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MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS
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作者 Lulu FANG Jihua MA +1 位作者 Kunkun SONG Xin YANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1594-1608,共15页
For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflect... For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined. 展开更多
关键词 continued fractions product of partial quotients Hausdorff dimension
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ARBITRARILY LONG ARITHMETIC PROGRESSIONS FOR CONTINUED FRACTIONS OF LAURENT SERIES 被引量:3
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作者 胡动刚 胡学海 《Acta Mathematica Scientia》 SCIE CSCD 2013年第4期943-949,共7页
A famous theorem of Szemer'edi asserts that any subset of integers with posi- tive upper density contains arbitrarily arithmetic progressions. Let Fq be a finite field with q elements and Fq((X^-1)) be the power ... A famous theorem of Szemer'edi asserts that any subset of integers with posi- tive upper density contains arbitrarily arithmetic progressions. Let Fq be a finite field with q elements and Fq((X^-1)) be the power field of formal series with coefficients lying in Fq. In this paper, we concern with the analogous Szemeredi problem for continued fractions of Laurent series: we will show that the set of points x ∈ Fq((X-1)) of whose sequence of degrees of partial quotients is strictly increasing and contain arbitrarily long arithmetic progressions is of Hausdorff dimension 1/2. 展开更多
关键词 Szemeredi theorem continued fractions Laurent series Hausdorff dimension
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Block Matrix Representation of a Graph Manifold Linking Matrix Using Continued Fractions 被引量:1
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作者 Fernando I. Becerra López Vladimir N. Efremov Alfonso M. Hernandez Magdaleno 《Applied Mathematics》 2014年第13期1894-1902,共9页
We consider the block matrices and 3-dimensional graph manifolds associated with a special type of tree graphs. We demonstrate that the linking matrices of these graph manifolds coincide with the reduced matrices obta... We consider the block matrices and 3-dimensional graph manifolds associated with a special type of tree graphs. We demonstrate that the linking matrices of these graph manifolds coincide with the reduced matrices obtained from the Laplacian block matrices by means of Gauss partial diagonalization procedure described explicitly by W. Neumann. The linking matrix is an important topological invariant of a graph manifold which is possible to interpret as a matrix of coupling constants of gauge interaction in Kaluza-Klein approach, where 3-dimensional graph manifold plays the role of internal space in topological 7-dimensional BF theory. The Gauss-Neumann method gives us a simple algorithm to calculate the linking matrices of graph manifolds and thus the coupling constants matrices. 展开更多
关键词 GRAPH MANIFOLDS continued fractions LAPLACIAN Matrices KALUZA-KLEIN
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MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS 被引量:1
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作者 Lulu FANG Jihua MA +1 位作者 Kunkun SONG Min WU 《Acta Mathematica Scientia》 SCIE CSCD 2021年第6期1896-1910,共15页
Let x∈(0,1)be a real number with continued fraction expansion[a_(1)(x),a_(2)(x),a_(3)(x),⋯].This paper is concerned with the multifractal spectrum of the convergence exponent of{a_(n)(x)}_(n≥1) defined by τ(x):=in... Let x∈(0,1)be a real number with continued fraction expansion[a_(1)(x),a_(2)(x),a_(3)(x),⋯].This paper is concerned with the multifractal spectrum of the convergence exponent of{a_(n)(x)}_(n≥1) defined by τ(x):=inf{s≥0:∑n≥1an^(-s)(x)<∞}. 展开更多
关键词 multifractal analysis convergence exponent continued fractions
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A SUFFICIENT CONDITION OF CONVERGENCE FOR CLIFFORD CONTINUED FRACTIONS
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作者 李永群 王仙桃 《Acta Mathematica Scientia》 SCIE CSCD 2011年第1期8-14,共7页
In this article, a sufficient condition for a Clifford continued fraction to be convergent is established, and some applications are given.
关键词 Clifford continued fraction sufficient condition CONVERGENCE APPLICATION
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Continued Fractions and Dynamics
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作者 Stefano Isola 《Applied Mathematics》 2014年第7期1067-1090,共24页
Several links between continued fractions and classical and less classical constructions in dynamical systems theory are presented and discussed.
关键词 continued fractions Fast and SLOW Convergents IRRATIONAL ROTATIONS Farey and GAUSS Maps Transfer Operator Thermodynamic FORMALISM
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Two Dual Expansions for Generalized Bivariate Thiele-Type Matrix Valued Interpolating Continued Fractions
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作者 顾传青 《Advances in Manufacturing》 SCIE CAS 1997年第2期87-90,共4页
A new method for the construction of bivariate matrix valued rational interpolants on a rectangulargrid is introduced. The rational interpolants are expressed in the continued fraction form with scalardenominator. Til... A new method for the construction of bivariate matrix valued rational interpolants on a rectangulargrid is introduced. The rational interpolants are expressed in the continued fraction form with scalardenominator. Tile matrix quotients are based oil the generalized inverse for a matrix, Which is found to beeffective in continued fraction interpolation. In this paper, tWo dual expansions for bivariate matrix valuedThiele-type interpolating continued fractions are presented, then, tWo dual rational interpolants are definedout of them. 展开更多
关键词 matrix valued rational interpolant continued fraction expansions.
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An Efficient PRBG Based on Chaotic Map and Engel Continued Fractions
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作者 Atef Masmoudi William Puech Mohamed Salim Bouhlel 《Journal of Software Engineering and Applications》 2010年第12期1141-1147,共7页
In recent years, a variety of chaos-based cryptosystems have been proposed. Some of these systems are used in designing a pseudo random bit generator (PRBG) for stream cipher applications. Most of the chaotic systems ... In recent years, a variety of chaos-based cryptosystems have been proposed. Some of these systems are used in designing a pseudo random bit generator (PRBG) for stream cipher applications. Most of the chaotic systems used in cryptography have good chaotic properties like ergodicity, sensitivity to initial values and sensitivity to control parameters. However, some of them are not very suitable for use in cryptography because of their non-uniform density function, and their relatively small key space. To be used in cryptography, a PRBG may need to meet stronger requirements than for other applications. In particular, various statistical tests can be applied to the outputs of such generators to conclude whether the generator produces a truly random sequence or not. In this paper, we propose a PRBG based on the use of the standard chaotic map with large key space and the Engle Continued Fractions (ECF) map. The outputs of the standard map are used as the inputs of ECF-map. The chaotic nature of the standard map and the good statistical properties of the ECF map motivate us to design a new PRBG for stream cipher applications. The numerical simulation analysis indicates that our PRBG produces bit sequences possessing excellent statistical and cryptographic properties. 展开更多
关键词 CRYPTOGRAPHY continued FRACTION STATISTICAL TESTS PRBG CHAOTIC MAP
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On Continued Fractions and Their Applications
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作者 Zakiya M. Ibran Efaf A. Aljatlawi Ali M. Awin 《Journal of Applied Mathematics and Physics》 2022年第1期142-159,共18页
Continued fractions constitute a very important subject in mathematics. Their importance lies in the fact that they have very interesting and beautiful applications in many fields in pure and applied sciences. This re... Continued fractions constitute a very important subject in mathematics. Their importance lies in the fact that they have very interesting and beautiful applications in many fields in pure and applied sciences. This review article will reveal some of these applications and will reflect the beauty behind their uses in calculating roots of real numbers, getting solutions of algebraic Equations of the second degree, and their uses in solving special ordinary differential Equations such as Legendre, Hermite, and Laguerre Equations;moreover and most important, their use in physics in solving Schrodinger Equation for a certain potential. A comparison will also be given between the results obtained via continued fractions and those obtained through the use of well-known numerical methods. Advances in the subject will be discussed at the end of this review article. 展开更多
关键词 continued Fraction EQUATION Numerical Method ROOTS SERIES FINITE
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The Levels-Recursive Algorithm for Vector Valued Interpolants by Triple Branched Continued Fractions
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作者 Shuo Tang Xuhui Wang 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2006年第2期137-142,共6页
A kind of triple branched continued fractions is defined by making use of Samel- son inverse and Thiele-type partial inverted di?erences [1]. In this paper, a levels-recursive algorithm is constructed and a numerical ... A kind of triple branched continued fractions is defined by making use of Samel- son inverse and Thiele-type partial inverted di?erences [1]. In this paper, a levels-recursive algorithm is constructed and a numerical example is given. 展开更多
关键词 Levels-Recursive算法 向量估计 连分数 部分逆
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Block Based Bivariate Blending Rational Interpolation via Symmetric Branched Continued Fractions
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作者 Qianjin Zhao Jieqing Tan 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2007年第1期63-73,共11页
This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide th... This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method. 展开更多
关键词 插值 函数构造论 二变量 非线性特征
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基于分数低阶协方差的阵列式超声波测风方法
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作者 单泽彪 谢世娟 +2 位作者 刘小松 刘云清 王启万 《仪器仪表学报》 EI CAS CSCD 北大核心 2024年第6期75-82,共8页
考虑到当前基于时差法的超声波测风方法是间歇式测量,并且在脉冲噪声背景下测风精度较差,提出一种基于分数低阶协方差的阵列式超声波连续测风方法。该方法采用由一个发射超声波换能器和4个接收换能器组成的超声波测风阵列结构,依托该阵... 考虑到当前基于时差法的超声波测风方法是间歇式测量,并且在脉冲噪声背景下测风精度较差,提出一种基于分数低阶协方差的阵列式超声波连续测风方法。该方法采用由一个发射超声波换能器和4个接收换能器组成的超声波测风阵列结构,依托该阵列结构通过对其连续采样并进行分数低阶协方差运算处理以抑制脉冲冲击噪声的影响,然后结合多重信号分类算法即可实现风速风向的高精度连续测量。通过仿真对比实验和实际测量实验验证了所提方法的有效性及优越性,与其他超声波测风方法相比具有更强的噪声抑制能力及测风精度,在实测实验中风速和风向的测量误差分别为1.2%和2°,基本达到了超声波风速风向测量的精度要求。 展开更多
关键词 阵列式测风 脉冲噪声 ALPHA稳定分布 连续测风 分数低阶协方差
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一类由空间粗糙高斯噪声驱动分数阶动力学方程的性质研究
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作者 陆伟东 刘俊峰 《应用概率统计》 CSCD 北大核心 2024年第1期139-156,共18页
本文主要研究了一类空间粗糙高斯噪声驱动的分数阶动力学方程,其中高斯噪声关于时间是白色的,关于空间的相依结构由Hurst指数小于1/2的分数布朗运动的协方差刻画.基于Malliavin分析技巧,我们证明了该类方程温和解在Skorohod意义下的存在... 本文主要研究了一类空间粗糙高斯噪声驱动的分数阶动力学方程,其中高斯噪声关于时间是白色的,关于空间的相依结构由Hurst指数小于1/2的分数布朗运动的协方差刻画.基于Malliavin分析技巧,我们证明了该类方程温和解在Skorohod意义下的存在性.同时证明了其温和解矩的上、下界的估计.最后证明了其温和解关于时间和空间变量的Holder连续性. 展开更多
关键词 分数阶动力学方程 高斯噪声 Malliavin分析 矩估计 HOLDER连续性
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基于光谱处理方法的棉花叶绿素含量高光谱反演研究
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作者 买买提·沙吾提 李武耀 +1 位作者 崔锦涛 郑植 《棉花学报》 CSCD 北大核心 2024年第4期296-305,共10页
【目的】叶绿素含量可以用来评价棉花的长势情况,快速、准确和大面积监测棉花叶绿素含量,有助于实现精准农业。【方法】分别用0~2阶(步长为0.2)的分数阶微分处理和1~10尺度下的小波变换对田间测定的陆地棉和海岛棉等2种棉花的高光谱反... 【目的】叶绿素含量可以用来评价棉花的长势情况,快速、准确和大面积监测棉花叶绿素含量,有助于实现精准农业。【方法】分别用0~2阶(步长为0.2)的分数阶微分处理和1~10尺度下的小波变换对田间测定的陆地棉和海岛棉等2种棉花的高光谱反射率进行处理,提高棉花叶绿素含量反演精度。通过分析不同处理方式的光谱与叶绿素含量之间的相关性,筛选得出敏感波段;并运用支持向量机回归和随机森林回归模型分别构建棉花叶绿素含量高光谱估算模型。【结果】(1)在全波段范围内,2种棉花325~1075 nm光谱反射率曲线整体变化趋势基本相同,其反射率均随着叶绿素含量的增加而增大。(2)经连续小波变换和分数阶微分变换后,2种棉花高光谱数据和叶绿素含量的相关性有所增强。使用随机森林回归和小波能量系数7对陆地棉叶绿素含量的反演效果最好,建模集决定系数(coefficient of determination,R^(2))为0.931,均方根误差(root mean square error,RMSE)为0.782,剩余预测偏差(residual prediction deviation,RPD)为2.162;使用随机森林回归和小波能量系数6对海岛棉叶绿素含量的反演效果最佳,建模集R^(2)为0.932,RMSE为1.198,RPD为2.687。【结论】本研究可为棉花叶绿素含量遥感估算提供技术参考。 展开更多
关键词 陆地棉 长绒棉 叶绿素含量 冠层高光谱 连续小波变换 分数阶微分
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基于R-L分数阶定义的PCCM Boost变换器建模与分析 被引量:1
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作者 王仁明 李啸 张赟宁 《电源学报》 CSCD 北大核心 2024年第2期19-26,共8页
研究了基于R-L分数阶定义的电感电流伪连续PCCM(pseudo-continuous conduction mode)Boost变换器模型,并由此导出了变换器的状态平均模型,然后推导出升压比,直流静态工作点,电感电流波纹以及输出电压波纹的表达式。结果表明,与基于Caput... 研究了基于R-L分数阶定义的电感电流伪连续PCCM(pseudo-continuous conduction mode)Boost变换器模型,并由此导出了变换器的状态平均模型,然后推导出升压比,直流静态工作点,电感电流波纹以及输出电压波纹的表达式。结果表明,与基于Caputo分数阶定义下的变换器模型相应表达式比较,R-L分数阶定义下的直流静态工作点和升压比不仅与占空比相关,而且还与电感和电容的阶数有关,输出电压波纹的表达式不仅与分数阶电感的阶数α有关,与分数阶电容的阶数β也相关。电感和电容的阶数对状态变量的直流分量和分数阶PCCM Boost的稳态特性有很大影响。最后,在MATLAB/SIMULINK中搭建了R-L分数阶PCCM Boost变换器数学模型和电路模型,仿真结果显示R-L分数阶PCCM Boost变换器模型的分析结果比其他PCCM Boost模型的分析结果更加稳定,误差更小。 展开更多
关键词 BOOST变换器 分数阶模型 电感电流伪连续模式 状态空间平均法
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自适应Newton-Thiele有理插值及应用
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作者 李麟 檀结庆 邢燕 《合肥工业大学学报(自然科学版)》 CAS 北大核心 2024年第1期137-144,共8页
二元连分式插值是二元有理插值的重要组成部分;文章在前人研究的基础上,对Newton-Thiele有理插值构造过程进行改进。针对Newton-Thiele有理插值在插值过程出现逆差商不存在的情况,传统的解决方法是将相应的Thiele型插值连分式转换为New... 二元连分式插值是二元有理插值的重要组成部分;文章在前人研究的基础上,对Newton-Thiele有理插值构造过程进行改进。针对Newton-Thiele有理插值在插值过程出现逆差商不存在的情况,传统的解决方法是将相应的Thiele型插值连分式转换为Newton插值多项式,然而该处理方法会导致计算复杂度的增加。借鉴相关文献在一元有理插值上的选点方法,文章给出一种带终止条件的自适应贪婪选点算法,即在给定插值点中根据自适应条件筛选出局部点对函数进行构造,以提高Newton-Thiele有理插值函数构造过程的稳定性,提升运算效率。对非线性函数的插值结果表明:该算法的插值效果较好、误差较小;同时将该算法应用到图像修复中,并与其他相关算法的修复效果进行对比,进一步验证了该算法的有效性。 展开更多
关键词 连分式 逆差商存在性 Newton-Thiele有理插值 自适应贪婪算法 图像修复
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基于改进Hofstetter模型的杨木组分体积分数对其弹性参数的影响规律
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作者 王忠铖 杨娜 李久林 《木材科学与技术》 北大核心 2024年第2期12-19,共8页
木材的微观结构和组分构成是影响其弹性参数的重要因素,但关于木材组分体积分数变化对其弹性参数影响的研究相对较少。通过引入灰分因素,对Hofstetter木材连续微观力学模型进行改进,并在此基础上分析杨木组分的体积分数变化对其弹性参... 木材的微观结构和组分构成是影响其弹性参数的重要因素,但关于木材组分体积分数变化对其弹性参数影响的研究相对较少。通过引入灰分因素,对Hofstetter木材连续微观力学模型进行改进,并在此基础上分析杨木组分的体积分数变化对其弹性参数的影响规律。研究表明:改进的Hofstetter模型可较准确预测杨木的顺纹弹性模量,误差绝对值仅13.71%。结晶纤维素等自身刚度较大的组分体积分数增大时,杨木的弹性模量和剪切模量增幅较大;聚合物网络、无定形纤维素体积分数增大时,泊松比增幅较大;木质素、半纤维素体积分数变化对所有弹性参数的影响均较小。 展开更多
关键词 杨木 改进Hofstetter模型 连续介质假设 组分 弹性参数 组分体积分数变化
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分数阶Fourier变换的测不准原理
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作者 周悦 杨燕 《数学物理学报(A辑)》 CSCD 北大核心 2024年第2期257-264,共8页
该文参考Fourier变换的性质研究了离散分数阶Fourier变换的测不准原理以及连续分数阶Fourier变换在Lebesgue测度下的测不准原理,使得分数阶Fourier变换的测不准原理性质更一般化.
关键词 连续分数阶Fourier变换 离散分数阶Fourier变换 测不准原理
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Caputo-Hadamard型分数阶隐式微分方程周期边值问题解的存在性
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作者 张伟 张禹 倪晋波 《吉林大学学报(理学版)》 CAS 北大核心 2024年第4期851-857,共7页
用连续性定理讨论一类Caputo-Hadamard型分数阶隐式微分方程周期边值问题,得出了解的存在性结果,并给出具体实例进行说明.
关键词 Caputo-Hadamard型分数阶微分 分数阶隐式微分方程 周期边值问题 连续性定理 存在性
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Sylvester连分数展式中若干例外集的Hausdorff维数
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作者 廖旭 《数学杂志》 2024年第4期343-357,共15页
对于任意实数x∈(0,1],记x=[d_(1),d_(2),···]为x的Sylvester连分数展式,令ψ(n)为N上的正函数,本文研究了集合A(ψ):■的Hausdorff维数.通过构造覆盖和合适的Cantor型子集,我们得到了该集合的精确维数为■同时,本文还... 对于任意实数x∈(0,1],记x=[d_(1),d_(2),···]为x的Sylvester连分数展式,令ψ(n)为N上的正函数,本文研究了集合A(ψ):■的Hausdorff维数.通过构造覆盖和合适的Cantor型子集,我们得到了该集合的精确维数为■同时,本文还考虑了Sylvester连分数展式的部分商满足■的极限是零或无穷时的集合的Hausdorff维数. 展开更多
关键词 Sylvester连分数 HAUSDORFF维数 增长速度
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