MATHEMATICAL RESEARCH
Introduction to generalized Leonardo-Alwyn hybrid numbers ARXIV: 2405.13074
In [6], Gökbaş defined a new type of number sequence called Leonardo-Alwyn sequence. In this paper, we consider the generalized Leonardo-Alwyn hybrid numbers and investigate some of their properties. We also give some applications related to the generalized Leonardo-Alwyn hybrid numbers in matrices.
On some Properties of Generalized Tribonacci Spinors ARXIV: 2404.11620
Spinors are used in physics quite extensively. The goal of this study is also the spinor structure lying in the basis of the quaternion algebra. In this paper, first, we have introduced spinors mathematically. Then, we have defined Tribonacci spinors using the generalized Tribonacci quaternions. Later, we have established the structure of algebra for these spinors. Finally, we have proved some important formulas such as Binet and Cassini-like formulas which are given for some series of numbers in mathematics for Tribonacci spinors.
New approach to third-order Jacobsthal sequence (accepted in Palestine Journal of Mathematics)
On Generalized Bihyperbolic Third-order Jacobsthal Polynomials (accepted in Matematica Bohemica)
On Gauss Third-order Jacobsthal numbers and their applications. Analele Stiint ale Universitatii Alexandru Ioan Cuza din Iasi. New Series LXVII f.2 (2021), 231-241.
(With A. Wani and N. Malik) Matrix sequence of the binomial form of the complex combined Jacobsthal-Akin sequence. Palestine Journal of Mathematics 11(1) (2022), 292-304.
On bicomplex third-order Jacobsthal numbers. Complex Var. Elliptic Equ. 68, No. 1 (2023), 44-56.
(With S. Halici) On Quaternion-Gaussian Fibonacci Numbers and Their Properties. Analele Stiintifice ale Universitatii Ovidius Constanta, 29(1),2021, 71-82.
Investigation of Generalized Hybrid Fibonacci Numbers and Their Properties. Applied Mathematics E-Notes, 21 (2021), 110-118.
On third-order Jacobsthal polynomials and their properties. Miskolc Mathematical Notes 22(1) (2021), 123-132.
A note on dual third-order Jacobsthal vectors. Annales Mathematicae et Informaticae 52 (2020), 57-70.
An interesting generalized Fibonacci sequence: a two-by-two matrix representation. Afrika Matematika 32 (2020), 695-705.
Introduction to third-order Jacobsthal and modified third-order Jacobsthal hybrinomials. Discussiones Mathematica e General Algebra and Applications 41 (2021) 139-152.
Some Identities Involving (p, q)-Fibonacci and Lucas Quaternions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 69(2), (2020), 110-116.
Gaussian Third-order Jacobsthal and Gaussian Third-order Jacobsthal-Lucas polynomials and properties of them. Asian-European Journal of Mathematics, 2020.
On the third-order Horadam and geometric mean sequences. Indian J. Pure Appl. Math., 51(3) (2020), 1133-1141.
B2.pdfSome results on dual third-order Jacobsthal quaternions. FILOMAT Vol 33, No 7 (2019) 1865-1876.
B3.pdfComment On "On some Properties of Tribonacci Quaternion". Analele Stiintifice ale Universitatii Ovidius Constata, 28(1) (2020), 95-97.
B4.pdfA note on modified third-order Jacobsthal numbers. Proyecciones. Journal of Mathematics 39(2) (2020), 409-420.
On the third-order Jacobsthal and third-order Jacobsthal-Lucas sequences and their matrix representations. Mediterranean Journal of Mathematics, 16:32 (2019), 1-13.
The Gelin-Cesàro identity in some third-order Jacobsthal sequences. Notes on Number Theory and Discrete Mathematics, Vol. 25, 2019, No. 2, 57-67.
The Unifying Formula for all Tribonacci-type Octonions Sequences and Their Properties. Konuralp Journal of Mathematics, 7 (2) (2019) 292-299.
The third order Jacobsthal Octonions: Some combinatorial properties. Analele Stiintifice ale Universitatii Ovidius Constata, 26(3),(2018), 57-71.
Third-order Jacobsthal Generalized Quaternions. J. Geom. Symmetry Phys., 50 (2018), 11-27.
On Tribonacci and Tribonacci-Lucas Quaternions Polynomials. Palestine Journal of Mathematics, Vol. 8(1)(2019), 318-326.
Identities for third order Jacobsthal Quaternions. Advances in Applied Clifford Algebras, 27(2) (2017), 1043-1053.
A note on generalized Tribonacci Quaternions. Mediterranean Journal of Mathematics, 14:239 (2017), 1-12.
Dual Third-order Jacobsthal Quaternions. Proyecciones Journal of Mathematics, 37(4), (2018), 731-747.
On the properties of new families of Horadam Numbers. Konuralp Journal of Mathematics, 5(2), (2017), 43-48.
A1.pdfABSTRACT. In this paper, new families of generalized Fibonacci and Lucas numbers are introduced. In addition, we present the recurrence relations and the generating functions of the new families for k = 2.
Quadratic Approximation of Generalized Tribonacci Numbers. Discussiones Mathematicae-General Algebra and Applications, 32(2), (2018), 227-237.
A2.pdfABSTRACT. In this paper, we give quadratic approximation of generalized Tribonacci sequence {Vn}n≥0 defined by Vn = rVn−1 + sVn−2 + tVn−3 (n ≥ 3) and use this result to give the matrix form of the n-th power of a companion matrix of {Vn}n≥0. Then we re-prove the cubic identity or Cassini-type formula for {Vn}n≥0 and the Binet’s formula of the generalized Tribonacci quaternions.
On fourth-order jacobsthal quaternions. Journal of Mathematical Sciences and Modelling, 1(2), (2018), 73-79.
A3.pdfABSTRACT. In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. This generalizes some previous results given by Szynal-Liana and Włoch in [13], Torunbalci Aydin and Yuce in [14] and Cerda-Morales in [2].
METÁFORAS EN MATEMÁTICA
TALLERES EN CLASE
MET01.pdfProbabilidad en el camino de una hormiga: Una propuesta de enseñanza con uso de metáforas. Educación Matemática, 27(3) (2015), 197-210.
MET02.pdfUna propuesta con uso de metáforas: el caso de las probabilidades. Actas de la XX Jornada Nacional de Educación Matemática, Valparaíso, Chile, 2016.
PUBLICACIONES EDUCACIÓN MATEMÁTICA
Algunos trabajos realizados en didáctica de la estadística y probabilidad
Paseos al azar: Memorias de una pulga solitaria. Revista de Educación Matemática, 26(3) (2011), 7-21.
Matrix methods in Horadam sequences. Boletín de matemáticas, 19(2) (2012), 97-106.
Grupoide de movimientos y modelos de Gelfand para el grupo diédrico D(2n). Revista Morfismos, 15(2) (2011), 9-18.
Matrix representation of the q-jacobsthal numbers. Proyecciones Journal of Mathematics, 31(4) (2012), 345-354.
Estudio discreto del movimiento Browniano: Memorias de una hormiga caminante. Unión, Revista Iberoamericana de Educación Matemática, 32 (2012), 157-164.
The Hadamard product in generalized U(N)(p,q)-matrices. Acta Universitatis Apulensis, 34 (2013), 115-124.
On generalized Fibonacci and Lucas numbers by matrix methods. Hacettepe Journal of Mathematics and Statistics, 42(2) (2013), 173-179.
On q-Jacobsthal numbers. Selcuk Journal of Applied Mathematics, 14(2) (2013), 25-36.