A decomposition theorem for an analytic function

An analytic KAM-Theorem

We prove an analytic KAM-theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the theorem presented here is to provide exactly the estimates needed in [1].

A Decomposition Theorem for Domains

A domain constructor that generalizes the product is de ned. It is shown that with this constructor exactly the prime-algebraic coherent Scott-domains and the empty set can be generated from two-chains and boolean at domains. 3 List of Symbols I am identifying the symbols by the corresponding Latex(+Amssymb)-symbols. " uparrow # downarrow ! rightarrow ? bot > top leq geq 2 in W bigvee V bigwedg...

An Obstacle to a Decomposition Theorem for Near-Regular Matroids

Seymour’s Decomposition Theorem for regular matroids states that any matroid representable over both GF(2) and GF(3) can be obtained from matroids that are graphic, cographic, or isomorphic to R10 by 1-, 2-, and 3-sums. It is hoped that similar characterizations hold for other classes of matroids, notably for the class of near-regular matroids. Suppose that all near-regular matroids can be obta...

A Fixed Point Theorem for Analytic Functions

We denote that set by A(z,w,k) and (following [1]) call it the Apollonius circle of constant k associated to the points z and w. The set A(z,w,k) is a circle for all values of k other than 1 when it is a line. In this paper, we consider z,w ∈ U, show that if z = w, then necessarily A(z,w, √ (1−|w|2)/(1−|z|2)) meets the unit circle twice, consider the arc on the unit circle with those endpoints,...

A Martingale Decomposition Theorem