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 FRACTAL FUNCTION APPROXIMATION BASED ON WAVELET 基于小波的分形函数逼近 短句来源 The seismic wave function is resolved into amplitude modulation part and random one. For the latter, the fractal dimension and the relevant characterization parameters are yielded by using the Weirstrass Mandelbrot (W M) fractal function. 将爆炸地震波函数分解为调幅部分和随机部分 ,对于后者 ,应用Weirstrass Mandelbrot (W M )分形函数得到了分形维数及相关的特征参数 . 短句来源 Sea surfaces are modeled with analytical statistical model, numericalstatistical method, fractal function and the hybrid of statistics and fractal. 给出了一种用分形函数模拟海面时，由海面参数确定分形参数的具体方法； 提出了用统计模型和分形模型混合模拟海面的方法。 短句来源 The characteristics of the scattered waves amplitude distribution of a kind of two dimension WM fractal function are discussed. 讨论了一种二维Weierstrass分形函数在Kirchhoff近似下的电磁散射回波的幅值分布特征 . 短句来源 This paper introduces the B spline wavelet scaling function into fractal function approximation system and proposes a fractal function approximation algorithm based on wavelets. The algorithm fully exploits the consistency between the fractal and scaling functions in multi scale and multi resolution . 本文在分形函数逼近系统中引入基数B样条小波尺度函数 ,提出基于小波的分形函数逼近算法 ,该算法可充分利用尺度函数和分形函数在多尺度和多分辨性上的一致性。 短句来源 更多 “fractal function”译为未确定词的双语例句
 Continued Fractal Function in CG & Image Processing 连分式函数在图形图像中的应用 短句来源 The scattering characteristic of the rough surface modeling by two-dimensionally fractal function 海地粗糙面的二维分形模拟及其散射特性 短句来源 Differential of fractal function 分形函数的微分 短句来源 The new research methods and subject about the seismic fractal function and the law of the seismic temporal distribution are suggested. 提出地震分维函数与地震时序分布律新的研究方法及课题。 短句来源 In order to obtain the relationship between the acoustic emission process and fracture evolution of concrete material, the concept of relevant fractal function of acoustic emission process is given . The existence of fractal characteristics of acoustic emission process is proved through experiments firstly. 为了寻求混凝土材料声发射过程与断裂演化之间的关系，从实验入手，首先给出了声发射过程关联分维函数 的概念，并通过实验，证明了声发射过程分形特征的存在。 短句来源 更多 相似匹配句对
 Fractal of Function and its Measurement 函数分形及其度量 短句来源 Differential of fractal function 分形函数的微分 短句来源 The function of 睾丸激素的功能 短句来源 Fractal Graphics Fractal图形学 短句来源 Fractal in Crystals 晶体中的分形(Fractal)现象 短句来源 查询“fractal function”译词为用户自定义的双语例句

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 The distribution of the breaking strengths over the system is considered to be a fractal function. As an example, a "Weierstrass-like" fractal function is considered, for which the wavelet transform is related to a Jacobi theta function. In this paper, we use a fractal function to model the surface of sea, and fractal dimension is also an appropriate descriptor of roughness of sea surface. A normalized two dimensional band-limited Weierstrass fractal function is used for modeling the rough surface. Sign-changes of the Thue-Morse fractal function and Dirichlet L-series 更多 In the paPer,we think that fractal dimension and non-scaling region are two important characteristic Parameters of seismic fractal self-organization. The characteristics of correlative dimension at two levels and the main limits on dimension calculations are discussed.The relations between the growing structures of the strong seismic sequences and fractal principles are studied Primarily.The new research methods and subject about the seismic fractal function and the law of the seismic temporal distribution... In the paPer,we think that fractal dimension and non-scaling region are two important characteristic Parameters of seismic fractal self-organization. The characteristics of correlative dimension at two levels and the main limits on dimension calculations are discussed.The relations between the growing structures of the strong seismic sequences and fractal principles are studied Primarily.The new research methods and subject about the seismic fractal function and the law of the seismic temporal distribution are suggested. The characteristics about the temporal changes of the fractal dimensions and their applications on earthquake Prediction are analyzed. 本文认为,分维及无标度区是地震分形自组织两个重要特征参数。讨论了两个层次关联维特征及关联维 D_2计算的基本限制。初步探索了强震序列生长结构与分形原理间关系。提出地震分维函数与地震时序分布律新的研究方法及课题。分析了分维随时间变化特征及其在地震预报上的应用。 In this paper we present a new method -local accumulated deviation method for evaluating the fractal dimension of curves or one-dimensional (1D) surfaces. Our method is tested on various types of curves for Weierstrass- Mandelbrot fractal function and fractal Brownian motion with known fractal dimension. The results are good agreement with the theoritical values. Finally, using Monte -Carlo method, we simulated the randam rough (1D) surfaces with Gauss spectrum, and the new method is applied... In this paper we present a new method -local accumulated deviation method for evaluating the fractal dimension of curves or one-dimensional (1D) surfaces. Our method is tested on various types of curves for Weierstrass- Mandelbrot fractal function and fractal Brownian motion with known fractal dimension. The results are good agreement with the theoritical values. Finally, using Monte -Carlo method, we simulated the randam rough (1D) surfaces with Gauss spectrum, and the new method is applied to data from simulating surfaces. 本文提出了一维分形的分维估计方法—局部方差累积法。通过对已知分维数的Weiers trass函数和分数布朗运动的检验,估计的分维数与理论值有很好的吻合。最后,利用蒙特卡罗方法模拟了高期分布随机粗糙面,并对它们的分维给予了估计。 The widely existing nonlinear phenomena revealed by high-resolution geological records need to be explored With nonlinear scientific methods. As a comprehensive science which has far-reaching influence, nonlinear science has become very popular with the international scientific circle. The development and application of nonlinear science in geosciences is the prelude of the birth of a series of nonlinear geosciences. Fractal theory, time-series analysis and chaotic dynamics are hopefully the most promising... The widely existing nonlinear phenomena revealed by high-resolution geological records need to be explored With nonlinear scientific methods. As a comprehensive science which has far-reaching influence, nonlinear science has become very popular with the international scientific circle. The development and application of nonlinear science in geosciences is the prelude of the birth of a series of nonlinear geosciences. Fractal theory, time-series analysis and chaotic dynamics are hopefully the most promising nonlinear methods in Quaternary studies. Both neotectonic vertical movement and ancient climate changes are oscillating movement which, as a complicated irregular oscillation between regular oscillation (e. g. B-Z oscillation in chemistry) and chaos. The oscillation which is a so-called geophysical chaotic time-series results from the internal stochastic nature of the deter mined Earth system. In the frequency change of oscillation, bifurcation space and width of frequency separation are attenuating respectively in aocordance with the Feigenbaum constants δ and α. The oscillating movement of the Earth system is a transition to chaos. The uprise of mountains, the rise of continents, the fall of ocean floors and the change of the global sea level and a series of such intense changes are indications of chaos. Oscillation movement appears to be nonperiodically, rhythmic, it together with erosion of external forces, creates the undulating geomorphological landforms which are similar hierarchically at some extent. The geomorphological phenomena which have similarity are therefore one of resources of fractal concepts. By a couple of popular simple fractal functions, it is possible to "create" Various geomorphological landforms which are similar fairly with natural landforms. The artificial landforms which we call fractal landforms are called Mandelbrot landscape by mathematicians. It is significant for Quaternary studies: no matter how complicated the modern and ancient landforms appear to be, their mechanisms are simple. It is in accordance with traditional concepts of geosciences: landforms are a result of interaction of both internal and external forces. Simple fractal functions are helpful for the study of the interaction and its evolution characteristics. Relief of landforms is a height field. The conformity between Mandelbrot landscape and real landforms indicates that the geomorphological height field is fractal. The complexity of landforms, i.e. the complexity of the height field (or roughness) can be estimated by fractal dimension of their surface. The difference of fractal dimensions of landforms shows the difference of environmental conditions and the difference of evolution stages. The time-series of the Quaternary environmental change generally not random, i.e. not a Brownian condition, but a fractal Brownian movement(FBM), which has a long-term persistence. Whether a time-series is FBM or not can be decided by Hurst exponent. This provides us a theoretical base for forcasting the mean behaviour of volution. he time-series Hurst ex- ponents of lots of natural phenomena such as the change of precipitation, temperature and the water surface of river, lake and sea are all larger than 1/2, which indicates that every successive value of the time-series is not independent, i. e. they are not Gaussian variable or white Gaussian ncise. Although the traditional statistical methods have been used all the time, they cannot accurately describe the behaviour of time-series. It is desirable to use R/S(range over standard deviation). In the eyes of statisticians, time-series=trend +period + random Since the appearance of Chaotic theory, scientists have however found that the irregularity of time-series results from the stochasticity inside the system, so time-serles=chaos + fluctuation The freedom of a time-series is decided by its correlation dimension of the chaotic attractor of time-series, which also decide whether the time-serits is a stochastic system or a determined system of a limited dimension. If it is the latter, a nonlinear dynamic model can be inferred. Besides fractal dimension, Lyapunov exponent and Kolmogonov entropy(K-entropy) are usually used to describle the chaotic characteristics of time-series. When a system is chaotic the Lyapunov exponent is larger than 0(λ>0). In most cases K-entropy equals the sum of all plus Lyapunov exponents. For a order system K=0, for a stochastic system K=∞. When K=c (a limited value) the system is chaotic. The larger K is the stronger the chaos is. The characteristics of the Quaternary time-series will help us to know the further changes of environment. In the field of Quaternary studies, as the resolving power of data is enhancing, we will have a new insight into the Quaternary process. As we are facing a stern challenge like the catastrophe process of climate change, the traditional linear methods are obviously not enough. The system of climate like many other geographical systems is a nonlinear system. At critical condition a sequence of reaction caused by small events will exert influences on lots of elements in the system and lead to happening of great events. To solve the problem, the theory SOC(selforganized criticality) is much helpful. Nonlinear science is very important for Quaternary studies and it also will develop in turn in the field of Quaternary studies. 第四纪研究中最常用的非线性科学方法可能是分形理论、时间序列分析及混沌动力学。振荡在新构造运动和古气候变化中都是普遍存在的,它是介于有规振荡和混沌之间的中间阶段和过渡。分形理论可以描述地貌的状态和演化特征,混沌吸引子的分维又是混沌的一个重要参量。在时间序列分析中计算混沌吸引子的关联维、李雅普诺夫指数、赫斯特指数、柯尔莫果洛夫熵等可以更深入地揭示时间序列的性质,加深对演化过程的认识。 << 更多相关文摘 相关查询

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