Nonuniform isothermal curing of cylindrical products made of polymeric composites

Conclusion By increasing the curing temperature and reducing the winding rate, it is possible to obtain compressive radial stresses in a cylindrical product during the entire curing stage — which should prevent loss of integrity during the curing operation. When the duration of the curing process is limited, the magnitude of the compressive stresses will depend in an extreme manner on curing temperature. Meanwhile, in the general case, ensuring minimal residual stresses will not ensure the absence of tensile radial stresses during curing.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 873–877, September–October, 1988.     

From Multifractal Measures to Multifractal Wavelet Series

Given a positive locally finite Borel measure μ on R, a natural way to construct multifractal wavelet series is to set , where . Indeed, under suitable conditions, it is shown that the function F_μ inherits the multifractal properties of μ. The transposition of multifractal properties works with many classes of statistically selfsimilar multifractal measures, enlarging the class of processes which have self-similarity properties and controlled multifractal behaviors. Several perturbations of the wavelet coefficients and their impact on the multifractal nature of F_μ are studied. As an application, multifractal Gaussian processes associated with F_μ are created. We obtain results for the multifractal spectrum of the so-called W-cascades introduced by Arnéodo et al.     

Self-Conformal Multifractal Measures

A self-conformal measure is a measure invariant under a set of conformal mappings. In this paper we describe the local structure of self-conformal measures. For such a measure we divide its support into sets of fixed local dimension and give a formula for the Hausdorff and packing dimensions of these sets. Moreover, we compute the generalized dimensions of the self-conformal measure.     

Numerical solution of the problem of sound emission by a cylindrical piezoelectric vibrator excited by electric pulses

A numerical method is proposed to solve the nonstationary wave problem for a piezoelectric ceramic cylinder immersed in a liquid and excited by an electric signal. The method uses a finite-difference scheme constructed by the integro-interpolation method. A numerical experiment is conducted to analyze the transients in a thin-walled cylinder excited by a step electric pulse.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 30–37, 1987.     

统计自相似集的重分形分解

设K是由Graf定义的统计自相似集.本文构造了一支撑在K上的随机测 度p,并研究了结合P的K的重分形分解,得到了分形谱函数f(α)的表达式.     

Multifractal Decomposition of Statistically Self-Similar Sets

Let K be a statistically self-similar set defined by Graf. In this paper, we construct a random measure ρ which is supported by K and study the multifractal decomposition for K with ρ. Under such a decomposition, we obtain the expression of the spectrum function ƒ(α). Received July 18, 1997, Accepted October 13, 2000     

Multifractal structure and product of matrices

There is a well established multifractal theory for self-similar measures generated by non-overtapping contractive similutudes. Our report here concerns those with overlaps. In particular we restrict our attentionto the important classes of self-similar measures that have matrix representations. The dimension spectra andthe L-spectra are analyzed through the product of matrices. There are abnormal behaviors on the multifrac-tal structure and they will be discussed in detail.     

Multifractal Components of Multiplicative Set Functions

We analyze the multifractal spectrumof multiplicative set functions on a self-similar set with open set condition. We show that the multifractal components carry self-similar measures which maximize the dimension. This gives the dimension of a multifractal component as the solution of a problem of maximization of a quasiconcave function satisfying a set of linear constraints. Our analysis covers the case of multifractal components of self-similar measures, the case of Besicovitch normal sets of points, the multifractal spectrum of the relative logarithmic density of a pair of self-similar measures, the multifractal spectrum of the Liapunov exponent of the shift mapping and the intersections of all these sets. We show that the dimension of an arbitrary union of multifractal components is the supremum of the dimensions of the multifractal components in the union. The multidimensional Legendre transform is introduced to obtain the dimension of the intersection of finitely many multifractal components.     

Multifractal analysis of non-uniformly hyperbolic systems

We prove a multifractal formalismfor Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville-Pomeau map.     

Exceptional Set and Multifractal Analysis

In this note we consider a one-parameter family of Cantor-sets with overlapping cylinders. For a set of zero measure of parameters (exceptional set) the dimension of the attractor drops as a result of the intersection between the cylinders. We find a connection between multifractal analysis and the size of this exceptional set.     

局部熵的高维重分形分析

对不变测度建立了高维形式的重分形分析,即考察与多维参数相关联的重分形分解.利用非紧集或非不变集的高维(q,μ)熵,给出了局部熵的高维重分形谱的一个关系式.     

Multifractal variation for projections of measures

The aim of this work is to provide a relationship between the relative multifractal spectra of orthogonal projections of a measure μ in Euclidean space and those of μ. As an application we study the relative multifractal analysis of the projections of a measure.     

Multifractal analysis of foreign exchange data

In this paper we perform multifractal analyses of five daily Foreign Exchange (FX) rates. These techniques are currently used in turbulence to characterize scaling and intermittency. We show the multifractal nature of FX returns, and estimate the three parameters in the universal multifactal framework, which characterize all small and medium intensity fluctuations, at all scales. For large fluctuations, we address the question of hyperbolic (fat) tails of the distributions which are characterized by a fourth parameter, the tail index. We studied both the prices fluctuations and the returns, finding no systematic difference in the scaling exponents in the two cases. We discuss and compare our results with several recent studies, and show how the additive models are not compatible with data: Brownian, fractional Brownian, Lévy, Truncated Lévy and fractional Lévy models. We analyse in this framework the ARCH(1), GARCH(1,1) and HARCH (7) models, and show that their structure functions scaling exponents are undistinguishable from that of Brownian motion, which means that these models do not adequately describe the scaling properties of the statistics of the data. Our results indicate that there might exist a multiplicative ‘flux of financial information’, which conditions small‐scale statistics to large‐scale values, as an analogy with the energy flux in turbulence. Copyright © 1999 John Wiley & Sons, Ltd.     

Multifractal nature of extensive air showers

Cherenkov images are multifractal in nature. We show that multifractal behaviour of Cherenkov images arises due to multiplicative nature of pair production and bremsstrahlung processes in the longitudinal shower development passage.     

Multifractal spectra and multifractal zeta-functions

We introduce multifractal zetafunctions providing precise information of a very general class of multifractal spectra, including, for example, the multifra     

Geometric Constructions in Multifractal Geometry

This is a survey on geometric constructions in multifractal analysis of measures. We show that the multifractal formalism introduced by Olsen [Ol11] and Peyriére [Pey] leads to a multifractal geometry for product measures, for slices of measures (i.e. intersections of measures with lower dimensional subspaces), and for general intersections of measures, which is analogous to the fractal geometry for product sets, for slices of sets (i.e. intersections of sets with lower dimensional subspaces), and for general intersections of sets, respectively.     

广义Moran集的重分形分解

该文考虑广义Ｍｏｒａｎ集的重分形分解问题,讨论了在不附加压缩尺度具有正的下界条件的情形下广义Ｍｏｒａｎ集的重分形分解集的Ｈａｕｓｄｏｒｆｆ维数问题．     

MULTIFRACTAL DECOMPOSITION OF FRACTALS WITH FINITE MEMORY

The authors study recursive structures with ＂finite memory＂ in Euclidean matric space and the multifractal decomposition of the corresponding fractals. For any two positive numbers q,β, and such a recursive structure, a linear operator V^q,β in finite dimensional space is defined. The multifractal spectrum is given by the spectral radius of Vq,^β.