Results 11 to 20 of about 668 (225)
Continued Fraction Representations of the Generalized Operator Entropy
Tatra Mountains Mathematical Publications, 2023 Abstract The direct calculation of the generalized operator entropy proves to be difficult due to the appearance of rational exponents of matrices. The main motivation of this work is to overcome these difficulties and to present a practical and efficient method for this calculation using its representation by the matrix continued ...
Sarra Ahallal, Said Mennou, Ali Kacha
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Hyperelliptic continued fractions and generalized Jacobians [PDF]
American Journal of Mathematics, 2019 For a complex polynomial $D(t)$ of even degree, one may define the continued fraction of $\sqrt{D(t)}$. This was found relevant already by Abel in 1826, and later by Chebyshev, concerning integration of (hyperelliptic) differentials; they realized that, contrary to the classical case of square roots of positive integers treated by Lagrange and Galois ...
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Entropy, 2012 We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb) at thermal equilibrium at temperature T (either with ab initio dissipation or without it).
Ramon F. Alvarez-Estrada
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A generalization of continued fractions
Journal of Number Theory, 2011 Simple continued fractions are expressions of the form \(a_0+{1\over a_1+{\strut 1\over a_2+\cdots }}\), where \(a_i \in \mathbb{Z}\) and \(a_i \geq 1\) for \(i \geq 1\); the expansion may be finite or infinite. In this paper, the authors study what happens when the \(1\)'s in the numerators are replaced by a fixed but arbitrary positive integer \(N\).
Anselm, Maxwell, Weintraub, Steven H.
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The Generating Function of Ternary Trees and Continued Fractions [PDF]
The Electronic Journal of Combinatorics, 2006 Michael Somos conjectured a relation between Hankel determinants whose entries ${1\over 2n+1}{3n\choose n}$ count ternary trees and the number of certain plane partitions and alternating sign matrices. Tamm evaluated these determinants by showing that the generating function for these entries has a continued fraction that is a special case of Gauss's ...
Ira M. Gessel, Guoce Xin
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A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method
Advances in Mathematical Physics, 2012 We discuss how to obtain black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second-order ordinary differential equations.
H. T. Cho +4 more
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Fractal and FractionalThe paper deals with the problem of representing special functions by branched continued fractions, particularly multidimensional A- and J-fractions with independent variables, which are generalizations of associated continued fractions and Jacobi ...
Roman Dmytryshyn, Serhii Sharyn
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Continued Fractions and Generalized Patterns
European Journal of Combinatorics, 2002 In [BS] Babson and Steingrimsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Let $f_{τ;r}(n)$ be the number of $1\mn3\mn2$-avoiding permutations on $n$ letters that contain exactly $r$ occurrences of $τ$, where $τ$ a generalized pattern on $k$ letters.
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Convergence criteria of branched continued fractions
Researches in MathematicsThe convergence criteria of branched continued fractions with N branches of branching and branched continued fractions of the special form are analyzed.
I.B. Bilanyk, D.I. Bodnar, O.G. Vozniak
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A special case of rational θs for terminating θ-expansions [PDF]
Surveys in Mathematics and its Applications, 2013 There have been quite a few generalizations of the usual continued fraction expansions over the last few years. One very special generalization deals with θ-continued fraction expansions or simply θ-expansions introduced by Bhattacharya and Goswami [A ...
Santanu Chaktaborty
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