Results 21 to 30 of about 92,586 (253)
Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
Mathematics, 2016 The main objective of this paper is to generalize the Extended Irreversible Thermodynamics in order to include the anomalous transport in systems in non-equilibrium conditions.
Abel Garcia-Bernabé +3 more
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Generalized Continued Logarithms and Related Continued Fractions
J. Integer Seq., 2016 We study continued logarithms as introduced by Bill Gosper and studied by J. Borwein et. al.. After providing an overview of the type I and type II generalizations of binary continued logarithms introduced by Borwein et. al., we focus on a new generalization to an arbitrary integer base $b$.
Jonathan M. Borwein +2 more
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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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Circuit complexity of knot states in Chern-Simons theory
Journal of High Energy Physics, 2019 We compute an upper bound on the circuit complexity of quantum states in 3d Chern-Simons theory corresponding to certain classes of knots. Specifically, we deal with states in the torus Hilbert space of Chern-Simons that are the knot complements on the 3-
Giancarlo Camilo +3 more
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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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A New Algorithm to Approximate Bivariate Matrix Function via Newton-Thiele Type Formula
Journal of Applied Mathematics, 2013 A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid. The rational interpolant is of the form motivated by Tan
Rongrong Cui, Chuanqing Gu
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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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Non-Equilibrium Liouville and Wigner Equations: Moment Methods and Long-Time Approximations
Entropy, 2014 We treat the non-equilibrium evolution of an open one-particle statistical system, subject to a potential and to an external “heat bath” (hb) with negligible dissipation.
Ramon F. Álvarez-Estrada
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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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