On the Equality of Hausdorff Dimensions and Conformal Measures of Parabolic Maps

Let f, g be two parabolic maps of degree ≥ 2. HD(J) denotes the Hausdorff dimension of the Julia set J and m f and m g denote the t-conformal measure supported on the Julia set J(f) and J(g) respectively. In this paper we show that if J(f) and J(g) are locally connected and f and g topologically conjugate, then HD(J(f)) = HD(J(g)), mg = mfoh-1 .

CONFORMAL RESTRICTION MEASURES ON LOOPS SURROUNDING AN INTERIOR POINT

A conformal restriction measure is a probability measure which is used to describe the law of a random connected subset in a simply connected domain that satisfies a certain conformal restriction property. Usually there are three kinds of conformal restriction measures: one (called the chordal restriction measure) has two given boundary points of the random set, the second (called the radial restriction measure) has one boundary point and one interior point in the random set, and the third (called the tri-chordal restriction measure) has three boundary points in the random set. In this article, we will define a new probability measure such that the random set associated to it contains one given interior point and does not intersect with the boundary. Furthermore, we will show that this measure can be characterized by one parameter;we will also construct this one-parameter family of measures in two ways and obtain several properties.

On the Continuity of Julia Sets and Hausdorff Dimension of N CP and Parabolic Maps

Denote by HD（J（f）） the Hausdorff dimension of the Julia set J（f） of a rational function f. Our first result asserts that if f is an NCP map, and fn → f horocyclically,preserving sub-critical relations, then fn is an NCP map for all n ≥≥ 0 and J（fn） →J（f） in the Hausdorff topology. We also prove that if f is a parabolic map and fn is an NCP map for all n ≥≥ 0 such that fn→4 f horocyclically, then J（fn） → J（f） in the Hausdorff topology, and HD（J（fn）） →4 HD（J（f））.

Derivation and conformity measurement of a popular explicit analytic Borowy 2C PV module model

A popular explicit analytic Borowy 2C PV module model is proposed for power generation prediction.The maximum power point and the open-circuit point which are calculated in this model cannot be equal to the data given by manufacturers under standard test condition(STC).The derivation of this model has never been mentioned in any literatures.The parameter forms of 2C model in this paper are more simplified,and the model is decomposed into a STC sub-model and an incremental sub-model.The STC model is derived successfully from an ideal single-diode circuit model.Relative error estimations are developed to do the conformity error measurements.The analysis results showed that though the biases at those critical points are very small,the conformity will depend on both of the two ratio values I_(m)/I_(sc) and V_(m)/V_(oc),which can be used to verify whether 2C model is applicable for the PV module produced by a particular manufacturer.

MEASURES AND THEIR DIMENSION SPECTRUMS FOR COOKIE-CUTTER SETS IN R^d

The characteristics of cookie-cutter sets in R^d are investigated. A Bowen's formula for the Hausdorff dimension of a cookie-cutter set in terms of the pressure function is derived. The existence of self-similar measures, conformal measures and Gibbs measures on cookie-cutter sets is proved. The dimension spectrum of each of these measures is analyzed. In addition, the locally uniformly a-dimensional condition and the fractal Plancherel Theorem for these measures are shown. Finally, the existence of order-two density for the Hausdorff measure of a cookie-cutter set is proved.