KaydedilenlerDerginizi ekleyin

Dergiler / Fundamental Journal of Mathematics and Applications / 2022 / Cilt: 5 Sayı: 1

Construction of Networks by Associating with Submanifolds of Almost Hermitian Manifolds

Arif GÜRSOY
Sayfa
21–31
Yayın Tarihi
2022-03-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Moreover, we give some results and relations among holomorphic submanifolds, totally real submanifolds, CR-submanifolds, slant submanifolds, semi-slant submanifolds, hemi-slant submanifolds, and bi-slant submanifolds in almost Hermitian manifolds in terms of graph theory.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The idea that data lies in a non-linear space has brought up the concept of manifold learning as a part of machine learning and such notion is one of the most important research fields of today.
📊
Temel Bulgular & Veri:The main idea here is to design the data as a submanifold model embedded in a high-dimensional manifold.
💡
Sonuç & Katkı:Moreover, we give some results and relations among holomorphic submanifolds, totally real submanifolds, CR-submanifolds, slant submanifolds, semi-slant submanifolds, hemi-slant submanifolds, and bi-slant submanifolds in almost Hermitian manifolds in terms of graph theory.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Almost Hermitian manifold · Digraphs · Graph theory

Abstract

The idea that data lies in a non-linear space has brought up the concept of manifold learning as a part of machine learning and such notion is one of the most important research fields of today. The main idea here is to design the data as a submanifold model embedded in a high-dimensional manifold. On the other hand, graph theory is one of the most important research areas of applied mathematics and computer science. As a result, many researchers investigate new methods for machine learning on graphs. From the above information, it is seen that the theory of submanifolds and graph theory have become two important concepts in machine learning and nowadays, the geometric deep learning research area using these two concepts has emerged. By combining these two fields, this article aims to present the relationships between submanifolds of complex manifolds with the help of graphs. In this paper, we build some directed networks by identifying with submanifolds of almost Hermitian manifolds. Moreover, we give some results and relations among holomorphic submanifolds, totally real submanifolds, CR-submanifolds, slant submanifolds, semi-slant submanifolds, hemi-slant submanifolds, and bi-slant submanifolds in almost Hermitian manifolds in terms of graph theory.

🔖

Bu Makaleye Atıf Yap

GÜRSOY, A. (2022). Construction of Networks by Associating with Submanifolds of Almost Hermitian Manifolds. Fundamental Journal of Mathematics and Applications, Cilt: 5 Sayı: 1, 21–31. https://ajindex.com/articles/905676

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. M. Aquib, J. W. Lee, G. E. Vilcu, D. W. Yoon, Classification of Casorati ideal Lagrangian submanifolds in complex space forms, Differ. Geom. Appl., 63 (2019), 30-49
  2. J. Lee, G. E. Vˆılcu, Inequalities for generalized normalized d-Casorati curvatures of slant submanifolds in quaternionic space forms, Taiwanese J. Math., 19(3) (2015), 691-702
  3. W. M. Othman, S. A. Qasem, C. Ozel, Characterizations of contact CR-warped products of nearly cosymplectic manifolds in terms of endomorphisms, Int. J. Maps Math., 1(2) (2018), 137-153
  4. G. E. Vˆılcu, An optimal inequality for Lagrangian submanifolds in complex space forms involving Casorati curvature, J. Math. Anal., 465(2) (2018), 1209-1222
  5. S. K. Yadav, S. K. Chaubey, On Hermitian manifold satisfying certain curvature conditions, Int. J. Maps Math., 3(1) (2020), 10-27
  6. F. Etayo, On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen, 53(1-2) (1998), 217-223
  7. B. Y. Chen, O. Garay, Pointwise slant submanifolds in almost Hermitian manifolds, Turk. J. Math., 36(4) (2012), 630-640
  8. C. Murathan, B. Sahin, A study of Wintgen like inequality for submanifolds in statistical warped product manifolds, J. Geom., 109(2) (2018), 1-18
  9. N. Zheng, J. Xue, Statistical Learning and Pattern Analysis for Image and Video Processing, Springer Science & Business Media, 2009
  10. R. A. Fiorini, Computerized tomography noise reduction by CICT optimized exponential cyclic sequences (OECS) co-domain, Fundam. Inform. 141(2–3) (2015), 115-34
  11. F. Monti, D. Boscaini, J. Masci, E. Rodola, J. Svoboda, M. M. Bronstein, Geometric deep learning on graphs and manifolds using mixture model cnns, In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2017) (2017), (pp. 5115-5124)
  12. M. Shahzad, F. Sultan, S. I. A. Shah, M. Ali, H. A. Khan, W. A. Khan, Physical assessments on chemically reacting species and reduction schemes for the approximation of invariant manifolds, J. Mol. Liq., 285 (2019), 237-243
  13. M. Shahzad, F. Sultan, M. Ali, W. A. Khan, S. Mustafa, Modeling multi-route reaction mechanism for surfaces: a mathematical and computational approach, Appl. Nanosci., 10(12) (2020), 5069-5076
  14. A. Carriazo, L. Fernandez, Submanifolds associated with graphs, Proc. Am. Math. Soc., 132(11) (2004), 3327-3336
  15. L. Boza, A. Carriazo, L. M. Fernandez, Graphs associated with vector spaces of even dimension: A link with differential geometry, Linear