We give a proof that Total Variation {a,,(.)} < 1 can be replaced by Sup{u,(.)} e 1 in Glimm's method whenever a coordinate system of Riemann invariants is present. The argument is somewhat simpler but in the same spirit as that given by Glimm in his celebrated paper of 1965. 0 1990 Academic Press, Inc. We consider the Cauchy problem u, + F(u), = 0, (1) 4-G 0) = u,(x), (2) where (1) denotes a s...

A parametric approach is developed to the method of S-tree diagrams and its generalization for investigation of the hierarchical substructure of N-body nonlinearly interacting systems (e.g., clusters of galaxies). The introduction of a parametric function allows us to take into account the individual features of the particles which do not have a direct influence on the dynamics of the system bu...

In this report, we present a simple geometric generation principle for the fractal that is obtained when applying Newton's method to nd the roots of a general complex polynomial with real coee-cients. For the case of symmetric polynomials z ? 1, the generation mechanism is derived from rst principles. We discuss the case of a general cubic and are able to give a description of the arising fract...

The hazard rate is a statistical indicator commonly used in lifetime analysis. The Birnbaum-Saunders (BS) model is a life distribution originated from a problem pertaining to material fatigue that has been applied to diverse fields. The BS model relates the total time until failure to some type of cumulative damage that is normally distributed. The generalized BS (GBS) distribution is a class o...

In least squares, least absolute deviations, and even generalized M-estimation, outlying observations sometimes strongly influence the estimation result, masking an important and interesting relationship existing in the majority of observations. The S-estimators are a class of estimators that overcome this difficulty by smoothly downweighting outliers in fitting regression functions to data. In...

Allowing for gene-environment correlation, Jensen (1975) reports that under a wide range of assumptions, the twin data show that onehalf ~o th~ee-fourths of IQ variance is accounted for by genetic factors. But that conc1usion;~fa11swhen an arbitrary specification is relaxed. ON JENSEN'S METHOD FOR TWINS

A general class of Newton algorithms on Graßmann and Lagrange–Graßmann manifolds is introduced, that depends on an arbitrary pair of local coordinates. Local ⋆ corresponding author The first author was partially supported by a grant from BMBF within the FprofUnd programme. The second and third author are with National ICT Australia Limited which is funded by the Australian Government’s Departme...

Let C[[z]] be the ring of power series over an effective ring C. In [BK78], it was first shown that differential equations over C[[z]] may be solved in an asymptotically efficient way using Newton’s method. More precisely, if M(n) denotes the complexity in order two polynomials of degree < n over C, then the first n coefficients of the solution can be computed in time O(M(n)). However, this com...