Fibonacci Numbers, Basis Reduction, and Integer Programming

Patakı, Gabor
Tural, Mustafa Kemal


Fibonacci series-based pairwise comparison scale for analytic hierarchy process
Can Ylldlrlm, Boǧaç; Karakaya, Gülşah; Gönül, Mustafa Sinan (2021-01-01)
The Analytic Hierarchy Process (AHP) is one of the most widely used quantitative tools in multi-criteria decision-making problems. Despite its popularity and use due to its simple but systematic procedure, AHP has limitations especially in terms of the numerical comparison scale used in one of its core steps: pairwise comparisons. AHP is based on verbal comparisons of alternatives/criteria, which are, then, converted into quantitative scores with a one-To-one mapping between the verbal comparisons and a pre...
Pseudopotential Theory of Atomic Short-Range Order and its Comparison with Experiments
Katsnelson, A. A.; Mehrabov, Amdulla (1978-10-11)
Archimedean Cones in Vector Spaces
Emelyanov, Eduard (2017-01-01)
In the case of an ordered vector space (briefly, OVS) with an order unit, the Archimedeanization method was recently developed by Paulsen and Tomforde [4]. We present a general version of the Archimedeanization which covers arbitrary OVS. Also we show that an OVS (V, V+) is Archimedean if and only if inf(tau is an element of{tau}), y is an element of L(x(tau) - y) = 0 for any bounded below decreasing net {x(tau)}(tau) in V, where L is the collection of all lower bounds of {x(tau)}(tau), and give characteriz...
Elliptic curves and use of their endomorphism rings in cryptography
Sülçe, Ali Mert; Akyıldız, Ersan; Department of Cryptography (2019)
Although elliptic curves have been studied for hundreds of years, the inception of elliptic curve cryptography is 1985 by Koblitz’s and Miller’s independent proposals that is based on the discrete logarithm problem on an elliptic curve defined over a finite field. After that date, there are a lot of advances and studies in elliptic curve cryptography(ECC) which provide high security with relatively small block sizes and high speed compared to the other public key cryptosystems. For instance, 160-bit ellipti...
Lagrangian perturbations of lagrangian nodal spheres in the complex plane
Genlik, Deniz; Finashin, Sergey; Department of Mathematics (2018)
Classification of monotone Lagrangian tori in C^2 up to Hamiltonian isotopy and rescaling is still an open problem and the only classes of such tori that are currently known are Clifford and Chekanov tori. In this thesis, we analyze how these two classes of tori can be obtained by Lagrangian perturbations of a Lagrangian nodal sphere in C^2.
Citation Formats
G. Patakı and M. K. Tural, “Fibonacci Numbers, Basis Reduction, and Integer Programming,” 2007, Accessed: 00, 2021. [Online]. Available: