The Experts below are selected from a list of 240 Experts worldwide ranked by ideXlab platform
R. Johansson - One of the best experts on this subject based on the ideXlab platform.
-
Continued-Fraction approximation for multivariable system identification
Proceedings of 1995 34th IEEE Conference on Decision and Control, 1995Co-Authors: R. JohanssonAbstract:This paper presents identification methods for multivariable system identification using matrix Fraction descriptions and the matrix Continued Fraction description (CFA) approach which, in turn, yields a lattice-type order-recursive structure. An n-stage optimization algorithm for system parameter estimation of the induced lattice structure parameters is presented, n being the polynomial order of a terminating CFA. Once the matrix Continued-Fraction expansion has been determined, it is straightforward to obtain solutions to both the left and right coprime factorizations of transfer function estimates and, in addition, solution to problems of state estimation (observer design) and pole-assignment control. All calculation of transfer functions on the form of right and left coprime factorizations, calculation of state variable observers and regulators can be made using causal polynomial transfer functions defined by means of matrix sequences of the Continued-Fraction expansion applied in causal and stable forward-order and backward-order recursions.
-
Multivariable system identification via Continued-Fraction approximation
Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1994Co-Authors: R. JohanssonAbstract:This paper presents theory for multivariable system identification using matrix Fraction descriptions and the matrix Continued Fraction description approach which, in turn, yields a lattice-type order-recursive structure. Once the matrix Continued-Fraction expansion has been determined, it is straightforward to obtain solutions to both the left and right coprime factorizations of transfer function estimates and, in addition, solution to problems of state estimation (observer design) and pole-assignment control. An important and attractive technical property is that calculation of transfer functions in the form of right and left coprime factorizations, calculation of state variable observers and regulators all can be made using causal polynomial transfer functions defined by means of matrix sequences of the Continued-Fraction expansion applied in causal and stable forward-order and backward-order recursions.
Nayandeep Deka Baruah - One of the best experts on this subject based on the ideXlab platform.
-
some congruences deducible from ramanujan s cubic Continued Fraction
International Journal of Number Theory, 2011Co-Authors: Nayandeep Deka Baruah, Kanan Kumari OjahAbstract:We present some interesting Ramanujan-type congruences for some partition functions arising from Ramanujan's cubic Continued Fraction. One of our results states that if p3(n) is defined by $\sum_{n = 0}^\infty p_3(n)q^n := (q;q)_\infty^{-3}$, then p3(9n + 8) ≡ 0 (mod 34).
-
explicit evaluations of ramanujan gollnitz gordon Continued Fraction
Monatshefte für Mathematik, 2008Co-Authors: Nayandeep Deka Baruah, Nipen SaikiaAbstract:In this paper, we establish several theorems for the explicit evaluations of Ramanujan-Gollnitz-Gordon Continued Fraction by using some parameterizations of Ramanujan’s theta-functions.
-
some general theorems on the explicit evaluations of ramanujan s cubic Continued Fraction
Journal of Computational and Applied Mathematics, 2003Co-Authors: Nayandeep Deka Baruah, Nipen SaikiaAbstract:In 2001, Jinhee Yi found many explicit values of the famous Rogers-Ramanujan Continued Fraction by using modular equations and transformation formulas for theta-functions. In this paper, we use her method to find some general theorems for the explicit evaluations of Ramanujan's cubic Continued Fraction.
-
modular equations for ramanujan s cubic Continued Fraction
Journal of Mathematical Analysis and Applications, 2002Co-Authors: Nayandeep Deka BaruahAbstract:Abstract In this paper we present two new identities providing relations between Ramanujan's cubic Continued Fraction G(q) and the two Continued Fractions G(q5) and G(q7).
Jun Wu - One of the best experts on this subject based on the ideXlab platform.
-
beta expansion and Continued Fraction expansion
Journal of Mathematical Analysis and Applications, 2008Co-Authors: Bing Li, Jun WuAbstract:For any real number β>1, let e(1,β)=(e1(1),e2(1),…,en(1),…) be the infinite β-expansion of 1. Define ln=sup{k⩾0:en+j(1)=0for all1⩽j⩽k}. Let x∈[0,1) be an irrational number. We denote by kn(x) the exact number of partial quotients in the Continued Fraction expansion of x given by the first n digits in the β-expansion of x. If {ln,n⩾1} is bounded, we obtain that for all x∈[0,1)∖Q, lim infn→+∞kn(x)n=logβ2β*(x),lim supn→+∞kn(x)n=logβ2β*(x), where β*(x), β*(x) are the upper and lower Levy constants, which generalize the result in [J. Wu, Continued Fraction and decimal expansions of an irrational number, Adv. Math. 206 (2) (2006) 684–694]. Moreover, if lim supn→+∞lnn=0, we also get the similar result except a small set.
-
arithmetic and metric properties of oppenheim Continued Fraction expansions
Journal of Number Theory, 2007Co-Authors: Baowei Wang, Jun WuAbstract:We introduce a class of Continued Fraction expansions called Oppenheim Continued Fraction (OCF) expansions. Basic properties of these expansions are discussed and metric properties of the digits occurring in the OCF expansions are studied.
-
on a new Continued Fraction expansion with non decreasing partial quotients
Monatshefte für Mathematik, 2004Co-Authors: Cor Kraaikamp, Jun WuAbstract:We investigate metric properties of the digits occurring in a new Continued Fraction expansion with non-decreasing partial quotients, the so-called Engel Continued Fraction (ECF) expansion.
Yoon Kyung Park - One of the best experts on this subject based on the ideXlab platform.
-
arithmetic of the ramanujan gollnitz gordon Continued Fraction
Journal of Number Theory, 2009Co-Authors: Yoon Kyung ParkAbstract:Text We extend the results of Chan and Huang [H.H. Chan, S.-S. Huang, On the Ramanujan–Gollnitz–Gordon Continued Fraction, Ramanujan J. 1 (1997) 75–90] and Vasuki, Srivatsa Kumar [K.R. Vasuki, B.R. Srivatsa Kumar, Certain identities for Ramanujan–Gollnitz–Gordon Continued Fraction, J. Comput. Appl. Math. 187 (2006) 87–95] to all odd primes p on the modular equations of the Ramanujan–Gollnitz–Gordon Continued Fraction v(τ) by computing the affine models of modular curves X(Γ) with Γ=Γ1(8)∩Γ0(16p). We then deduce the Kronecker congruence relations for these modular equations. Further, by showing that v(τ) is a modular unit over Z we give a new proof of the fact that the singular values of v(τ) are units at all imaginary quadratic arguments and obtain that they generate ray class fields modulo 8 over imaginary quadratic fields.
Joseph Vandehey - One of the best experts on this subject based on the ideXlab platform.
-
new normality constructions for Continued Fraction expansions
Journal of Number Theory, 2016Co-Authors: Joseph VandeheyAbstract:Abstract Text Adler, Keane, and Smorodinsky showed that if one concatenates the finite Continued Fraction expansions of the sequence of rationals 1 2 , 1 3 , 2 3 , 1 4 , 2 4 , 3 4 , 1 5 , ⋯ into an infinite Continued Fraction expansion, then this new number is normal with respect to the Continued Fraction expansion. We show a variety of new constructions of Continued Fraction normal numbers, including one generated by the subsequence of rationals with prime numerators and denominators: 2 3 , 2 5 , 3 5 , 2 7 , 3 7 , 5 7 , ⋯ . Video For a video summary of this paper, please visit https://youtu.be/L7uyAQ7hS74 .
-
Continued Fraction normality is not preserved along arithmetic progressions
arXiv: Number Theory, 2015Co-Authors: Byron Heersink, Joseph VandeheyAbstract:It is well known that if $0.a_1a_2a_3\dots$ is the base-$b$ expansion of a number normal to base-$b$, then the numbers $0.a_ka_{m+k}a_{2m+k}\dots$ for $m\ge 2$, $k\ge 1$ are all normal to base-$b$ as well. In contrast, given a Continued Fraction expansion $\langle a_1,a_2,a_3,\dots\rangle$ that is normal (now with respect to the Continued Fraction expansion), we show that for any integers $m\ge 2$, $k\ge 1$, the Continued Fraction $\langle a_k, a_{m+k},a_{2m+k},a_{3m+k},\dots\rangle$ will never be normal.
-
new normality constructions for Continued Fraction expansions
arXiv: Number Theory, 2015Co-Authors: Joseph VandeheyAbstract:Adler, Keane, and Smorodinsky showed that if one concatenates the finite Continued Fraction expansions of the sequence of rationals \[ \frac{1}{2}, \frac{1}{3}, \frac{2}{3}, \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{1}{5}, \cdots \] into an infinite Continued Fraction expansion, then this new number is normal with respect to the Continued Fraction expansion. We show a variety of new constructions of Continued Fraction normal numbers, including one generated by the subsequence of rationals with prime numerators and denominators: \[ \frac{2}{3}, \frac{2}{5}, \frac{3}{5}, \frac{2}{7}, \frac{3}{7}, \frac{5}{7},\cdots. \]
