusps.
There exist many different ways of determining the best linear unbiased estimation of regression coefficients in general regression model. In Part I of this article it is shown that all these ways are numerically equivalent almost everyvhere. In Part II conditions are considered under which all the unbiased estimations of the unknown covariance matrix scalar factor are numerically equivalent almost everywhere.