Recently, Belbachir and Bencherif have expanded Fibonacci and Lucas polynomials using bases of Fibonacci-and Lucas-like polynomials. Here, we provide simplified proofs for the expansion formulaethat in essence a computer can do. Furthermore, for 2 of the 5 instances, we find q-analogues.

Cite this article: Lucas J, Canty DJ (2013) The Impact of Routine Focused Transthoracic Echocardiography Immediately before Renovascular Surgery in Patients with End Stage Renal Disease– A Brief Report. Int J Clin Anesthesiol 1(3): 1017. *Corresponding author Dr. Jennifer A Lucas, MBBS FANZCA, Consultant Anaesthetist, Department of Anaesthesia and Perioperative Medicine, Monash Medical Centre, ...

Let L denote the n th Lucas number, where n is a natural number. n 2 Using elementary techniques, we find all solutions of the equation: Ln px where p is prime and p (i000. KEY Wi’RDS AND PHRASES. Lucas number 1985 AMS SUBJECT CLASSIFICATION CODE. IIB39 1. NTRODUCTION Let. n denote a natural number. Let L denote the n th Lucas number, that is, n L1=1, L2=3, Ln Ln_l+Ln_2 for n_ 3. In [1], J.H.E....

Berentsen, Camera, and Waller (henceforth BCW) have written a nice piece that illustrates the effects of monetary policy when the distribution of money balances is non-degenerate across the population at the time of a policy action. The model is very helpful in addressing the issues at hand, and I felt that the article is, in general, quite instructive. Perhaps the closest relative of this arti...

We obtain some new identities for the generalized Fibonacci polynomial by a approach, namely, Q(x) matrix.
 These including Cassini type identity and Honsberger formula can be applied to polynomial
 sequences such as polynomials, Lucas Pell Pell-Lucas polynomials so on, which
 generalize previous results in references.

§1. Overview. Philosophers and mathematicians have drawn lots of conclusions from Gödel’s incompleteness theorems, and related results from mathematical logic. Languages, minds, and machines figure prominently in the discussion. Gödel’s theorems surely tell us something about these important matters. But what? A descriptive title for this paper would be “Gödel, Lucas, Penrose, Turing, Feferman,...

Globalization is accompanied by increasing current account imbalances. They can undermine the positive impacts of increasing international cooperation and trade on economic growth. By applying an economic growth model that requests for long-term compensation of short-term current account deficits, we derive patterns of international trade. Model output, however, is challenged by empirical data ...

Emerging markets exhibit high returns to capital, the ‘Lucas Paradox,’ alongside volatile growth rate regimes. We investigate the role of long-run risks, i.e., risk due to fluctuations in economic growth rates, in leading to return differentials across countries. We take the perspective of a US investor and outline an empirical strategy to identify risky growth shocks and quantify their implica...

In this paper, we consider the relationships between the sums of the Fibonacci and Lucas numbers and 1-factors of bipartite graphs. 1. Introduction The Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n > 2 Fn = Fn 1 + Fn 2 where F1 = F2 = 1: The Lucas Sequence, fLng ; is de…ned by the recurrence relation, for n > 2 Ln = Ln 1 + Ln 2 where L1 = 1; L2 = 3: The permanent of an ...

Let p be an odd prime and q = pm. Let l be an odd positive integer. Let p ≡ −1 (mod l) or p ≡ 1 (mod l) and l | m. By employing the integer sequence an = l−1 2 ∑ t=1 ( 2 cos π(2t− 1) l )n , which can be considered as a generalized Lucas sequence, we construct all the permutation binomials P (x) = xr + xu of the finite field Fq .