We propose, within the context of the dynamics of a holomorphic germ in ℂ, a definition of 'attracting basin' of a fixed point. We prove that the inverse germ of an endomorphism of ℂ with a repulsive fixed point in 0, satisfying a supplementary technical hypothesis, admits an attracting...

The identification and assessment of prognostic factors is one of the major tasks in clinical research. The assessment of one single prognostic factor can be done by recently established methods for using optimal cutpoints. Here, we suggest a method to consider an optimal selected prognostic...

The additive structure of multiplicative semigroup Z(.) mod in residue ring = (+, .) mod (odd prime ) is analysed. The group of units in (.) is cyclic of order ( − 1), with inner product = of || = − 1 coprime to |} = . The -th power units form a subgroup of order ||/, with ||/|| = ( ≥ 2),...

Let denote the transitive tournament on vertices. Let () denote the graph obtained from by replacing each vertex with an independent set of size ≥ 1. The following result is proved: Let = 1/2, = 5/6 and = 1 − 2 for ≥ 4. For every 0 there exists = (, , ) such that for every undirected...

We present several selection theorems for Borel relations, involving only Borel sets and functions, all of which can be obtained as consequences of closely related theorems proved in [3], [4], [5], [6], involving coanalytic sets. The relevant proofs given there use substantial set theoretic...

Let = {, …, } be a family of graphs. A graph with edges is called if for linear combination of the form () + … + () = where each is a nonnegative integer, there is a coloring of the edges of with + … + colors such that exactly color classes induce each a copy of ; for = 1, …, . We prove...

The problem of hypothesis testing about two Poisson means is addressed. The usual conditional test (-test) and a test based on estimated -values (-test) are considered. The exact properties of the tests are evaluated numerically. Numerical studies indicate that the -test is almost exact because...