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Showing 1 to 20 of 43 for “"Fibonacci"”.
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Fibonacci sequences
… in the thirteenth century, Leonardo de Pisa, or, Fibonacci, introduced his famous rabbit problem, which may be stated simply as follows: assume that rabbits reproduce at a rate such that one pair is born each month from each pair of adults not less than two months old. If one pair is present …
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Elgenvalues of Fibonacci-like Sequences
The familiar Fibonacci sequence 1,1,2,3,5,8,13,... can be described by the recurrence relation x(0) = 1, x(1) = 1, x(n) = x(n-1) + x(n-2). For this relation, as n → oo, x(n+1) → 1 +√5 x(n) 2 ' which is the familiar golden ratio. This value is also the dominant eigenvalue of the above recurrence …
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Around the Fibonacci Numeration System
Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can …
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Γενικευμένα πολυώνυμα Fibonacci και κατανομές πιθανότητας
Η τόσο συχνή εμφάνιση της ακολουθίας Fibonacci στη φύση καθώς και ο συσχετισμός της με πλείστους τομείς της μαθηματικής επιστήμης έδωσε αφορμή να ενταθεί η έρευνα στην περιοχή αυτή. Και τούτο ιδιαίτερα τις τελευταίες δύο δεκαετίες. Τα πολυώνυμα Fibonacci k-τάξης αποτελούν μία από τις ευρύτερες …
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The Z-densities of the Fibonacci Sequence
… made a conjecture about the Z-densities of the Fibonacci sequence, F(n), based on computational results. For a prime p, Z(p) is the ``Fibonacci entry-point of n" or the smallest positive integer n such that p divides F(n), M(m,x) is the number of primes p is less than x such that m divides Z(p), …
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Linear Forms in Logarithms and Fibonacci Numbers
… Omar Kihel, pertaining to Diophantine triples of Fibonacci numbers. To go along with this will be introductory material not included in said paper which establishes the mathematical concepts therein and offers some historical perspective and motivation. The initial aim of the paper was to explore …
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Fibonacci Sets In Discrepancy Theory and Numerical Integration
<p> We study the Fibonacci Sets from the point of view of their quantity with respect to discrepancy and numerical integration. We give a Fourier analytic proof of the fact that symmetrized Fibonacci Set has asymptotically minimal L2 discrepancy. This approach also yields an exact formula for this …
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Integer Compositions, Gray Code, and the Fibonacci Sequence
… and Gray Code to integer compositions and the Fibonacci sequence through the use of analytic combinatorics, Zeckendorf's Theorem, and generating functions.</p>
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ΜΕΓΙΣΤΟ ΜΗΚΟΣ ΡΟΗΣ ΕΠΙΤΥΧΙΩΝ ΚΑΙ ΠΟΛΥΩΝΥΜΑ ΤΥΠΟΥ-FIBONACCI
… MOMENTS OF LN. OUR FORMULAS ARE IN TERMS OF FIBONACCI-TYPE POLYNOMIALS OF ORDER K. WE INTRODUCE AND STUDY A NEW DISTRIBUTION, THE BINOMIAL DISTRIBUTION OF ORDER K AND DERIVE THE EXACT DISTRIBUTION OF IT. APPLICATIONS OF THE RANDOM VARIABLES WHICH WE STUDY ARE GIVEN IN RELIABILITY OF …
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Prime And Irreducible Elements In Z<sub>x</sub> , Hamiltonian Cycles In Concentric Circle Graphs, And Fibonacci Sequences In Z<sub>x</sub>
… circle graphs. In the third part, we discuss the Fibonacci sequence in Z<sub>x</sub>. All of the theorems stated in our thesis are new to us.
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Differential posets and dual graded graphs
… an r-differential poset is bounded above by the Fibonacci sequence and that there is a unique poset with such a maximum rank sequence. We also prove that a 1-differential lattice is either Young's lattice or the Fibonacci lattice. In the second part of the thesis, we present a series of new …
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Divisibility Conditions for Fibonomial Coefficients
… 3. Both these primes have the property that the Fibonacci entry point of $p$ is $p+1$. We study the fibonomial triangle mod 5, showing with a theorem of Knuth and Wilf that the triangle has a recurring structure under divisibility by five. While this result is not new, our method of proof is new …
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New Methods for Finding Non-Left-Orderable and Unique Product Groups
… in hyperbolic 2- and 3- space, and Fibonacci groups.
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Biloba for chamber ensemble
… mainly systems based on palindromes and the Fibonacci series. Palindromes can manifest themselves in multifarious way, from the number of beats in a group of measures in a phrase to the unfolding of pitches in a musical gesture. One instance of the usage of the Fibonacci series is in the time …
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Arithmetic and dynamical systems
… S that the power series f(z) generated by the Fibonacci series with all primes in S removed has a natural boundary.
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A hybrid computer parameter optimization study of the two-area load frequency control problem \
… techniques are used. One is based upon the Fibonacci search method, and the other is a direct search method. The optimum control settings are compared with industry recommended standards.
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Isomorphisms amongst certain classes of cyclically presented groups
… Repovs and Spaggiari. The abelianization of the Fibonacci groups F(2, n) was proved by Lyndon to be finite and its order can be expressed in terms of the Lucas numbers. Bardakov and Vesnin have asked if there is a formula for the order of the abelianization of G_n(m, k) groups that can be …
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Space-Efficient and Noise-Robust Quantum Factoring
… efficient and reversible exponentiation with Fibonacci numbers in the exponent, rather than the usual powers of 2, adapting work by Kaliski (arXiv:1711.02491) from the classical reversible setting to the quantum setting. This technique also allows us to perform quantum modular exponentiation …
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Aðferðir til sköpunar og greiningar punkta með netafræði
… Til þess greinum við tvær punktamengi: Fibonacci-grindur (með ítarlega yfirferð á eiginleikum þeirra) og punktamengin sem hafa tengda β-grind fyrir óvenju hátt β. Sem partur af þessu verkefni þróuðum við skilvika útfærslu til að reikna β-grindir og önnur nándarnet af margvíðum …
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Studies on Gopala-Hemachandra Codes and their Applications
Gopala-Hemachandra codes are a variation of the Fibonacci universal code and have applications in data compression and cryptography. We study a specific parameterization of Gopala-Hemachandra codes and present several results pertaining to these codes. We show that GH_{a}(n) always exists for any n …
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