DIMENSIONS OF MEASURE ON GENERAL SIERPINSKI CARPET

Let S = Pi(i=1)(infinity){0, 1, ..., r - 1} and (R) over bar the general Sierpinski carpet, Let mu be the induced probability measure on (R) over bar of <(mu)over tilde> on S by phi, where phi is the natural surjection from S onto (R) over bar and <(mu)over tilde> is the infinite product probability measure corresponding to probability vector (b(0), ..., b(r-1)) with b(i) = a(i)(logn) (m-1)/m(alpha). Authors show that dim(H) mu = (C) under bar(L)(mu) = (C) over bar(L)(mu) = (C) under bar(mu) = (C) over bar C(mu) = alpha.

ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION

In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.

Some Results on the Upper Convex Densities of the Self-Similar Sets at the Contracting-Similarity Fixed Points

In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.

THE PACKING MEASURE OF A CLASS OF GENERALIZED SIERPINSKI CARPET

For 1/4< a <(?)/4, let S1(x) =ax, S2(x)=1-a+ax, x∈[0,1]. Ca is the attractor of the iteratedfunction system {S1,S2}, then the packing measure of Ca×Ca isPs(a)(Ca×Ca) = 4·2s(a)(1-a)s(a),where s(a) = -loga4.

NOTE ON THE PAPER “ AN NEGATIVE ANSWER TO A CONJECTURE ON THE SELF-SIMILAR SETS SATISFYING THE OPEN SET CONDITION”

In this paper, we present a more simple and much shorter proof for the main result in the paper ＂ An negative answer to a conjecture on the self-similar sets satisfy- ing the open set condition＂, which was published in the journal Analysis in Theory and Applications in 2009.

A NOTE ON MULTIFRACTAL PACKING DIMENSION OF MEASURES

The relations between the multifractal packing dimension of Borel probability measures and the asymptotic behavior of the function Ф＊（x）=limsup logv（B（x,r））-qlogu（B（x,r））/logr are discussed and some applications are given.

A study of making use of computer-aided projection fringe system to measure breast dimension

To measure breast basic dimension by using computer-aided projection fringe system.Methods A system has been developed for measuring breast basic dimension based on computer-aided projection fringe measurement and programming software.Plastic manikins breast’s SN-N (sternal notch to nipple distance),N-ML (nipple to midline distance),N-N (internipple distance),MBW (base width of breast) and N-IMF (nipple to inframammary fold distance) are measured with this system.At the same time,these items are also measured with routine ruler.Results This study indicate that the system has some merits:① non-touching measurement;② it is very rapid,the patient measured need hold his breath only 0.5 second,and all the time it takes is about 2.5 minutes;③ the measurement’s sensitivity is as high as to 0.6 mm,which meets the clinic requirement entirely;④ the measurement’s accuracy of the system is not significantly when comparing to the routine ruler’s.Conclusion Computer-adided projection fringe system for measuring breast basic dimension is feasible and advanced.14 refs,1 fig.

Hausdorff measure of sets of finite type of one-sided symbolic space

Some estimation formulae and a computation formula for the hausdorff meausre fo the sets of finite type of the one-sided symbolic space are given

A NOTE ON THE ASYMPTOTICS OF THE POLYMER MEASURES IN ONE DIMENSION

Given g∈(0,∞), we prove thatfor some constant C∈(0,∞), where (g, T) is the polymer measure defined on C_0([0, T]→R^1), and {W(t)}t∈[0,T] is the corresponding coordinate process.