منابع مشابه
Fibonacci sequence, golden section, Kalman filter and optimal control
A connection between the Kalman filter and the Fibonacci sequence is developed. More precisely it is shown that, for a scalar random walk system in which the two noise sources (process and measurement noise) have equal variance, the Kalman filter’s estimate turns out to be a convex linear combination of the a priori estimate and of the measurements with coefficients suitably related to the Fibo...
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We bridge mathematical number theory with that of optimal control and show that a generalised Fibonacci sequence enters the control function of finite horizon dynamic optimisation problems with one state and one control variable. In particular, we show that the recursive expression describing the first-order approximation of the control function can be written in terms of a generalised Fibonacc...
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In this paper some properties of a generalization of Fibonacci sequence are investigated. Then we solve the Diophantine equations $x^2pmkxy-y^2pm x=0$, where $k$ is positive integer, and describe the structure of solutions.
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We know that ( ) mod n F p forms a periodic sequence (vide Theorem 4). Let ( ) h p denote the length of the sequence. Let p be a prime such that: { } ( ) 2,3 mod 5 p ≡ a sufficient and necessary condition to ensure that ( ) 2 2 h p p + . We shall denote this group 1 G F . Let { } 1, 2 , , k D d d d = be the non-empty set of k divisors of 2 2 p + . Then for ( ) [ ] 1 min G i F h p d = such that ...
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ژورنال
عنوان ژورنال: Journal of Optimization Theory and Applications
سال: 2012
ISSN: 0022-3239,1573-2878
DOI: 10.1007/s10957-012-0061-2