Hulya Kadioglu

@yildiz.edu.tr

Proffessor at Department of Mathematics and Science Education
Yildiz Technical University

Hulya Kadioglu


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https://researchid.co/kadiogluhulya

RESEARCH, TEACHING, or OTHER INTERESTS

Geometry and Topology, Education
8

Scopus Publications

57

Scholar Citations

4

Scholar h-index

1

Scholar i10-index

Scopus Publications

  • Classification of 8-dimensional Nilsolitons by Symbolic Computation
    Hülya KADIOĞLU
    Gazi University Journal of Science, 2022
    In this paper, we develop an algorithm to classify 8 dimensional nilsolitons with simple nilsoliton derivation. We restrict our classifications to the nilsolitons corresponding to singular Gram matrix with nullity 1-3. This work can be considered as a continuation paper to our previous study where we introduced a procedure to classify algebras in dimension 8 that admit simple derivations and singular Gram matrices U. Having the singular Gram matrices, there exists infinitely many solutions to Uv =[1]_m , where the solutions are exactly the squares of the structure constants. Also, the structure constants have to satisfy the Jacobi identity for the algebra to be a Lie algebra. In our previous work, we did not introduce a procedure to create and solve the Jacobi identity(s). In this study, we take care of this issue by using computer algorithms for each index set. Thus, we complete classification of all 8 dimensional in-decomposable nilsolitons with the nullity of corresponding Gram matrix is in the set {0,1,2,3}. We provide several examples to illustrate the algorithm. For the implementation process of the newly introduced algorithm, we use MATLAB R2020b.
  • A COMPUTATIONAL APPROACH FOR THE CLASSIFICATIONS OF ALL POSSIBLE DERIVATIONS OF NILSOLITONS IN DIMENSION 9
    Hulya Kadioglu
    Thermal Science, 2022
    In mathematics and engineering, a manifold is a topological space that locally resembles Euclidean space near each point. Defining the best metric for these manifolds have several engineering and science implications from controls to optimization for generalized inner product applications of Gram Matrices that appear in these applications. These smooth geometric manifold applications can be formalized by Lie Groups and their Lie Algebras on its infinitesimal elements. Nilpotent matrices that are matrices with zero power with left-invariant metric on Lie group with non-commutative properties namely non-abelian nilsoliton metric Lie algebras will be the focus of this article. In this study, we present an algorithm to classify eigenvalues of nilsoliton derivations for 9-D non-abelian nilsoliton metric Lie algebras with non-singular Gram matrices.
  • On Some Structural Components of Nilsolitons
    Hulya Kadioglu
    Mathematical Problems in Engineering, 2021
    In this paper, we study nilpotent Lie algebras that admit nilsoliton metric with simple pre-Einstein derivation. Given a Lie algebra η , we would like to compute as much of its structure as possible. The structural components we consider in this study are the structure constants, the index, and the rank of the nilsoliton derivations. For this purpose, we prove necessary or sufficient conditions for an algebra to admit such metrics. Particularly, we prove theorems for the computation of the Jacobi identity for a given algebra so that we can solve the system of the equation(s) and find the structure constants of the nilsoliton.
  • Prolongations of isometric actions to vector bundles
    Hulya Kadioglu
    Turkish Journal of Mathematics, 2020
    In this paper, we define an isometry on a total space of a vector bundle E by using a given isometry on the base manifold M. For this definition, we assume that the total space of the bundle is equipped with a special metric which has been introduced in one of our previous papers. We prove that the set of these derived isometries on E form an imbedded Lie subgroup Ge of the isometry group I E . Using this new subgroup, we construct two different principal bundle structures based one on E and the other on the orbit space E/Ge. Key words: Fiber bundles, isometry group, vector bundles, principal bundles
  • A computational procedure on higher-dimensional nilsolitons
    Hulya Kadioglu
    Mathematical Methods in the Applied Sciences, 2019
    In this paper, we develop algorithmic approach to classify nilsoliton metrics on dimension 8. This approach includes finding eigenvalue type of the nilsoliton derivation, the nullity type, the index of the algebra. It can be considered as a continuation of our papers in Abstract and Applied analysis, volume 2013, 1 to 7, (2013), with article ID 871930, and in Journal of Symbolic Computation 50 (2013), 350 ‐ 373. In our previous work, we classified only ordered type, nilsoliton metric Lie algebras ie, the algebras with the derivation type (1 < 2 < 3… < n) in dimension 8 and 9. Here, we consider more general case. We consider such metrics with simple derivations on an indecomposable nilpotent Lie algebra. In one of our previous study, we have already classified nilsoliton metric Lie algebras with nonsingular Gram matrix in dimension 8 in Journal of Symbolic Computation, vol: 50, 350 ‐ 373, 2013. Here, we focus on the metrics with singular Gram matrix. We also develop faster algorithm in classifying such metrics.
  • Canonical involution on double jet bundles
    Hülya KADIOĞLU
    Turkish Journal of Mathematics, 2017
    In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures. We also show that the manifold charts induced by primary and secondary structures belong to the same atlas. We prove that double jet bundles can be considered as a quotient of second order jet bundle. We show that there exists a natural involution that interchanges between primary and secondary vector bundle structures on double jet bundles.
  • Classification of ordered type soliton metric lie algebras by a computational approach
    Hülya Kadıoğlu
    Abstract and Applied Analysis, 2013
    We classify some soliton nilpotent Lie algebras and possible candidates in dimensions 8 and 9 up toisomorphy.We focus on type of derivations, where is the dimension of the Lie algebras. We present algorithms to generate possible algebraic structures.
  • Computational methods for nilsoliton metric Lie algebras I
    Hülya Kadioglu, Tracy L. Payne
    Journal of Symbolic Computation, 2013

RECENT SCHOLAR PUBLICATIONS

  • Development of the Inventory of Elementary Mathematics Pre-service Teachers’ Study Strategies During Distance Education
    Ş Gökcen, H Kadıoğlu
    International Journal of Educational Studies in Mathematics, 74-90 , 2025
    2025
  • A p-Sum Representation of the 1-Jets of p-Velocities
    H Kadıoğlu
    COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS 15 (1) , 2024
    2024
  • Classification of 8-dimensional Nilsolitons by Symbolic Computation
    H KADIOĞLU
    Gazi University Journal of Science, 1-1 , 2022
    2022
    Citations: 2
  • A computational approach for the classifications of all possible derivations of nilsolitons in dimension 9
    H Kadioglu
    Thermal Science 26 (Spec. issue 2), 759-783 , 2022
    2022
  • Research Article On Some Structural Components of Nilsolitons
    H Kadioglu
    2021
  • On some structural components of nilsolitons
    H Kadioglu
    Mathematical Problems in Engineering 2021 (1), 5540584 , 2021
    2021
    Citations: 4
  • A Computational Approach for the Classifications of 8-dimensional Nilsolitons
    H KADIOGLU
    Authorea Preprints , 2020
    2020
  • Öğretmen adaylarının TÜBİTAK araştırma proje deneyimleri üzerine nitel bir araştırma
    H Kadıoğlu
    2020
    Citations: 4
  • İlköğretim matematik öğretmenlerinin ters yüz sınıf modeline ilişkin görüşlerinin incelenmesi
    Ş Gökcen, H Kadıoğlu
    2020
    Citations: 2
  • 5. SINIF KESİRLER SADELEŞTİRME-GENİŞLETME İŞLEMLERİ İLE İLGİLİ BİR MATERYAL ÖRNEĞİ
    ŞN Koç, H Kadıoğlu
    EĞİTİM ARAŞTIRMALARI KONGRESİ (FSMVU-EAK2020) TAM METİN KİTABI, 229 , 2020
    2020
  • Prolongations of isometric actions to vector bundles
    H KADIOĞLU
    Turkish Journal of Mathematics 44 (2), 378-388 , 2020
    2020
    Citations: 1
  • A computational procedure on higher‐dimensional nilsolitons
    H Kadioglu
    Mathematical Methods in the Applied Sciences 42 (16), 5390-5397 , 2019
    2019
    Citations: 6
  • A note on the dimension of isometry group of a Riemannian manifold
    H Kadioglu
    New Trends in Mathematical Sciences 5 (2), 273-276 , 2017
    2017
  • Canonical involution on double jet bundles
    H KADIOĞLU
    Turkish Journal of Mathematics 41 (4), 854-868 , 2017
    2017
  • On the prolongations of homogeneous vector bundles
    H Kadıoğlu
    Communications Faculty of Sciences University of Ankara Series A1 … , 2016
    2016
  • Metric structures on fibered manifolds through partitions of unity
    H Kadioglu, R Fisher Jr
    New Trends in Mathematical Sciences 4 (2), 266-272 , 2016
    2016
    Citations: 3
  • Computational methods for nilsoliton metric Lie algebras I
    H Kadioglu, TL Payne
    Journal of Symbolic Computation , 2013
    2013
    Citations: 26
  • Classification of ordered type soliton metric Lie algebras by a computational approach
    H Kadıoğlu
    Abstract and Applied Analysis 2013 (1), 871930 , 2013
    2013
    Citations: 7
  • PROLONGATIONS OF LIE ALGEBRA REPRESENTATIONS
    H Kadioglu, E Esin, Y Yayli
    Advances and Applications in Mathematical Sciences 10 (5), 533-542 , 2011
    2011
  • On the Prolongations of Representations of Lie Groups
    H Kadioglu, E Esin
    arXiv preprint arXiv:1310.2015 , 2010
    2010
    Citations: 2

MOST CITED SCHOLAR PUBLICATIONS

  • Computational methods for nilsoliton metric Lie algebras I
    H Kadioglu, TL Payne
    Journal of Symbolic Computation , 2013
    2013
    Citations: 26
  • Classification of ordered type soliton metric Lie algebras by a computational approach
    H Kadıoğlu
    Abstract and Applied Analysis 2013 (1), 871930 , 2013
    2013
    Citations: 7
  • A computational procedure on higher‐dimensional nilsolitons
    H Kadioglu
    Mathematical Methods in the Applied Sciences 42 (16), 5390-5397 , 2019
    2019
    Citations: 6
  • On some structural components of nilsolitons
    H Kadioglu
    Mathematical Problems in Engineering 2021 (1), 5540584 , 2021
    2021
    Citations: 4
  • Öğretmen adaylarının TÜBİTAK araştırma proje deneyimleri üzerine nitel bir araştırma
    H Kadıoğlu
    2020
    Citations: 4
  • Metric structures on fibered manifolds through partitions of unity
    H Kadioglu, R Fisher Jr
    New Trends in Mathematical Sciences 4 (2), 266-272 , 2016
    2016
    Citations: 3
  • Classification of 8-dimensional Nilsolitons by Symbolic Computation
    H KADIOĞLU
    Gazi University Journal of Science, 1-1 , 2022
    2022
    Citations: 2
  • İlköğretim matematik öğretmenlerinin ters yüz sınıf modeline ilişkin görüşlerinin incelenmesi
    Ş Gökcen, H Kadıoğlu
    2020
    Citations: 2
  • On the Prolongations of Representations of Lie Groups
    H Kadioglu, E Esin
    arXiv preprint arXiv:1310.2015 , 2010
    2010
    Citations: 2
  • Prolongations of isometric actions to vector bundles
    H KADIOĞLU
    Turkish Journal of Mathematics 44 (2), 378-388 , 2020
    2020
    Citations: 1
  • Development of the Inventory of Elementary Mathematics Pre-service Teachers’ Study Strategies During Distance Education
    Ş Gökcen, H Kadıoğlu
    International Journal of Educational Studies in Mathematics, 74-90 , 2025
    2025
  • A p-Sum Representation of the 1-Jets of p-Velocities
    H Kadıoğlu
    COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS 15 (1) , 2024
    2024
  • A computational approach for the classifications of all possible derivations of nilsolitons in dimension 9
    H Kadioglu
    Thermal Science 26 (Spec. issue 2), 759-783 , 2022
    2022
  • Research Article On Some Structural Components of Nilsolitons
    H Kadioglu
    2021
  • A Computational Approach for the Classifications of 8-dimensional Nilsolitons
    H KADIOGLU
    Authorea Preprints , 2020
    2020
  • 5. SINIF KESİRLER SADELEŞTİRME-GENİŞLETME İŞLEMLERİ İLE İLGİLİ BİR MATERYAL ÖRNEĞİ
    ŞN Koç, H Kadıoğlu
    EĞİTİM ARAŞTIRMALARI KONGRESİ (FSMVU-EAK2020) TAM METİN KİTABI, 229 , 2020
    2020
  • A note on the dimension of isometry group of a Riemannian manifold
    H Kadioglu
    New Trends in Mathematical Sciences 5 (2), 273-276 , 2017
    2017
  • Canonical involution on double jet bundles
    H KADIOĞLU
    Turkish Journal of Mathematics 41 (4), 854-868 , 2017
    2017
  • On the prolongations of homogeneous vector bundles
    H Kadıoğlu
    Communications Faculty of Sciences University of Ankara Series A1 … , 2016
    2016
  • PROLONGATIONS OF LIE ALGEBRA REPRESENTATIONS
    H Kadioglu, E Esin, Y Yayli
    Advances and Applications in Mathematical Sciences 10 (5), 533-542 , 2011
    2011