Fibonacci and Lucas Numbers
On the spectral norms of r circulant matrices with the biperiodic Fibonacci and Lucas numbers
... In this paper, we obtain new upper and lower bounds for the spectral norms of the r- circulant matrices Q and L whose entries are the biperiodic Fibonacci and biperiodic Lucas numbers. This study can ...
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The upper bound estimation on the spectral norm of r circulant matrices with the Fibonacci and Lucas numbers
... respectively. This paper gives an upper bound estimation of the spectral norm for r-circulant matrices with Fibonacci and Lucas numbers. The result is more accurate than the corresponding results of ...
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On the Norms of r Hankel Matrices Involving Fibonacci and Lucas Numbers
... usual Fibonacci and Lucas numbers, respectively. Then, we obtained upper and lower bounds for the spectral norm of matrix A . We compared our bounds with exact value of matrix A ’s spectral norm. ...
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On the Norms of r Toeplitz Matrices Involving Fibonacci and Lucas Numbers
... Lots of article have been written so far, which concern estimates for spectral norms of Toeplitz matrices, which have connections with signal and image processing, time series analysis and many other problems [6]-[8]. ...
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New identities involving generalized Fibonacci and generalized Lucas numbers
... generalized Fibonacci and generalized Lucas ...famous numbers of Fibonacci, Lucas, Pell and Pell-Lucas numbers are also deduced as special cases of the two derived ...
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ON THE HYPERBOLIC FIBONACCI MATRIX FUNCTIONS
... the Fibonacci and Lucas numbers to the formulas of classical hyperbolic matrix functions, we will define hyperbolic Fibonacci matrix func- tions and we will deal with some of their ...
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Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s——Part I Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci Goniometry
... bolic Fibonacci and Lucas functions based on the golden mean [6-8]—and a proof of the existence of infinite number of similar hyperbolic functions - hyperbolic Fi- bonacci and Lucas -functions ( ...
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On Fibonacci and Lucas Vectors and Quaternions
... the Fibonacci vectors, Lucas vectors and their vector products considering two Fibonacci vectors, two Lucas vectors and one of each ...by Fibonacci and Lucas vectors with respect ...
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On the norms of circulant and r circulant matrices with the hyperharmonic Fibonacci numbers
... classical Fibonacci and Lucas numbers ...with Fibonacci and Lucas number ...classical Fibonacci and Lucas number ...
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Sums of Squares of Fibonacci Numbers with Prime Indices
... of Fibonacci and Lucas identities involving both Fibonacci and Lucas numbers appeared in various journals [1]-[3] and books [4] [5] over the ...of Fibonacci and Lucas ...
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A Note on Stability of a Linear Functional Equation of Second Order Connected with the Fibonacci Numbers and Lucas Sequences
... the Lucas sequences see, ...the Fibonacci numbers p 1, q −1, x0 0 and x1 1, the Lucas numbers p 1, q −1, x0 2 and x1 1, the Pell numbers p 2, q −1, x0 0 and x1 1, the ...
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On the norms of an r circulant matrix with the generalized k Horadam numbers
... other upper and lower bounds for the spectral norms of r-circulant matrices associated with the k-Fibonacci and k-Lucas numbers, respectively. It is clear that the same study about similar subject ...
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Financial Cycles: A Key To Deciphering Seismic Cycles?
... Keywords: 9/56 year cycle, financial panics, earthquakes, Dow Jones Industrial Average, annual one day falls, Phi ratio, Fibonacci numbers, Lucas numbers, Introduction A 9/56 year grid w[r] ...
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A NEW GENERALIZATION OF FIBONACCI AND LUCAS TYPE SEDENIONS
... Akkus and Kizilaslan [17], de…ned a more general quaternion sequence by receiving com- ponents from complex sequences. Then, they gave some properties and identities related to these quaternions. In [18] K¬z¬late¸ s ...
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The sums of the reciprocals of Fibonacci polynomials and Lucas polynomials
... of Fibonacci polynomials and Lucas polyno- mials, and obtained many interesting results, see ...the Fibonacci numbers and Pell num- bers, and obtained some important ...the Fibonacci ...
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Some properties of the generalized Fibonacci and Lucas sequences related to the extended Hecke groups
... the Lucas sequence, similar to the generalized Fibonacci sequence given in Koruo ˘glu and ¸Sahin in ...generalized Fibonacci sequence and the generalized Lucas sequence, and we find polynomial ...
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Even odd and difference property(s) of fibonacci numbers
... the Fibonacci series has even-odd and difference ...two numbers are always odd when we consider ...two numbers are always odd and next number is always ...total Fibonacci series ...the ...
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Integral points on the elliptic curve y2=x3+27x−62
... MSC: 11B25; 11B37 Keywords: elliptic curves; integral point; generalized Fibonacci and Lucas sequences.. The generalized Fibonacci sequence Un P, Q and the Lucas sequence Vn P, Q are defi[r] ...
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Binomial Transforms of Generalized Fibonacci-Like Sequences
... generalized Fibonacci-Like sequences associated with Fibonacci and Lucas ...generalized Fibonacci-Like sequences and their binomial ...
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On Fibonacci functions with Fibonacci numbers
... a Fibonacci function. Theorem . If f (x) is a Fibonacci function, then the limit of quotient f (x+) f (x) ...a Fibonacci function f (x), we have cases: (i) f (x) > , f (x + ) > ; (ii) f ...
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