Multivariate Discrete Distributions with a Product-Type Dependence

A discrete multivariate probability distribution for dependent random variables, which contains the Poisson and Geometric conditionals distributions as particular cases, is characterized by means of conditional expectations of arbitrary one-to-one functions. Independence of the random variables is also characterized in terms of these conditional expectations. For certain exchangeable and partially exchangeable random variables with a joint distribution of this form it is shown that maximum likelihood estimates coincide with the simple method of moments estimates, suggesting that these models offer a pragmatic way to analyze certain dependent data.     

Zur Lojasiewicz-Ungleichung für differenzierbare Funktionen

Let f be a C^∞-function satisfying a Lojasiewicz-inequality. Is it possible that the Taylor series of f is the zero-series in some point? We will show here that this is not possible.     

On single and bimodal optimum buckling loads of clamped columns

We study the problem of determining the optimum shape of a thin, elastic, clamped column of given length and volume, such that the fundamental buckling load is a maximum. The column cross-sections are assumed to be geometrically similar, and a minimum allowable value is specified for the cross-sectional area.Investigating the optimization problem parametrically in terms of this minimum constraint, we reveal a significant feature. There exists a threshold value for the constraint, beyond which the optimum columns are all associated with single mode optimum buckling loads, whereas, for any value of the constraint less than the threshold value, the optimum columns are associated with bimodal fundamental buckling loads.This bimodal behaviour necessitates an extension and a mathematical reformulation of the current optimization problem, which is outlined and solved in the paper. In particular, we revise the result hitherto considered to be the optimum solution for an unconstrained column with clamped ends.