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CIRCULANT AND NEGACYCLIC MATRICES VIA TETRANACCI NUMBERS
Ozkoc, Arzu,Ardiyok, Elif The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.4
In this paper, the explicit determinants of the circulant and negacyclic matrix involving Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$ are expressed by using only Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$. Also euclidean norms and spectral norms of circulant and negacyclic matrices have been obtained.
ON STRONGLY θ-e-CONTINUOUS FUNCTIONS
Ozkoc, Murad,Aslim, Gulhan Korean Mathematical Society 2010 대한수학회보 Vol.47 No.5
A new class of generalized open sets in a topological space, called e-open sets, is introduced and some properties are obtained by Ekici [6]. This class is contained in the class of $\delta$-semi-preopen (or $\delta-\beta$-open) sets and weaker than both $\delta$-semiopen sets and $\delta$-preopen sets. In order to investigate some different properties we introduce two strong form of e-open sets called e-regular sets and e-$\theta$-open sets. By means of e-$\theta$-open sets we also introduce a new class of functions called strongly $\theta$-e-continuous functions which is a generalization of $\theta$-precontinuous functions. Some characterizations concerning strongly $\theta$-e-continuous functions are obtained.
CIRCULANT AND NEGACYCLIC MATRICES VIA TETRANACCI NUMBERS
( Arzu Ozkoc ),( Elif Ardiyok ) 호남수학회 2016 호남수학학술지 Vol.38 No.4
In this paper, the explicit determinants of the circu- lant and negacyclic matrix involving Tetranacci sequence Mn and Companion-Tetranacci sequence K<sub>n</sub> are expressed by using only Tetranacci sequence M<sub>n</sub> and Companion-Tetranacci sequence Kn . Also euclidean norms and spectral norms of circulant and negacyclic matrices have been obtained.
Simultaneous integer sequences and solving the Pell equation
ARZU OZKOC 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.2
Let k ≥ 1 be a fixed integer. In this work, we set two simultaneous integer sequences defined by Xn = (4k2 + 1)Xn-1 + (4k2 + 1)Xn-2 - Xn-3 and Yn = (4k2 + 1)Yn-1 + (4k2 + 1)Yn-2 - Yn-3 for n ≥ 3 with initial terms X0 = 1, X1 = 2k2+1, X2 = 8k4+8k2+1 and Y0 = 0, Y1 = 2k, Y2 = 8k3+4k and derived some algebraic identities on them. Further, we are able to determine all integer solutions of the Pell equation x2-(k2 +1)y2 = 1 as (xn, yn) = (Xn, Yn) for every n ≥ 1.