Results 21 to 30 of about 1,829,984 (205)
Some properties of continued fractions with applications in morkov processes [PDF]
, 1972 Several results for continued fractions are first derived and are then shown to be applicable to numerical solution of differential-difference equations arising from linear birth-death processes.
O'donohoe, M R, Murphy, J A
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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 geometric generalization of continued fractions for imaginary quadratic fields [PDF]
, 2021 The Euclidean Algorithm for the integers is well known and yields a finite continued fraction expansion for each rational number. Geometrically, successive convergents in this expansion correspond to endpoints of edges in the Farey tessellation of the ...
Scheckelhoff, Kristen +1 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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On Cantor Sets Defined by Generalized Continued Fractions [PDF]
, 2022 We study a special class of generalized continuous fractions, both in real and complex settings, and show that in many cases, the set of numbers that can be represented by a continued fraction for that class form a Cantor set.
Hedvig, Danielle, Gorodetski, Masha
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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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