We consider a class of iterated function systems (IFSs) of contracting similarities of Rn, introduced by Hutchinson, for which the invariant set possesses a natural Hölder continuous parameterization by the unit interval. When such an invariant set is homeomorphic to an interval, we give necessary conditions in terms of the similarities alone for it to possess a quasisymmetric (and as a corolla...

environment assigning intervals to program variables. Writing X = {x1 ← �1� � � � � x� ← ��} for the function X mapping x� to �� such that X (x�) = ��, � = 1� � � � � �, the interval invariance equations would be 4 One of the 64 bits is used for garbage collection. 12 P. C�����   X1 = {x ← [min_int� max_int]} X2 = {x ← [1� 1] � L X3(x) = ∅ ? ∅ : let [�� �] = X3(x) in [min(� + 1� ma...

We provide escape rates formulae for piecewise expanding interval maps with ‘random holes’. Then we obtain rigorous approximations of invariant densities of randomly perturbed metabstable interval maps. We show that our escape rates formulae can be used to approximate limits of invariant densities of randomly perturbed metastable systems.

The homogeneity of binary functions on the unit interval [0, 1] is a very useful property in many real practical applications. This paper studies circle complex plane. generalization both rotational invariance and ratio scale for fuzzy operations. We show that function homogeneous if only it rotationally invariant invariant. Moreover, we consider simplification operators.