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ON THE FRACTIONAL CALCULUS FUNCTIONS OF A FRACTAL FUNCTION 认领 引用 被引量：4
1
作者 YaoKui SuWeiyi ZhouSongping 《Applied Mathematics(A Journal of Chinese Universities)》 2002年第4期377-381,共5页
Based on the combination of fractional calculus with fractal functions, a new type of functions is introduced; the definition, graph, property and dimension of this function are discussed.
关键词 fractal function fractional calculus box dimension Hausdorff dimension.
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K-Dimension and Hlder Exponent for Bush Type Fractal Functions 认领 引用
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作者 王宏勇 《Journal of Southwest Jiaotong University(English Edition)》 2006年第4期400-403,共4页
Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fracta... Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fractal dimensional relations in which the K-dimension equals the box dimension and packing dimension were presented; moreover, the exact Holder exponent were obtained for such Bush type functions. 展开更多
关键词 Bush type function Fractal function K-Dimension Holder exponent
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ON SPACES OF FRACTAL FUNCTIONS 认领 引用 被引量：2
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作者 Qian Xiaoyuan 《Analysis in Theory and Applications》 1996年第1期42-52,共11页
In this paper we Ointroduce linear-spaces consisting of continuous functions whose graphs are the attactars of a special class of iterated function systems. We show that such spaces are finite dimensional and give the... In this paper we Ointroduce linear-spaces consisting of continuous functions whose graphs are the attactars of a special class of iterated function systems. We show that such spaces are finite dimensional and give the bases of these spaces in an implicit way. Given such a space, we discuss how to obtain a set of knots for whah the Lagrange interpolation problem by the space is uniquely solvable. 展开更多
关键词 IGS ON SPACES OF FRACTAL FUNCTIONS IFS
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A Class of Fractal Functions and Their Dimension Estimates 认领 引用 被引量：4
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作者 WANG Hong-yong YANG Shou-zhi 《Chinese Quarterly Journal of Mathematics》 2000年第4期84-90,共7页
In this paper,we furst construct a claas of fraetal funerions by means of b-adic fraction andinfinite series expressions.Then we investigate the fractal dimensions of the graphs of these funcrionsand Holder continuity... In this paper,we furst construct a claas of fraetal funerions by means of b-adic fraction andinfinite series expressions.Then we investigate the fractal dimensions of the graphs of these funcrionsand Holder continuity.Some of results of dimensions are obtained. 展开更多
关键词 b-adic fraction fractal function fractal dimension Holder continuity
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Wavelet-Based Fractal Function Approximation 认领 引用 被引量：1
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作者 Zhang Hejei Tao Ran Zhou Siyong & Wang Yue 《Journal of Systems Engineering and Electronics》 EI 1999年第4期60-66,共7页
In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which th... In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression. 展开更多
关键词 B-spline Wavelet scaling function Fractal function Approximation Quadratic programming.
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A Geometric Based Connection between Fractional Calculus and Fractal Functions 认领 引用
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作者 Yong Shun LIANG Wei Yi SU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第2期537-567,共31页
Establishing the accurate relationship between fractional calculus and fractals is an important research content of fractional calculus theory.In the present paper,we investigate the relationship between fractional ca... Establishing the accurate relationship between fractional calculus and fractals is an important research content of fractional calculus theory.In the present paper,we investigate the relationship between fractional calculus and fractal functions,based only on fractal dimension considerations.Fractal dimension of the Riemann-Liouville fractional integral of continuous functions seems no more than fractal dimension of functions themselves.Meanwhile fractal dimension of the Riemann-Liouville fractional differential of continuous functions seems no less than fractal dimension of functions themselves when they exist.After further discussion,fractal dimension of the Riemann-Liouville fractional integral is at least linearly decreasing and fractal dimension of the Riemann-Liouville fractional differential is at most linearly increasing for the Holder continuous functions.Investigation about other fractional calculus,such as the Weyl-Marchaud fractional derivative and the Weyl fractional integral has also been given elementary.This work is helpful to reveal the mechanism of fractional calculus on continuous functions.At the same time,it provides some theoretical basis for the rationality of the definition of fractional calculus.This is also helpful to reveal and explain the internal relationship between fractional calculus and fractals from the perspective of geometry. 展开更多
关键词 Fractional calculus fractal functions fractal dimension fractional calculus equation relationship
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ON THE CONTINUITY AND DIFFERENTIABILITY OF AKIND OF FRACTAL INTERPOLATION FUNCTION 认领 引用
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作者 李红达 叶正麟 高行山 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第4期471-478,共8页
The sufficient conditions of Holder continuity of two kinds of fractal interpolation functions defined by IFS (Iterated Function System) were obtained. The sufficient and necessary condition for its differentiability ... The sufficient conditions of Holder continuity of two kinds of fractal interpolation functions defined by IFS (Iterated Function System) were obtained. The sufficient and necessary condition for its differentiability was proved. Its derivative was a fractal interpolation function generated by the associated IFS, if it is differentiable. 展开更多
关键词 fractal interpolation function Holder continuity differentiability
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On cubic Hermite coalescence hidden variable fractal interpolation functions 认领 引用 被引量：2
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作者 Puthan Veedu Viswanathan Arya Kumar Bedabrata Chand 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第1期55-76,共22页
Hermite interpolation is a very important tool in approximation theory and nu- merical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermit... Hermite interpolation is a very important tool in approximation theory and nu- merical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermite interpolant is unique for a prescribed data set, and hence lacks freedom for the choice of an interpolating curve, which is a crucial requirement in design environment. Even though there is a rather well developed fractal theory for Hermite interpolation that offers a large flexibility in the choice of interpolants, it also has the short- coming that the functions that can be well approximated are highly restricted to the class of self-affine functions. The primary objective of this paper is to suggest a gl-cubic Hermite in- terpolation scheme using a fractal methodology, namely, the coalescence hidden variable fractal interpolation, which works equally well for the approximation of a self-affine and non-self-affine data generating functions. The uniform error bound for the proposed fractal interpolant is established to demonstrate that the convergence properties are similar to that of the classical Hermite interpolant. For the Hermite interpolation problem, if the derivative values are not actually prescribed at the knots, then we assign these values so that the interpolant gains global G2-continuity. Consequently, the procedure culminates with the construction of cubic spline coalescence hidden variable fractal interpolants. Thus, the present article also provides an al- ternative to the construction of cubic spline coalescence hidden variable fractal interpolation functions through moments proposed by Chand and Kapoor [Fractals, 15（1） （2007）, pp. 41-53]. 展开更多
关键词 cubic Hermite interpolant cubic spline fractal interpolation function coalescence hidden vari-able convergence.
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HAAR EXPANSIONS OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS AND THEIR LOGICAL DERIVATIVES 认领 引用 被引量：1
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作者 Sha Zhen Chen Gang Zhejiang University,China 《Analysis in Theory and Applications》 1993年第4期73-88,共16页
In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their... In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α. 展开更多
关键词 HAAR EXPANSIONS OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS AND THEIR LOGICAL DERIVATIVES der Haar FIF
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HOLDER PROPERTY OF FRACTAL INTERPOLATION FUNCTION 认领 引用 被引量：3
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作者 沙震 《Analysis in Theory and Applications》 1992年第4期45-57,共13页
The purpose of this paper is to prove a Holder property about the fractal interpolation function L(x), ω(L,δ)=O(δ~α), and an approximate estimate |f-L|≤2{α(h)+||f||/1-h2-D·h2-D}, where D is a fractal ... The purpose of this paper is to prove a Holder property about the fractal interpolation function L(x), ω(L,δ)=O(δ~α), and an approximate estimate |f-L|≤2{α(h)+||f||/1-h2-D·h2-D}, where D is a fractal dimension of L(x). 展开更多
关键词 Pro IL HOLDER PROPERTY OF FRACTAL INTERPOLATION FUNCTION
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Energy and Laplacian of fractal interpolation functions 认领 引用
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作者 LI Xiao-hui RUAN Huo-jun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2017年第2期201-210,共10页
Abstract. In this paper, we first characterize the finiteness of fractal interpolation functions （FIFs） on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling fa... Abstract. In this paper, we first characterize the finiteness of fractal interpolation functions （FIFs） on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on the Sierpinski gasket （SG）. As an application, we prove that the solution of the following Dirichlet problem on SG is a FIF with uniform vertical scaling factor 1/5 ：△=0 on SG ／ {q1, q2, q3}, and u（qi）=ai, i = 1, 2, 3, where qi, i=1, 2, 3, are boundary points of SG. 展开更多
关键词 Dirichlet problem fractal interpolation function Sierpinski gasket energy Laplacian.
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DIMENSION AND DIFFERENTIABILIIY OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS 认领 引用 被引量：2
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作者 WANG GUOZHONG Department of Mathematics, Zhejiang University Hangzhou 310027 《Applied Mathematics(A Journal of Chinese Universities)》 1996年第1期85-100,共16页
In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dim... In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dimension, its packing dimension,and a lower bound of its Hansdorff dimension. 展开更多
关键词 Fractal interpolation function dimension differentiability
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Graph-Directed Coalescence Hidden Variable Fractal Interpolation Functions 认领 引用
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作者 Md. Nasim Akhtar M. Guru Prem Prasad 《Applied Mathematics》 2016年第4期335-345,共11页
Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the... Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets. 展开更多
关键词 Iterated Function System Graph-Directed Iterated Function System Fractal Interpolation Functions Coalescence Hidden Variable FIFs
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Fractal characteristics investigation on electromagnetic scattering from 2-D Weierstrass fractal dielectric rough surface 认领 引用 被引量：3
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作者 任新成 郭立新 《Chinese Physics B》 SCIE EI CAS 2008年第8期2956-2962,共7页
A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. T... A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing. 展开更多
关键词 dielectric rough surface 2-D band-limited Weierstrass fractal function fractal characteristics Kirchhoff approximation
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基于分形理论的多孔材料设计及表征研究进展 认领 引用 被引量：1
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作者 薛新 葛绍祥 +1 位作者 魏雨函 廖娟 《材料工程》 EI CAS CSCD 北大核心 2026年第5期200-212,共13页
多孔材料内部空腔的复杂性、孔隙分布的随机性以及孔径的多尺度性对孔隙细观结构的定量表征带来困难。分形理论因其在表征复杂结构自相似性和多尺度性方面的独特优势,近年受到广泛关注。本文综述了分形理论在多孔材料领域的研究发展历程... 多孔材料内部空腔的复杂性、孔隙分布的随机性以及孔径的多尺度性对孔隙细观结构的定量表征带来困难。分形理论因其在表征复杂结构自相似性和多尺度性方面的独特优势,近年受到广泛关注。本文综述了分形理论在多孔材料领域的研究发展历程,分析了不同尺度下多孔材料单一和多重分形特征的提取与表征方法,对基于多重分形优化的先进工程材料应用案例进行了归纳,重点讨论了分形理论在多孔材料力学性能、传热性能和渗透性能表征研究中的进展,指出基于分形理论指导多孔材料优化设计及性能表征过程中,主要存在细观结构-宏观多功能特性之间的关联物理机制不明确、预测/优化模型算法效率和精度低的问题,对分形理论在多孔材料未来的研究发展和潜在的工程应用前景,如考虑跨尺度效应、多物理场耦合分析、机器学习优化策略等进行了展望。 展开更多
关键词 多孔材料 分形维数 特征提取 分形结构设计 多功能特性
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基于多重分形优化的图像超分辨率重建 认领 引用
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作者 姚勋祥 刘培培 +3 位作者 徐英城 范清兰 包芳勋 张云峰 《山东大学学报（理学版）》 CAS CSCD 北大核心 2026年第3期96-110,共15页
图像超分辨率旨在从低分辨率图像中重建包含丰富纹理细节的高分辨率图像。已有研究表明,精细结构主要对应于傅里叶域中的高频成分,但多数现有方法缺乏针对高频信息的自适应处理机制,容易导致边缘模糊或纹理紊乱。针对上述问题,本文在非... 图像超分辨率旨在从低分辨率图像中重建包含丰富纹理细节的高分辨率图像。已有研究表明,精细结构主要对应于傅里叶域中的高频成分,但多数现有方法缺乏针对高频信息的自适应处理机制,容易导致边缘模糊或纹理紊乱。针对上述问题,本文在非下采样轮廓波变换(non-subsampled contourlet transform,NSCT)域内开展超分辨率研究,将图像分解为多个具有不同频率特性的子带。不同子带所包含的频率信息与图像细节程度密切相关,本文将其定义为图像粗糙度特征。此外,对各子带图像应用分形分析方法,利用分形对图像粗糙度的数学表征能力,描述图像信息的多种频率细节。在此基础上,构建多子带下的多重分形模型,并在各子带上自适应生成相应的分形表示,从而将超分辨率重建过程转化为一个多重分形优化问题。实验结果表明,本研究所提出的方法能够有效恢复图像高频细节。 展开更多
关键词 图像超分辨 非下采样轮廓波变换 分形插值函数 图像粗糙度 分形维度 多重分形
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不同变质程度煤的不同变质程度煤的孔隙-官能团协同作用对气体吸附的影响孔隙-官能团协同作用对气体吸附的影响* 认领 引用
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作者 吴春雷 史波波 +1 位作者 李佳 薛勇 《中国安全科学学报》 EI CAS CSCD 北大核心 2026年第7期135-143,共9页
为揭示不同变质程度煤的孔隙结构、表面官能团与O2、N2和CO2吸附特性的内在关联,选取长焰煤(DX)、气煤(TX)、烟煤(YCW)和无烟煤(XT)4种典型煤样,综合利用低温液氮/CO2吸附、压汞、弗伦克尔-哈尔西-希尔(FHH)分形模型及傅里... 为揭示不同变质程度煤的孔隙结构、表面官能团与O2、N2和CO2吸附特性的内在关联,选取长焰煤(DX)、气煤(TX)、烟煤(YCW)和无烟煤(XT)4种典型煤样,综合利用低温液氮/CO2吸附、压汞、弗伦克尔-哈尔西-希尔(FHH)分形模型及傅里叶变换红外(FTIR)光谱技术表征煤的微观结构,并在20、30和40℃温度及0.1~1.0 MPa条件下开展O2、N2和CO2的吸附试验。结果表明:随变质程度升高,微孔孔容和比表面积呈“先减小→后增加→再减小”的非单调演化,烟煤(YCW)微孔最发达且分形维数最高(2.68);含氧官能团含量随变质程度增加而降低,芳香度逐渐升高;非极性气体(O2、N2)的吸附能力严格受微孔体积控制,遵循YCW>XT>DX>TX的顺序;而极性气体(CO2)的吸附受“孔隙-官能团”协同效应主导,呈现YCW>TX>XT>DX的差异化特征;3种气体均为物理吸附,等量吸附热大小顺序为CO2>O2>N2。 展开更多
关键词 孔隙结构 分形维数 官能团特征 气体吸附 等量吸附热 煤变质程度
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基于S函数的虚拟樱桃树枝干分形结构模型构建 认领 引用
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作者 杨立伟 余小宝 +3 位作者 王志立 吕树盛 侯冲 刘刚 《中国农机化学报》 北大核心 2026年第7期154-159,166,共6页
为提升樱桃树管理的精准度和效率,降低管理成本,构建虚拟樱桃树枝干模型。以不同生长年龄段细纺锤形樱桃树枝干作为研究对象,利用区间概率法和分枝比值法研究樱桃树的分枝分布,同时采用植物生长的S函数推断其主干的生长函数。根据分枝... 为提升樱桃树管理的精准度和效率,降低管理成本,构建虚拟樱桃树枝干模型。以不同生长年龄段细纺锤形樱桃树枝干作为研究对象,利用区间概率法和分枝比值法研究樱桃树的分枝分布,同时采用植物生长的S函数推断其主干的生长函数。根据分枝分布以及主干生长函数,构建樱桃树分枝分布抽象函数,通过蒙特卡罗法,随机生成符合分枝分布的分枝数。据此编写参数L系统文法规则,构建不同生长年龄虚拟樱桃树枝干分形结构模型。利用Houdini软件验证文法规则,并根据构建的L系统文法规则绘制出虚拟樱桃树枝干分形结构模型。为避免分形结构模型连接处出现缺口或不圆滑等问题,使用圆台等效模型构建虚拟枝干,并运用二次B样条进行模型优化。分形结构模型表明,进行6次迭代的分形结构模型展现符合真实樱桃树的分形螺旋排列结构特点,结构模型分枝数目与真实樱桃树一致,并且满足樱桃树分枝的分布趋势。 展开更多
关键词 樱桃树 S函数 虚拟枝干模型 分形结构
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A Study on Radar Cross Section of the Two-Dimensionally Fractal Rough Surface 认领 引用
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作者 Gao Ming-qin Zhang Yuan-qiao +1 位作者 Xu Peng-gen Peng Jin-sheng 《Wuhan University Journal of Natural Sciences》 EI CAS 1999年第2期74-77,共4页
The analysis of the RCS from the rough sea and ground surface is made. The two dimensionally band limited fractal function is used to model the sea and ground surface, the scattered electromagnetic field is calculated... The analysis of the RCS from the rough sea and ground surface is made. The two dimensionally band limited fractal function is used to model the sea and ground surface, the scattered electromagnetic field is calculated by using Kirchhoff approximation. The validity of this result is assured by some references, which indicates that the methods are reliable. 展开更多
关键词 RCS rough surface two dimensionally fractal function Kirchhoff approximation
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化学机械抛光中表面粗糙度的过渡过程 认领 引用
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作者 彭晨宁 吕玉山 刘电飞 《机械工程师》 2026年第2期23-25,30,共3页
化学机械抛光(CMP)是一种将机械研磨和化学腐蚀相结合的技术,是实现纳米级平滑表面的关键技术。为了研究在CMP中从粗糙到光滑表面的过渡过程,基于能量的原理和分形函数建立了硅片表面形貌曲线随时间变化的数学模型,并结合计算机仿真和试... 化学机械抛光(CMP)是一种将机械研磨和化学腐蚀相结合的技术,是实现纳米级平滑表面的关键技术。为了研究在CMP中从粗糙到光滑表面的过渡过程,基于能量的原理和分形函数建立了硅片表面形貌曲线随时间变化的数学模型,并结合计算机仿真和试验,研究了抛光的过渡过程中表面粗糙度随时间衰减的情况,深入探讨了不同加工参数(如抛光压力和抛光盘转速)对表面粗糙度衰减速率的影响。结果表明,试验所得的衰减曲线与仿真所得的理论曲线基本一致,其误差在8.15%~9.37%的范围内。在较高转速下,表面粗糙度衰减得更快;在较高的压强下,粗糙度衰减得快,但获得的稳态值也随之升高。 展开更多
关键词 化学机械抛光(CMP) 表面粗糙度 过渡过程 分形函数 能量法
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