Araştırmacılar(33)

• Akpınar, Ayşe Karanlık
• Altunba, Murat
• Altunbaş, Murat
• Amirali, Gabil
• Amirali, Ilhame
• Amiraliyev, Gabil M.
• Amiraliyev, Gabli M.
• Çakmak, Ali
• Çelik, Ercan
• Durmaz, Muhammet Enes
• Erışr, Tülay
• Erişir, Tülay
• Eser, Engin
• Göçer, Ali Aykut
• Gunduz, Birol
• İsabeyoǧlu, Zeynep
• Kiziltuğ, Sezai̇
• Kiziltuʇ, Sezai
• Kudu, Mustafa
• Manav Tatar, Nesrin
• Okumus, Israfil
• Okur, Muzaffer
• Ozupek, Ertugrul
• Özdin, Tufan
• Özkan, Engin
• Panakhov, Etibar S
• Sat, Murat
• Savaş, N.
• Taşyurdu, Yasemin
• Yagmur, Nihat
• Yapman, Ömer
• Yayli, Yusuf
• Yiǧider, Muhammed

• ArticleYalnız künye2026/r/ebyu/18864
  Exploring novel Fermat polynomials and their transformative properties

  Kuloglu, Bahar; Eser, Engin; Özkan, Engin

  In this research, we present a novel family of polynomials that are derived from Fermat numbers. Alongside these newly introduced polynomials, we provide a series of important identities and properties, including the Binet formula and generating functions, which are fundamental to understanding their structure. We also show that Fermat polynomials can be efficiently expressed using matrix representations, enabling an exploration of fundamental properties derived from the invariance of the determinants of these matrices. This approach provides new perspectives on the internal connections within these polynomials. In addition, many different transforms have been considered with the help of polynomials of these new number sequences, and these transforms can play a role in many areas from secure key generation to differential equation solutions. These transformations shed light on the deeper structural properties of the Fermat polynomials and reveal intricate connections between these polynomials and other well-established mathematical constructs, enhancing our understanding of their broader implications in the field of number theory and beyond.

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• ArticleYayıncıda açık erişim2026/r/ebyu/18774
  POLYNOMIALS OF BALANCING, BALANCING-LUCAS SEQUENCES AND k-BALANCING, k-BALANCING-LUCAS SEQUENCES

  Özkan, Engin; Eser, Engin; Uysal, Mine

  In this work, we introduce Balancing, Balancing-Lucas polynomials, and k-Balancing, k-Balancing-Lucas polynomials. We exhibit some important theorems: Cassini, Catalan, Vajda, d'Ocagne, and Honsberger identities for Balancing, BalancingLucas polynomials, and k-Balancing, k-Balancing-Lucas polynomials. We give the concepts of recurrence relation, characteristic equation, roots of the characteristic equation, Binet formula, and generating function for polynomials, which are important for number sequences.

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• ArticleYalnız künye2026/r/ebyu/11049
  Half inverse problem for the discontinuous Dirac operator with the spectral parameter boundary conditions

  Wang, Kai; Xu, Xin-Jian; Sat, Murat; Zhang, Ran

  In this work, we consider the Dirac operator with the spectral parameter boundary conditions and the jump condition at the pointπ . We investigate the spectral properties and establish a new uniqueness 2 theorem of the half inverse problem for discontinuous impulsive Dirac operator operators by constructing the Weyl function and exploiting its relevant properties. We conclude that if the potential is known on (0,ϕ(π) ϕ(π) ), where <π, then the potential on (0, π), the partial parameters in the boundary conditions and 2 2 2 jump conditions can be uniquely determined by only one spectrum.

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• ArticleYayıncıda açık erişim2026/r/ebyu/10982
  On Fibonacci and Lucas Quasi-quaternions: Theoretical insights and graphical representations

  Uysal, Mine; Kuloğlu, Bahar; Özkan, Engin

  In this paper, we introduce Fibonacci and Lucas quasi-quaternions by combining classical number sequences with the structure of quasi-quaternion algebra. We investigate their fundamental algebraic properties, including real and imaginary parts, conjugates, norms, and recurrence relations. We establish Binet-type formulas, generating functions, and sum formulas for these sequences in the quasi-quaternionic setting. In addition, we derive several classical identities, such as the Cassini, Catalan, d’Ocagne, Vajda, and Honsberger identities, adapted to Fibonacci and Lucas quasi-quaternions. Furthermore, we present matrix representations of these structures and obtain explicit expressions for the powers of the associated matrices. We also consider De Moivre-type formulas in the quasi-quaternion framework and analyze the behavior of these sequences under repeated operations. The graphical representations complement the theoretical results by illustrating the structural and asymptotic behavior of these quasi-quaternionic sequences.

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• ArticleYalnız künye2026/r/ebyu/10934
  QUATERNIONS WHOSE COMPONENTS ARE BLAISE AND BLAISE-LUCAS NUMBERS

  Uysal, M.; Özkan, E.; Soykan, Y.

  In this paper, we introduce a new application of Blaise and Blaise-Lucas numbers. We define quaternions of the Blaise and Blaise-Lucas numbers. We calculate some important theorems; Cassini, Catalan, Vajda and d’Ocagne identities for quaternions of the Blaise and Blaise-Lucas numbers. We give the concepts of recurrence relation, characteristic equation, roots of the characteristic equation, Binet formula and generating function for these numbers. Finally, we give matrices representation of the Blaise and Blaise-Lucas Quaternions.

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• ArticleYalnız künye2026/r/ebyu/10923
  Partial Inverse Nodal Problems for Eigenparameter Dependent Sturm-Liouville Problems

  Wu, Dong-Jie; Yang, Chuan-Fu; Sat, Murat

  In this work, we are concerned with inverse nodal problems of Sturm-Liouville operators with eigenparameter dependent boundary conditions on the interval [0, 1]. It is shown that a twin dense subset of the nodal set in a subinterval [a1,a2]⊂[0,1](a1<12<a2) uniquely determines all parameters of the boundary conditions and the potential (up to a constant) on the interval [0, 1].

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• ArticleYayıncıda açık erişim2026/r/ebyu/10863
  On the Point at Infinity of Elliptic Curves and a New Group Structure on the Quadratic Curve x2

  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.

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• ArticleYalnız künye2026/r/ebyu/10762
  Characterization of ∗-(strongly) regular rings in terms of G-projections

  Özdin, Tufan

  A unit-picker is a map G that associates to every ring R a well-defined set G(R) of central units in R which contains 1R and is invariant under isomorphisms of rings and closed under taking inverses, and which satisfies certain set containment conditions for quotient rings, corner rings and matrix rings. Let G be a unit-picker. An element q of a ring R is G-idempotent, a special kind of the strongly regular element, if q2=uq for some unit picker u of R, or equivalently, q=ue, where u is a unit picker and e is an idempotent of R. In a ring R with involution ∗, projections are self-adjoint idempotents. As a natural generalization of projections, an element q of a ring R is called a G-projection if q2=uq=uq∗ for some self-adjoint unit-picker u of a ∗-ring R, or equivalently, q=up, where p is a projection. We characterize ∗-(strongly) regular rings in terms of the G-projection element.

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• ArticleAçık Erişim2026/r/ebyu/10723
  On a sequence related to Mersenne numbers and its connections to the Horadam sequence

  Eser, Engin; Goy, Taras; Özkan, Engin

  Mersenne numbers, introduced by Marin Mersenne in the early 17th century and known since antiquity for their deep links to prime number theory, have long fascinated mathematicians. In this study, we introduce a second-order sequence derived from consecutive Mersenne numbers, which we refer to as the Trisenne sequence. Our objective is to investigate its structural properties and to establish relationships between the Trisenne numbers and the general Horadam (or generalized Fibonacci) sequence through their generating functions. The connection between these families is analyzed using both ordinary and exponential generating functions, with particular emphasis on classical cases such as the Fibonacci, Lucas, Pell, and Jacobsthal sequences. We also discuss the historical context and mathematical lineage of Horadam sequences, tracing their origin to the work of Edouard Lucas and Alwyn Horadam. Theoretical results are illustrated with explicit examples, and several related identities are presented.

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• ArticleYalnız künye2026/r/ebyu/10601
  (s,t)-Fermat, (s,t)-Fermat–Lucas Sequences and Their Applications on Hyperbolic Quaternions

  Akkuş, H.; Özkan, E.

  Abstract: In this study, we define the -Fermat and -Fermat–Lucas sequences. For these sequences, we give many features such as the characteristic equation and Binet formulas. We obtain the relations between these sequences. Then we find different representations of finding terms of these sequences. Also, we show the relationship between the positive and negative terms of the sequences and get the relationship between three consecutive terms. We present the generating functions and sum formulas of these sequences. In addition, we calculate special identities of these sequences such as Catalan identity, Melham’s identity, d’Ocagne identity, etc. We examine the relationships of -Fermat sequence with Fibonacci, Pell, Jacobsthal, Balancing, Oresme sequences and -Fermat–Lucas sequence with Lucas, Pell–Lucas, Jacobsthal–Lucas, Balancing–Lucas, Oresme–Lucas sequences. Moreover, we present on the application of -Fermat and -Fermat–Lucas sequences to hyperbolic quaternions. Furthermore, we define hyperbolic -Fermat and -Fermat–Lucas quaternions. For these hyperbolic quaternions, we give many properties such as Binet formulas. Finally, the terms of the -Fermat and -Fermat–Lucas sequences are associated with their hyperbolic quaternion values.

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