The fractal properties for the non - degenerat diffusion processes 非退化擴(kuò)散過程樣本的分形性質(zhì)
Fractal properties of vegetation pattern 植被格局的分形特征
At first , the fractal property of hexangular lattice is illustrated from two aspects which are the definition of fractal and the form of hexangular lattice 首先從分形的定義以及六角格子的形成過程兩個(gè)方面說明了其分形特性。
Furthermore , the fractal properties of the level sets and inverse image of compact sets of n - dimension non - degenerate diffusion processes is also considered by professor yang in [ 2 ] , and some new results are obtained in this paper 另外,楊新建教授在文獻(xiàn)[ 2 ]中研究了緊集上非退化擴(kuò)散過程樣本的水平集和逆像集的一些分形性質(zhì),本文在這方面也做了一些工作。
In this way , the self - similar multi - fractal property of the hadronic system produced in z0 ( ) decay is strictly confirmed and the corresponding fractal dimensions and levy index are obtained in the first time using the high statistics data from the l3 experiment at lep 這樣就精確地驗(yàn)證了在z ~ o衰變能量下的e ~ + e ~ -對(duì)撞末態(tài)強(qiáng)子系統(tǒng)是多重自相似分形,并首次用實(shí)驗(yàn)測(cè)出了相應(yīng)的分形維數(shù)與l vy指數(shù)。
Futhermore , fractal analysis has achieved some important development . several fractal functions , such as the weierstrass functions , the besicovitch functions , the rademacher functions , the takagi functions , etc , and their graph dimensions and fractal properties are investigated extensively due to the special fractal structures 幾個(gè)分形函數(shù), weierstrass函數(shù), besicovitch函數(shù), rademacher函數(shù), takagi函數(shù)等,由于它們所特有的分形性質(zhì),在分形研究中占有重要地位,因此,它們的分形維數(shù)、圖象模擬的研究,也成為當(dāng)前的重要課題。
After that , the multifractal spectra dq - q are computed by fixed - mass method . the results show that in the studied scaling range different types of landscapes and profiles in different directions perform different fractal properties , that is , the d value and crossover length ^ decrease in turns with the landform type from high - moutain , mid - low mountain to basin , and the profile parallel to wear grooves often has lower d values ( < 1 . 5 ) than those perpendicular to wear grooves do ( 1 . 5 ) in the same section 提出以地貌分形特點(diǎn)和渡越長度為依據(jù)的地貌層次界定方案,研究指出了5km左右應(yīng)為宏觀臨界點(diǎn):不同構(gòu)造地貌區(qū)、不同取向的剖線的多重分形譜值域范圍寬窄表現(xiàn)出中低山區(qū)高山區(qū)盆地區(qū),垂直構(gòu)造地貌斜坡方向斜交方向平行方向的特點(diǎn),表明了內(nèi)外營力作用的不均勻性和方向性。
Furthermore , the dq value ranges of profile multifarctal spectra in different landform types and in different directions of the same sections perform different properties and anisotrpies . it can be concluded that the landscape fractal properties depends closely on the int ensity , manner and inhomogenity of exogenic and inogenic processess , and with the properties , we can study quantatively the dynamic geomorphic process . by using the same methods just above , local fractal dimensions d , crossover length tc and the multifractal spectra dq - q of two large - scale landform profiles ( across and along tianshan mountain ranges respectively ) are calculated . the results show that in the studied scaling range the two profiles perform different scaling properties , and both of them can be divided to three evident different linear scaling subsections 不同類型地貌區(qū)二維地貌表面也表現(xiàn)出多度域分形特征,而且隨著觀測(cè)尺度的增加,每個(gè)區(qū)間的分維值均表現(xiàn)為依次減小,表明外營力作用的影響逐漸被內(nèi)營力作用所取代:不同類型地貌區(qū)在相應(yīng)區(qū)間的分維值表現(xiàn)為高山區(qū)中低山區(qū)盆地區(qū),體現(xiàn)了不同類型地貌表面粗糙性或復(fù)雜性的差異,因此分維值大小可作為地貌表面外營力侵蝕作用強(qiáng)度的重要指標(biāo):利用標(biāo)度區(qū)的間斷點(diǎn)和各種地貌類型表面分維值或宏觀效應(yīng)趨于一致,提出5 - 6km左右可作為地貌的宏觀臨界點(diǎn),并且與利用地貌剖線研究所得到的5km這一數(shù)值是基本吻合的。