Measurement Uncertainty Analysis of the Rotary-scan Method for the Measurable Dimension of Cylindrical Workpieces

The measurement uncertainty analysis is carried out to investigate the measurable dimensions of cylindrical workpieces by the rotary-scan method in this paper.Due to the difficult alignment of the workpiece with a diameter of less than 3 mm by the rotary scan method,the measurement uncertainty of the cylindrical workpiece with a diameter of 3 mm and length of 50 mm which is measured by a roundness measuring machine,is evaluated according to GUM(Guide to the Expression of Uncertainty in Measurement)as an example.Since the uncertainty caused by the eccentricity of the measured workpiece is different with the dimension changing,the measurement uncertainty of cylindrical workpieces with other dimensions can be evaluated the same as the diameter of 3 mm but with different eccentricity.Measurement uncertainty caused by different eccentricities concerning the dimension of the measured cylindrical workpiece is set to simulate the evaluations.Compared to the target value of the measurement uncertainty of 0.1μm,the measurable dimensions of the cylindrical workpiece can be obtained.Experiments and analysis are presented to quantitatively evaluate the reliability of the rotary-scan method for the roundness measurement of cylindrical workpieces.

Soft measurement model of ring's dimensions for vertical hot ring rolling process using neural networks optimized by genetic algorithm

Vertical hot ring rolling(VHRR) process has the characteristics of nonlinearity,time-variation and being susceptible to disturbance.Furthermore,the ring's growth is quite fast within a short time,and the rolled ring's position is asymmetrical.All of these cause that the ring's dimensions cannot be measured directly.Through analyzing the relationships among the dimensions of ring blanks,the positions of rolls and the ring's inner and outer diameter,the soft measurement model of ring's dimensions is established based on the radial basis function neural network(RBFNN).A mass of data samples are obtained from VHRR finite element(FE) simulations to train and test the soft measurement NN model,and the model's structure parameters are deduced and optimized by genetic algorithm(GA).Finally,the soft measurement system of ring's dimensions is established and validated by the VHRR experiments.The ring's dimensions were measured artificially and calculated by the soft measurement NN model.The results show that the calculation values of GA-RBFNN model are close to the artificial measurement data.In addition,the calculation accuracy of GA-RBFNN model is higher than that of RBFNN model.The research results suggest that the soft measurement NN model has high precision and flexibility.The research can provide practical methods and theoretical guidance for the accurate measurement of VHRR process.

Green Measurements for Software Product Based on Sustainability Dimensions

Software is a central component in the modern world and vastly affects the environment’s sustainability.The demand for energy and resource require-ments is rising when producing hardware and software units.Literature study reveals that many studies focused on green hardware;however,limited efforts were made in the greenness of software products.Green software products are necessary to solve the issues and problems related to the long-term use of soft-ware,especially from a sustainability perspective.Without a proper mechanism for measuring the greenness of a particular software product executed in a specific environment,the mentioned benefits will not be attained.Currently,there are not enough works to address this problem,and the green status of software products is uncertain and unsure.This paper aims to identify the green measurements based on sustainable dimensions in a software product.The second objective is to reveal the relationships between the elements and measurements through empirical study.The study is conducted in two phases.Thefirst phase is the theoretical phase,where the main components,measurements and practices that influence the sustainability of a software product are identified.The second phase is the empirical study that involved 103 respondents in Malaysia investigating current practices of green software in the industrial environment and further identifying the main sustainability dimensions and measurements and their impact on achiev-ing green software products.This study has revealed seven green measurements of software product:Productivity,Usability,Cost Reduction,Employee Support,Energy Efficiency,Resource Efficiency and Tool Support.The relationships are statistically significant,with a significance level of less than 0.01(p=0.000).Thus,the hypothesised relationships were all accepted.The contributions of this study revolve around the research perspectives of the measurements to attain a green software product.

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 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 .

THE HAUSDORFF DIMENSION AND MEASURE IN GENERALIZED GEOMETRIC GRAPH DIRECTED CONSTRUCTION

Abthors introduce the notation of generalized geometric constructions in Rm generated by a directed graph G and by a sequence of similarity ratios which are labelled with the edges of this graph. In this paper, it is obtained the Hausdorff dimension and measure of this construction object for some cases.

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.

The Hausdorff Dimension and Hausdorff Measure of Full Parry Measure Subset of Finite Type

All the full Parry measure subsets of a given subshift of finite type determined by an irreducible 0-1 matrix have the same Hausdorrf dimension and Hausdorff measure which coincide with those of the set of finite type.

Three Measurement Methods of Two-photon Absorption Cross-section

Through the experimental design and theoretical analysis, three technologies used for characterizing the two-photon absorption(TPA) properties, such as nonlinear transmission experiment and theory, Z-scan technology and two-photon induced fluorescence method, are introduced. The properties of the three experiments to be utilizable and realizable under desirable limitation are simply analyzed. The advantages of the measurements for TPA characterization are also analyzed.

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.

THE DIMENSION FOR RANDOM SUB-SELF-SIMILAR SET

In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.

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））.

HAUSDORFF DIMENSION OF GENERALIZED STATISTICALLY SELF-AFFINE FRACTALS

The authors consider generalized statistically self-affine recursive fractals K with random numbers of subsets on each level. They obtain the Hausdorff dimensions of K without considering whether the subsets on each level are non-overlapping or not. They also give some examples to show that many important sets are the special cases of their models.

Open Contours Extraction of Rotational Surface Oriented to Layer Measurement

With layer-measured contours, an algorithm that can extract the contour segments from a rotational surface is presented. The extraction can be divided into two stages, i. e. the rough segmentation and the refinement. In the rough segmenting stage, an optimal contour matching method is put forward to find similar contour segment from another closed contour with respect to the seed contour. In the refining stage, an iterative way that can extract a circular arc precisely is presented based on parameters identification and contour-ends expanding/shrinking operation. The algorithm can extract the open contour segments from a rotational surface precisely, as demonstrated in the examples. Based on the work of this paper, further research, such as parameter identification of 3 - D surface and CAD model creation, can be conducted.

The Multifractal Formalism for Measures, Review and Extension to Mixed Cases

The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.

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.

Decision Bayes Criteria for Optimal Classifier Based on Probabilistic Measures

This paper addresses the high dimension sample problem in discriminate analysis under nonparametric and supervised assumptions. Since there is a kind of equivalence between the probabilistic dependence measure and the Bayes classification error probability, we propose to use an iterative algorithm to optimize the dimension reduction for classification with a probabilistic approach to achieve the Bayes classifier. The estimated probabilities of different errors encountered along the different phases of the system are realized by the Kernel estimate which is adjusted in a means of the smoothing parameter. Experiment results suggest that the proposed approach performs well.

Measurements of Fractal Dimensions for Round Turbulent Jets

There is clear evidence of fractal behavior in several facets for turbulent flows.Based on the images obtained by the planar laser-induced fluorescence (PLIF) tech-nique, Sreenivasan and his co-workers (1986, 1990) have measured the fractal dimen-sions of turbulent flows and then obtained the widespread results.

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.

The Proof of the Sufficient and Necessary Conditions which Make the Hausdorff Measure of the Generalized Non-uniform Cantor Set'exist

The paper succeeds in the obtaining a class of generalized non-uniform Cantor set based on the iteration （1）： Si（x） = αix ＋ bi, x ∈ [0, 1], i = 1,2,…, m, where 0 〈 αi 〈 1, i = 1,2,…,m; bi ＋ αi 〉 0, i = 1,2,…,m- 1, b1 = 0 and αm ＋ bm = 1. Providing the sufficient and necessary conditions of its existence Hausdorff measure.