Some lacunarity properties of partial quotients of real numbers by Zhao, Xuan, Zhang, Zhenliang

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A Wirsing-type approach to some continued fraction expansion by Gabriela Ileana Sebe

“…Chan (2004) considered a certain continued fraction expansion and the corresponding Gauss-Kuzmin-Lévy problem. …”
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Probabilities as Values of Modular Forms and Continued Fractions by Riad Masri, Ken Ono

“…Thanks to this connection, we then show that certain ratios of probabilities are specializations of the Rogers-Ramanujan and Ramanujan- Selberg- Gordon-Göllnitz continued fractions. One particular evaluation depends on a result from Ramanujan's famous first letter to Hardy.…”
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Hankel determinants and Jacobi continued fractions for $q$-Euler numbers by Chern, Shane, Jiu, Lin

“…It is shown that the associated orthogonal polynomials for $q$-Euler numbers are given by a specialization of the big $q$-Jacobi polynomials, thereby leading to their corresponding Jacobi continued fraction expressions, which eventually serve as a key to our determinant evaluations.…”
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An Adaptive Image Inpainting Method Based on Continued Fractions Interpolation by Lei He, Yan Xing, Kangxiong Xia, Jieqing Tan

“…In view of the drawback of most image inpainting algorithms by which texture was not prominent, an adaptive inpainting algorithm based on continued fractions was proposed in this paper. In order to restore every damaged point, the information of known pixel points around the damaged point was used to interpolate the intensity of the damaged point. …”
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On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i>₃ and Their Ratios by Roman Dmytryshyn, Tamara Antonova, Sofiia Hladun

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Some New Explicit Values of Quotients of Ramanujan’s Theta Functions and Continued Fractions by Nipen Saikia

“…We evaluate some new explicit values of quotients of Ramanujan’s theta functions and use them to find explicit values of Ramanujan’s continued fractions.…”
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Location of approximations of a Markoff theorem by K. C. Prasad, M. Lari, P. Singh

Subjects: “…continued fractions…”
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A Gauss-Kuzmin Theorem for Continued Fractions Associated with Nonpositive Integer Powers of an Integer m≥2 by Dan Lascu

“…We consider a family {τm:m≥2} of interval maps which are generalizations of the Gauss transformation. For the continued fraction expansion arising from τm, we solve a Gauss-Kuzmin-type problem.…”
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Qualitative Analysis of the Discretization of a Continuous Fractional Order Prey-Predator Model with the Effects of Harvesting and Immigration in the Population by Md. Jasim Uddin, Sarker Md. Sohel Rana

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Convergence of composition sequences of bilinear and other transformations {fn},fn→z by John Gill

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Units in families of totally complex algebraic number fields by L. Ya. Vulakh

“…Multidimensional continued fraction algorithms associated with GLn(ℤk), where ℤk is the ring of integers of an imaginary quadratic field K, are introduced and applied to find systems of fundamental units in families of totally complex algebraic number fields of degrees four, six, and eight.…”
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Lagrange, central norms, and quadratic Diophantine equations by R. A. Mollin

“…We consider the Diophantine equation of the form x2−Dy2=c, where c=±1,±2, and provide a generalization of results of Lagrange with elementary proofs using only basic properties of simple continued fractions. As a consequence, we achieve a completely general, simple, and elegant criterion for the central norm to be 2 in the simple continued fraction expansion of D.…”
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Some Criteria for Class Numbers to Be Non-One by Ahmad Issa, Hasan Sankari

“…In this paper, we give some criteria for class numbers of certain real quadratic fields to be greater than one, depending on the solvability of the general Pell equation, ideals in quadratic orders, and the period length of the simple continued fraction expansions of d.…”
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Active and Passive Realization of Fractance Device of Order 1/2 by B. T. Krishna, K. V. V. S. Reddy

“…In this paper, rational approximation is obtained by using continued fraction expansion. The rational approximation thus obtained is synthesized as a ladder network. …”
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Some theorems on the explicit evaluation of Ramanujan's theta-functions by Nayandeep Deka Baruah, P. Bhattacharyya

“…Berndt et al. and Soon-Yi Kang have proved many of Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions in terms of Weber-Ramanujan class invariants. …”
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Infinite Paths of Minimal Length on Suborbital Graphs for Some Fuchsian Groups by Khuanchanok Chaichana, Pradthana Jaipong

“…Moreover, we investigate infinite paths of minimal length in graphs and give the recursive representation of continued fraction of such vertex.…”
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Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications by Soo Hwan Kim

“…We introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which need not have the topological structure. …”
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A New Approach to General Interpolation Formulae for Bivariate Interpolation by Le Zou, Shuo Tang

“…The general interpolation formulae include general interpolation formulae of symmetric branched continued fraction, general interpolation formulae of univariate and bivariate interpolation, univariate block based blending rational interpolation, bivariate block based blending rational interpolation and their dual schemes, and some interpolation form studied by many scholars in recent years. …”
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A Mathematical Model for the Analysis of the Pressure Transient Response of Fluid Flow in Fractal Reservoir by Jin-Zhou Zhao, Cui-Cui Sheng, Yong-Ming Li, Shun-Chu Li

“…The analytical solutions are constructed in the Laplace space and presented in a pattern with one continued fraction—the similar structure of solution. The pattern can bring convenience to well test analysis programming. …”
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