期刊文献+
共找到53篇文章
< 1 2 3 >
每页显示 20 50 100
MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS
1
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
下载PDF
ARBITRARILY LONG ARITHMETIC PROGRESSIONS FOR CONTINUED FRACTIONS OF LAURENT SERIES 被引量:3
2
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
下载PDF
MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS 被引量:1
3
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
下载PDF
A SUFFICIENT CONDITION OF CONVERGENCE FOR CLIFFORD CONTINUED FRACTIONS
4
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
下载PDF
Two Dual Expansions for Generalized Bivariate Thiele-Type Matrix Valued Interpolating Continued Fractions
5
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.
下载PDF
On Continued Fractions and Their Applications
6
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
下载PDF
p-adic Continued Fractions Ⅲ
7
作者 王连祥 莫德泽 《Acta Mathematica Sinica,English Series》 SCIE 1986年第4期299-308,共10页
1.Introduction In order to discuss the irrationality, the transcendence and the algebraic independence for p-adic numbers, the first author introduced in two previous papers [1, 2] a simple form for p-adic continued f... 1.Introduction In order to discuss the irrationality, the transcendence and the algebraic independence for p-adic numbers, the first author introduced in two previous papers [1, 2] a simple form for p-adic continued fraction which is called p-adic simple continued fraction by making use of the algebraic theory of continued fraction in the real field mentioned by Schmidt, and gave a sufficient condition for certain p-adic integers which and whose sum, defference, product and quotient are all p-adic transcendental numbers. 展开更多
关键词 p-adic continued fractions exp REAL
原文传递
Classification and counting on multi-continued fractions and its application to multi-sequences
8
作者 DAI ZongDuo FENG XiuTao 《Science in China(Series F)》 2007年第3期351-358,共8页
In the light of multi-continued fraction theories, we make a classification and counting for multi-strict continued fractions, which are corresponding to multi-sequences of multiplicity m and length n. Based on the ab... In the light of multi-continued fraction theories, we make a classification and counting for multi-strict continued fractions, which are corresponding to multi-sequences of multiplicity m and length n. Based on the above counting, we develop an iterative formula for computing fast the linear complexity distribution of multi-sequences. As an application, we obtain the linear complexity distributions and expectations of multi-sequences of any given length n and multiplicity m less than 12 by a personal computer. But only results of m=3 and 4 are given in this paper. 展开更多
关键词 multi-strict continued fractions multi-sequences linear complexity distribution
原文传递
Refined Convergents to the Associated Continued Fractions for Binary Sequences
9
作者 Dai Zongduo Zeng Kencheng State Key Laboratory of Information Security Academia Sinica Beijing, 100039 China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1994年第2期179-191,共13页
The relation between continued fractions and Berlekamp’s algorithm was studied by some reseachers. The latter is an iterative procedure proposed for decoding BCH codes. However, there remains an unanswered question w... The relation between continued fractions and Berlekamp’s algorithm was studied by some reseachers. The latter is an iterative procedure proposed for decoding BCH codes. However, there remains an unanswered question whether each of the iterative steps in the algorithm can be interpreted in terms of continued fractions. In this paper, we first introduce the so-called refined convergents to the continued fraction expansion of a binary sequence s, and then give a thorough answer to the question in the context of Massey’s linear feedback shift register synthesis algorithm which is equivalent to that of Berlekamp, and at last we prove that there exists a one- to-one correspondence between the n-th refined convergents and the length n segments. 展开更多
关键词 Refined Convergents to the Associated continued fractions for Binary Sequences
原文传递
The Limiting Case of Blending Differences for Bivariate Blending Continued Fraction Expansions 被引量:1
10
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
下载PDF
The Convergence of 1-Periodic Branched Continued Fraction of the Special Form in Parabolic Regions
11
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.
下载PDF
Gravity Field Imaging by Continued Fraction Downward Continuation: A Case Study of the Nechako Basin(Canada)
12
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
下载PDF
Continued Fraction Algorithm for Matrix Exponentials
13
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
下载PDF
Pacman Renormalization in Siegel Parameters of Bounded Type
14
作者 Carlos Antonio Marin-Mendoza Rogelio Valdez-Delgado 《Advances in Pure Mathematics》 2023年第10期674-693,共20页
A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorial... A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant. 展开更多
关键词 Siegel Parameters Pacman Renormalization Bounded Type continued Fraction
下载PDF
New Approach to Bivariate Blending Rational Interpolants 被引量:2
15
作者 ZOU Le TANG Shuo 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第2期280-284,共5页
Newton's polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of ... Newton's polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of bivariate blending rational interpolants.Characteristic theorem is discussed.We give some new blending interpolation formulae. 展开更多
关键词 associated continued fractions interpolation blending rational interpolants characteristic theorem
下载PDF
General Structures of Block Based Interpolational Function 被引量:1
16
作者 Zou LE TANG SHUO 《Communications in Mathematical Research》 CSCD 2012年第3期193-208,共16页
We construct general structures of one and two variable interpolation function, without depending on the existence of divided difference or inverse differences, and we also discuss the block based osculatory interpola... We construct general structures of one and two variable interpolation function, without depending on the existence of divided difference or inverse differences, and we also discuss the block based osculatory interpolation in one variable case. Clearly, our method offers marly flexible interpolation schemes for choices. Error terms for the interpolation are determined and numerical examples are given to show the effectlveness of the results. 展开更多
关键词 osculatory interpolation continued fractions interpolation blendingrational interpolation block based interpolation
下载PDF
ON THETA-TYPE FUNCTIONS IN THE FORM(x;q)∞
17
作者 Changgui ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2021年第6期2086-2106,共21页
As in our previous work [14], a function is said to be of theta-type when its asymptotic behavior near any root of unity is similar to what happened for Jacobi theta functions. It is shown that only four Euler infinit... As in our previous work [14], a function is said to be of theta-type when its asymptotic behavior near any root of unity is similar to what happened for Jacobi theta functions. It is shown that only four Euler infinite products have this property. That this is the case is obtained by investigating the analyticity obstacle of a Laplace-type integral of the exponential generating function of Bernoulli numbers. 展开更多
关键词 Q-SERIES Mock theta-functions Stokes phenomenon continued fractions
下载PDF
Three-Dimensional Generalized Inverse Matrix Rational Interpolation
18
作者 WANG Jin bo, GU Chuan qing Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200436, China 《Journal of Shanghai University(English Edition)》 CAS 2001年第4期276-281,共6页
In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fra... In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable. 展开更多
关键词 Tri variable matrix values rational interpolation generalized inverse Thiele type branched continued fractions matrix recursive algorithm
下载PDF
On the Family of Thue Equation |x^3+mx^2y-(m+3)xy^2+y^3|=k 被引量:2
19
作者 XIA Jingbo CHEN Jianhua ZHANG Silan 《Wuhan University Journal of Natural Sciences》 EI CAS 2006年第3期481-485,共5页
The family of cubic Thue equation which depend on two parameters | x^3 + mx^2 y-(m+3) xy^2+y^3|=k is studied. Using rational approximation, we give a smaller upper bound of the solution of the equation, that is... The family of cubic Thue equation which depend on two parameters | x^3 + mx^2 y-(m+3) xy^2+y^3|=k is studied. Using rational approximation, we give a smaller upper bound of the solution of the equation, that is quite better than the present result. Moreover, we study two inequalities | x^3 + mx^2y-(m + 3) xy^2+y^3 | =k≤2m+3 and |x^3 +mx^2y- (m+3)xy^2 + y^3| = k≤ (2m+3)^2 separately. Our result of upper bound make it easy to solve those inequalities by simple method of continuous fraction expansion. 展开更多
关键词 parametric Thue equation Thue inequality continuous fraction expansion bound search
下载PDF
Werner-Type Matrix Valued Rational Interpolation and Its Recurrence Algorithms 被引量:1
20
作者 顾传青 王金波 《Journal of Shanghai University(English Edition)》 CAS 2004年第4期425-438,共14页
In this paper, a practical Werner-type continued fraction method for solving matrix valued rational interpolation problem is provided by using a generalized inverse of matrices. In order to reduce the continued fracti... In this paper, a practical Werner-type continued fraction method for solving matrix valued rational interpolation problem is provided by using a generalized inverse of matrices. In order to reduce the continued fraction form to rational function form of the interpolants, an efficient forward recurrence algorithm is obtained. 展开更多
关键词 matrix valued rational interpolation Werner-type continued fraction forward recurrence algorithm.
下载PDF
上一页 1 2 3 下一页 到第
使用帮助 返回顶部