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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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ON THE CHOICES OF ACCELERATING CONVERGENCE FACTORS FOR LIMIT PERIODIC CONTINUED FRACTION K(an/1) 被引量:4
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作者 唐烁 檀结庆 朱功勤 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1996年第1期62-70,共9页
There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given... There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given for most frequently used ACFs. 展开更多
关键词 LIMIT PERIODIC continued fraction accelerating CONVERGENCE factor.
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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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The Limiting Case of Blending Differences for Bivariate Blending Continued Fraction Expansions 被引量:1
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作者 赵前进 檀结庆 《Northeastern Mathematical Journal》 CSCD 2006年第4期404-414,共11页
For a univariate function given by its Taylor series expansion, a continued fraction expansion can be obtained with the Viscovatov's algorithm, as the limiting value of a Thiele interpolating continued fraction or by... For a univariate function given by its Taylor series expansion, a continued fraction expansion can be obtained with the Viscovatov's algorithm, as the limiting value of a Thiele interpolating continued fraction or by means of the determinantal formulas for inverse and reciprocal differences with coincident data points. In this paper, both Viscovatov-like algorithms and Taylor-like expansions are incorporated to yield bivariate blending continued expansions which are computed as the limiting value of bivariate blending rational interpolants, which are constructed based on symmetric blending differences. Numerical examples are given to show the effectiveness of our methods. 展开更多
关键词 INTERPOLATION continued fractions symmetric blending differences expansion
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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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Continued Fraction Evaluation of the Universal Y’s Functions 被引量:1
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作者 Mohammed Adel Sharaf Abdel-naby Saad Saad Nihad Saad Abd El Motelp 《International Journal of Astronomy and Astrophysics》 2015年第1期15-19,共5页
In the present paper, an efficient algorithm based on the continued fractions theory was established for the universal Y’s functions of space dynamics. The algorithm is valid for any conic motion (elliptic, parabolic... In the present paper, an efficient algorithm based on the continued fractions theory was established for the universal Y’s functions of space dynamics. The algorithm is valid for any conic motion (elliptic, parabolic or hyperbolic). 展开更多
关键词 UNIVERSAL KEPLER EQUATION continued fraction Technique Y-Universal Function
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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 FRACTION TACTICS FOR CRYPTANALYSIS
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作者 李大兴 李大为 《Journal of Electronics(China)》 1992年第3期193-199,共7页
The continued fraction tactics for cryptanalysis based on Legendre Theorem ofcontinued fraction are proposed.
关键词 CRYPTANALYSIS continued fraction ALGORITHM
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Continued Fraction Algorithm for Matrix Exponentials
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作者 GU Chuan qing Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200436, China 《Journal of Shanghai University(English Edition)》 CAS 2001年第1期11-14,共4页
A recursive rational algorithm for matrix exponentials was obtained by making use of the generalized inverse of a matrix in this paper. On the basis of the n th convergence of Thiele type continued fraction expa... A recursive rational algorithm for matrix exponentials was obtained by making use of the generalized inverse of a matrix in this paper. On the basis of the n th convergence of Thiele type continued fraction expansion, a new type of the generalized inverse matrix valued Padé approximant (GMPA) for matrix exponentials was defined and its remainder formula was proved. The results of this paper were illustrated by some examples. 展开更多
关键词 matrix exponentials generalized inverse continued fraction algorithm Padé approximant
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Gravity Field Imaging by Continued Fraction Downward Continuation: A Case Study of the Nechako Basin(Canada)
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作者 ZHANG Chong ZHOU Wenna +1 位作者 LV Qingtian YAN Jiayong 《Acta Geologica Sinica(English Edition)》 SCIE CAS CSCD 2021年第S01期102-105,共4页
Interpretation of gravity data plays an important role in the study of geologic structure and resource exploration in the deep part of the earth,like the lower crust,the upper mantle(Lüet al.,2013,2019).The gravi... Interpretation of gravity data plays an important role in the study of geologic structure and resource exploration in the deep part of the earth,like the lower crust,the upper mantle(Lüet al.,2013,2019).The gravity anomaly reflects the lateral resolution of the underground mass distribution. 展开更多
关键词 depth estimation downward continuation gravity data continued fraction
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Continued Fraction Cartesian to Geodetic Coordinate Transformation
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作者 J.D.Turner A.Alnaqeb A.Bani Younes 《Computer Modeling in Engineering & Sciences》 SCIE EI 2016年第3期257-268,共12页
A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation.Conventional approaches for inverting the transformation use the natural ellipsoidal coordinates,this work e... A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation.Conventional approaches for inverting the transformation use the natural ellipsoidal coordinates,this work explores the use of the satellite ground-track vector as the differential correction variable.The geodetic latitude is recovered by well-known elementary means.A high-accuracy highperformance 3D vector-valued continued fraction iteration is constructed.Rapid convergence is achieved because the starting guess for the ground-track vector provides a maximum error of 30 m for the satellite height above the Earth’s surface,throughout the LEO-GEO range of applications.As a result,a single iteration of the continued fraction iteration yields a maximum error for the satellite height of 10??11 km.and maximum error for the geodetic anomaly of 10??9 rad.The coordinate transformation is completed by non-iteratively recovering the satellite height and the geodetic anomaly.No Taylor expansions are introduced and no Jacobian sensitivity calculations are required.For all practical applications the new algorithm provides a closed-form solution.The accuracy and algorithmic performance of the proposed approach is compared with other state of the art algorithms. 展开更多
关键词 GEODETIC TRANSFORMATION continued fraction singularity-free
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Algorithm for Fast Calculation of Hirzebruch-Jung Continued Fraction Expansions to Coding of Graph Manifolds
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作者 Fernando I. Becerra López Vladimir N. Efremov Alfonso M. Hernández Magdaleno 《Applied Mathematics》 2015年第10期1676-1684,共9页
We present a new algorithm for the fast expansion of rational numbers into continued fractions. This algorithm permits to compute the complete set of integer Euler numbers of the sophisticate tree graph manifolds, whi... We present a new algorithm for the fast expansion of rational numbers into continued fractions. This algorithm permits to compute the complete set of integer Euler numbers of the sophisticate tree graph manifolds, which we used to simulate the coupling constant hierarchy for the universe with five fundamental interactions. Moreover, we can explicitly compute the integer Laplacian block matrix associated with any tree plumbing graph. This matrix coincides up to sign with the integer linking matrix (the main topological invariant) of the graph manifold corresponding to the plumbing graph. The need for a special algorithm appeared during computations of these topological invariants of complicated graph manifolds since there emerged a set of special rational numbers (fractions) with huge numerators and denominators;for these rational numbers, the ordinary methods of expansion in continued fraction became unusable. 展开更多
关键词 Hirzebruch-Jung continued fraction Fast Expansion ALGORITHM GRAPH MANIFOLDS
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Continued Fraction Method for Approximation of Heat Conduction Dynamics in a Semi-Infinite Slab
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作者 Jietae Lee Dong Hyun Kim 《Applied Mathematics》 2014年第7期1061-1066,共6页
Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler computations and analyses. R... Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler computations and analyses. Rational approximations of the Laplace solutions such as the Pade approximation can be used for this purpose. For some heat conduction problems appearing in a semi-infinite slab, however, such rational approximations are not easy to obtain because the Laplace solutions are not analytic at the origin. In this article, a continued fraction method has been proposed to obtain rational approximations of such heat conduction dynamics in a semi-infinite slab. 展开更多
关键词 Heat Conduction Dynamics SEMI-INFINITE SLAB continued fraction PADE APPROXIMATION
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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 Convergence of 1-Periodic Branched Continued Fraction of the Special Form in Parabolic Regions
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作者 Dmytro I. Bodnar Mariia M. Bubniak 《Journal of Mathematics and System Science》 2014年第4期269-274,共6页
Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple ... Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple power series. We consider 1-periodic branched continued fraction of the special form which is an analog fraction with not equivalent variables if the values of that variables are fixed. We establish an analog of the parabola theorem for that fraction and estimate truncation error bounds for that fractions at some restrictions. We also propose to use weight coefficients for obtaining different parabolic regions for the same fraction without any additional restriction for first element. 展开更多
关键词 continued fractions 1-periodic branched continued fraction of special form CONVERGENCE uniform convergence truncation error bounds.
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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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