Transfinite mean value interpolation has recently emerged as a simple and robust way to interpolate a function f defined on the boundary of a planar domain. In this paper we study basic properties of the interpolant, including sufficient conditions on the boundary of the domain to guarantee interpolation when f is continuous. Then, by deriving the normal derivative of the interpolant and of a m...

In this short note , using concepts of p-Adic QFT and p-branes, we derive the transfinite M theory generalization of the inverse fine structure constant given by (αM ) −1 = 100 + 61φ . The orginal El Naschie and Selvam-Fadnavis inverse fine structure constant value (αHS) −1 = 100+60φ was based on a transfinite heterotic string theory and a quasiperiodic Penrose tiling formalism, respectively. H...

Ordinal Conditional Functions (OCFs) are one of the predominant frameworks to define belief change operators. In his original paper Spohn defines OCFs as functions from the set of worlds to the set of ordinals. But in subsequent paper by Spohn and others, OCFs are just used as functions from the set of worlds to natural numbers (plus eventually +∞). The use of transfinite ordinals in this frame...

We establish natural criteria under which normally iterable premice are for stacks of normal trees. Let [Formula: see text] be a regular uncountable cardinal. and an text]-sound premouse text]-iteration strategy (roughly, text]-strategy). define condensation property iteration strategies, inflation condensation. show that if has then is text]-iterable length trees each text]), moreover, we spec...

In this paper we study the combinatorial structure of the Hawaiian earring group, by showing that it can be represented as a group of transfinite words on a countably infinite alphabet exactly analogously to the representation of a finite rank free group as finite words on a finite alphabet. We define a big free group similarly as the group of transfinite words on given set, and study their gro...

MODELS OF TRANSFINITE REDUCTIONS

Let assume that Alice, Bob, and Charlie, the three classical people of cryptography are not limited anymore to perform a finite number of computations on real computers, but are limited to α computations and to α bits of memory, where α is a fixed infinite cardinal. For example α = א0 (the countable cardinal, i.e. the cardinal of N the set of integers), or α = C (the cardinal of the set R of re...