Thomas Koshy

Bio: Thomas Koshy is an academic researcher. The author has contributed to research in topics: Lucas sequence & Fibonacci number. The author has an hindex of 1, co-authored 1 publications receiving 337 citations.

The fibonacci numbers-exposed

Abstract: Among numerical sequences, the Fibonacci numbers Fn have achieved a kind of celebrity status. Indeed, Koshy gushingly refers to them as one of the "two shining stars in the vast array of integer sequences" [16, p. xi]. The second of Koshy's "shining stars" is the Lucas numbers, a close relative of the Fibonacci numbers, about which we will say more below. The Fibonacci numbers are famous for possessing wonderful and amazing properties. Some are well known. For example, the sums and differences of Fibonacci numbers are Fibonacci numbers, and the ratios of Fibonacci numbers converge to the golden mean. Others are less familiar. Did you know that any four consecutive Fibonacci numbers can be combined to form a Pythagorean triple? Or how about this: The greatest common divisor of two Fibonacci numbers is another Fibonacci number. More precisely, the gcd of F, and Fm is Fk, where k is the gcd of n and m.

On Fibonacci Quaternions

Abstract: In this paper, we investigate the Fibonacci and Lucas quaternions. We give the generating functions and Binet formulas for these quaternions. Moreover, we derive some sums formulas for them.

The Effects of Threading, Infection Time, and Multiple-Attacker Collaboration on Malware Propagation

Abstract: Self-propagating malware spreads over the network quickly and automatically. Malware propagation should be modeled accurately for fast detection and defense. State-of-the-art malware propagation models fail to consider a number of issues.First, the malware can scan a host for multiple vulnerabilities on multiple ports. Second, the vulnerability scanning can be done by multiple threads concurrently. Third, the exploitation of vulnerabilities and the infection of vulnerable hosts cannot be done instantly. Fourth, the malware propagation can start from multiple places in the network rather than a single release point.Finally, the malware copies can collaborate with each other to cause much more damage.Little was done to understand the effects of Multi-port scanning,Multi-threading, Infection time, Multiple starting points,and Collaboration (MMIMC) on malware propagation. This research quantitatively measures the effects of MMIMC on infected hosts. We employ the Fibonacci Number Sequence (FNS)to model the effects of infection time. We derive the Shift Property, which illustrates that different malware initialization scan be represented by shifting their propagations on the time axis. We prove the Linear Property, which shows that the effects of multiple-attacker collaboration can be represented by linear combinations of individual attacks. Experimental results show that the above issues significantly affect malware propagation and verify our analysis.

δ-Fibonacci numbers

Abstract: The scope of the paper is the definition and discussion of the polynomial generalizations of the Fibonacci numbers called here δ-Fibonacci numbers. Many special identities and interesting relations for these new numbers are presented. Also, different connections between δ-Fibonacci numbers and Fibonacci and Lucas numbers are proven in this paper.

Some topological and geometrical properties of new Banach sequence spaces

Abstract: In the present paper, we introduce a new band matrix and define the sequence space where is the k th Fibonacci number for every . We also establish some inclusion relations concerning this space and determine its α-, β-, γ-duals. Further, we characterize some matrix classes on the space and examine some geometric properties of this space. MSC:11B39, 46A45, 46B45, 46B20.