Fibonacci Numbers and Their Applications

ISBN-13: 9781402003271 / Angielski / Miękka / 2001 / 304 str.

Andreas N. Philippou;G.E. Bergum;Alwyn F. Horadam

Opis

It isn't that they can't see the solution. It is Approach your problems from the right end and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. O. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Oulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics," "CFD," "completely integrable systems," "chaos, synergetics and large-scale order," which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics."

Spis treści

Fibonaccene.- On a Class of Numbers Related to Both the Fibonacci and Pell Numbers.- A Property of Unit Digits of Fibonacci Numbers.- Some Properties of the Distributions of Order k.- Convolutions for Pell Polynomials.- Cyclotomy-Generated Polynomials of Fibonacci Type.- On Generalized Fibonacci Process.- Fibonacci Numbers of Graphs III: Planted Plane Trees.- A Distribution Property of Second-Order Linear Recurrences.- On Lucas Pseudoprimes which are Products of s Primes.- Fibonacci and Lucas Numbers and the Morgan-Voyce Polynomials in Ladder Networks and in Electric Line Theory.- Infinite Series Summation Involving Reciprocals of Pell Polynomials.- Fibonacci and Lucas Numbers and Aitken Acceleration.- On Sequences having Third-Order Recurrence Relations.- On the Solution of the Equation G n = P(x).- Distributions and Fibonacci Polynomials of Order k, Longest Runs, and Reliability of Consecutive-k-Out-Of-n : F Systems.- Fibonacci-Type Polynomials and Pascal Triangles of Order k.- A Note on Fibonacci and Related Numbers in the Theory of 2 x 2 Matrices.- Problems on Fibonacci Numbers and Their Generalizations.- Linear Recurrences having almost all Primes as Maximal Divisors.- On the Asymptotic Distribution of Linear Recurrence Sequences.- Golden Hops Around a Circle.