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Available online at www.sciencedirect.com International Journal of Approximate Reasoning
, 2007
"... www.elsevier.com/locate/ijar A generic qualitative characterization of independence of causal influence M.A.J. van Gerven *, P.J.F. Lucas, Th.P. van der Weide ..."
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www.elsevier.com/locate/ijar A generic qualitative characterization of independence of causal influence M.A.J. van Gerven *, P.J.F. Lucas, Th.P. van der Weide
Working notes of the workshop held during The
"... sidered most valuable. The contributions included in these workshop notes cover a wide range of topics, from learning to modelling, and from theory to the use of software tools to develop biomedical applications. We hope that the reader will be left with the feeling that developing Bayesian models i ..."
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. Haddawy, D. Hand, I.S. Kohane, P. Larra~naga, A. Lawson, L. Leibovici, T.Y. Leong, P.J.F. Lucas (cochair), S. Monti, L. OhnoMachado, K.G. Olesen, M. Paul, M. Ramoni, A. Riva, P. Sebastiani, G. Tusch, J. Wyatt, B. Zupan ). They carefully read and reviewed each submission. Each paper was reviewed
ON PRIMES IN THE FIBONACCI AND LUCAS SEQUENCES
"... Let Fn and Ln denote the Fibonacci and Lucas sequences, respectively. We will study when a prime p 1 (mod 4) divides L(p1)=4 or F(p1)=4. ..."
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Let Fn and Ln denote the Fibonacci and Lucas sequences, respectively. We will study when a prime p 1 (mod 4) divides L(p1)=4 or F(p1)=4.
GENERATING IDENTITIES FOR FIBONACCI AND LUCAS TRIPLES
"... Using the generating functions of {F A f and {L x f, n + m n + m n=0 n=0 where F ^ _ denotes the (n + m) Fibonacci number and L, denotes the (n + m) n+m n+m Lucas numbers many basic identities are easily deduced. From certain of these identities and the generating & & functions, we obtain i ..."
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Using the generating functions of {F A f and {L x f, n + m n + m n=0 n=0 where F ^ _ denotes the (n + m) Fibonacci number and L, denotes the (n + m) n+m n+m Lucas numbers many basic identities are easily deduced. From certain of these identities and the generating & & functions, we obtain
On the prime density of Lucas sequences
, 1996
"... . The density of primes dividing at least one term of the Lucas sequence fLn (P )g 1 n=0 ; defined by L 0 (P ) = 2; L 1 (P ) = P and Ln (P ) = PLn\Gamma1 (P ) + Ln\Gamma2 (P ) for n 2; with P an arbitrary integer, is determined. 1. Introduction Let P and Q be nonzero integers. Then the sequen ..."
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. The density of primes dividing at least one term of the Lucas sequence fLn (P )g 1 n=0 ; defined by L 0 (P ) = 2; L 1 (P ) = P and Ln (P ) = PLn\Gamma1 (P ) + Ln\Gamma2 (P ) for n 2; with P an arbitrary integer, is determined. 1. Introduction Let P and Q be nonzero integers
A contraction of the Lucas polygon
 Proc. Amer. Math. Soc
, 2004
"... Abstract. The celebrated GaussLucas theorem states that all the roots of the derivative of a complex nonconstant polynomial p lie in the convex hull of the roots of p, called the Lucas polygon of p. We improve the GaussLucas theorem by proving that all the nontrivial roots of p0 lie in a smaller ..."
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polynomial lie in a smaller convex polygon than predicted by the GaussLucas theorem. In fact, our result is closely related to the following consideration of J. L. Walsh. In [12, x3.4] J. L. Walsh wrote: \A deleted neighborhood of an arbitrary zero of p(z) can be assigned which is known to contain
The Order Of The Fibonacci And Lucas Numbers
"... this paper p (r) denotes the exponent of the highest power of a prime p which divides r and is referred to as the padic order of r. We characterize the padic orders p (Fn ) and p (Ln ), i.e., the exponents of a prime p in the prime power decomposition of Fn and Ln , respectively. The characte ..."
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can be found in Robinson [13] and Vinson [15]. The approach presented here is based on a refined analysis of the periodic structure of the Fibonacci numbers by exploring its properties, in particular, around the points where Fn j 0 (mod p): (The smallest n such that Fn j 0 (mod p) is called the rank
FIBONACCI AND LUCAS NUMBERS
, 1998
"... We present here two sievetype explicit formulas for rFibonacci and rLucas numbers (r = 2,3,...) that connect them with families of welldefined combinatorial numbers, and discuss some particular cases. 1. DEFINITIONS We consider the two main families of sequences {F „ (r) } and {L^} (r = 2,3,...) ..."
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,3,...), determined by the simplest general r*order linear recursion (<2 ^ denotes either F ^ or 1$) with initial conditions & r) = E G & («*/•) (i) F ^ = 0, FW = 1,..., F/> = 2' 2 (2 < j < r1); (2) W=r,W = \,...,Lf = 2Jl (l<j<rl). (3) F ^ and 1 $ are rFibonacci and rLucas
Reviewed by Rodica Luca References
"... Uniqueness of nonnegative solutions for semipositone problems on exterior domains. (English summary) J. Math. Anal. Appl. 394 (2012), no. 1, 432–437. The paper deals with the boundary value problem ⎨ −∆u = λK(x)f(u), x ∈ Ω, ..."
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Uniqueness of nonnegative solutions for semipositone problems on exterior domains. (English summary) J. Math. Anal. Appl. 394 (2012), no. 1, 432–437. The paper deals with the boundary value problem ⎨ −∆u = λK(x)f(u), x ∈ Ω,
DIOPHANTINE REPRESENTATION OF LUCAS SEQUENCES
, 1993
"... Un(P, 0 = PU^iP, 0QUn_2(P, 0 for n> 2, and the "associated " Lucas sequences {Vn(P, 0} are defined similarly with initial terms equal to 2 and P, for n = 0 and 1, respectively. The sequences of Fibonacci numbers and Lucas numbers are, of course, {Fn} = {U„(l,1)} and {Ln} = {V„(\,1) ..."
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)}. Several authors (e.g.,[3], [1], [6]) have discussed the conies whose equations are satisfied by pairs of successive terms of the Lucas sequences. In particular, it has been shown that (x, y)K, MVH) satisfies y 2Pxy + Qx 2 +eQ n = 0, where w „ = U„(P, Q)\fe =1 and w „ = F„(P, 0 if e = P 24Q.lt has
Results 1  10
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143