Okumus, Israfil; Celik, Ercan

Elliptic curves play a fundamental role in contemporary cryptography due to their deep algebraic properties and their ability to provide high levels of security with relatively small parameter sizes. The theoretical and practical foundations of elliptic curve cryptography (ECC) were established through independent contributions by Koblitz and Miller, whose pioneering work demonstrated that the group structure induced by elliptic curves could be effectively employed in public-key cryptographic schemes. Since then, ECC has become a cornerstone of modern cryptographic protocols, including widely deployed mechanisms such as the Elliptic Curve Digital Signature Algorithm (ECDSA). In this study, we re-examine the algebraic and geometric significance of the point at infinity. Rather than treating this element as an abstract artifact, we introduce an alternative geometric interpretation by associating the identity with the line at infinity. This perspective preserves the classical group law while offering a more intuitive and geometrically transparent understanding of the identity element within the elliptic curve framework. Motivated by the chord-and-tangent addition law on elliptic curves, we further extend these ideas to a non-elliptic setting by defining a new binary operation on the quadratic curve y = x2. Consequently, the resulting algebraic system forms an abelian group. The proposed approach not only enhances the conceptual clarity of the group law underlying elliptic curves but also illustrates how similar algebraic constructions can arise in alternative geometric contexts. These findings provide a theoretical framework that may inspire future explorations of cryptographic primitives beyond classical elliptic curve models.

Uysal, Mine; Ozkan, Engin

In this paper, we define a new application of Pell and Pell-Lucas numbers, the vectors of Pell and Pell-Lucas sequences. We examine them in 2 and 3 dimensions, then we give the definition of generalized vectors. Then, we define these vectors as vector sequences. We analyze the properties of these vectors both as linear algebra and as a number sequence. We first investigate the vectorial properties of these generalized vectors. Then, we define these generalized vectors as a sequence of numbers and give the recurrence relation. We also calculate the cosines of the angles between these vectors. Finally, we derive some important identities calculated in these number sequences for these vector sequences.

Yildiz, Fevkani; Akcay, Hulya; Astam, Aykut; Kundakci, Mutlu

In this paper, gallium oxide (Ga2O3) thin films at various substrate temperatures (Ts) were grown on Indium Tin Oxide (ITO), glass, p-type silicon by radio-frequency magnetron sputtering (RFMS). We investigated how structural, morphological and optical properties change with various Ts. XRD results of thin films grown on p-type silicon substrate suggest that crystallinity properties of synthesized thin films strongly depend on the Ts. From SEM and AFM analyses of Ga2O3 thin films grown on p-type silicon substrate, it was observed that when the temperature increased, a porous structure appeared, and the grain size changed depending on the Ts. Moreover, obtained results from the absorption measurements, the bandgap energy of Ga2O3 thin films grown on the p-type silicon substrate decreased with increasing substrate temperature.

Ozkan, Engin; Uysal, Mine

In this study, we present higher order Jacobsthal numbers. Then we define higher order Jacobsthal quaternions by using higher order Jacobsthal numbers. We give the concept of the norm and conjugate for these quaternions. We express and prove some propositions related to these quaternions. Also, we find the recurrence relation, the Binet formula and the generating function for these quaternions. Finally, we calculate Cassini, Catalan, Vajda and d’Ocagne identities for higher order Jacobsthal quaternions.

Firat, Ishak; Aslay, Fulya

Today which is called as the digital age with the considerably developing information systems, the constant increase in the data amount being recorded has revealed the concept of big data. Obtaining the strategic information which is crucial for decision-makers especially in managerial terms is only possible through processing these big data with accurate techniques. Data mining techniques have frequently been used in recent years in order to reach meaningful and useful knowledge among data stacks. In this study, the Apriori Algorithm was used for the managers of university library information systems, which provide data-oriented service, to make investment decisions in the future effectively and create user profiles. Within the scope of the study, an application was performed on the basis of an information system comprising of real data of Erzincan Binali Yıldırım University Central Library. By means of association rules, which are one of the descriptive models of data mining, ten different association rules regarding the joint borrowing of publications were applied and results were obtained in the confidence intervals of 57.1% and 95.8%. In addition, information such as library inventory, member profile, and publication borrowing habits were obtained and evaluations were made in line with this information at the end of the study.

Kandemir, Ali; Kaptaner Igci, Bahar; Aytac, Zeki; Fisne², Ahter

The status of the Adonis cyllenea var. paryadrica was re-evaluated and decided to change its taxonomic status to species level. In addition, information about pollen structure, ecology, conservation status and distribution map of the taxon were presented.