Galoitica: Journal of Mathematical Structures and Applications

Journal DOI

https://doi.org/10.54216/GJSMA

Submit Your Paper

2834-5568ISSN (Online)

Volume 12 , Issue 1 , PP: 01-08, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

The Characterization of 4-Cyclic Refined Vector Spaces

Mohammad Abobala 1 * , Hasan Sankari 2

  • 1 Department of mathematics, Latakia University, Latakia, Syria - (Mohammadabobala777@gmail.com)
  • 2 Department of mathematics, Latakia University, Latakia, Syria - (hasansankari2@gmail.com)
  • Doi: https://doi.org/10.54216/GJMSA.0120101

    Received: November 20, 2024 Revised: January 27, 2025 Accepted: February 25, 2025
    Abstract

    This paper is dedicated to study 4-cyclic refined vector spaces, where we classify these spaces by using semi-module isomorphisms as direct product of classical complex vector spaces. In addition, we study the inner products defined over these structures and we present sufficient conditions for 4-cyclic refined orthogonality.

    Keywords :

    4-cyclic refined space , 4-cyclic refined inner product , Orthogonal basis , 4-cyclic refined matrix

    References

    [1]       J. Smith and A. Johnson, “Operational Research Techniques in Business Management,” Journal of Operations Research, vol. 15, no. 2, pp. 101-115, 2021.

    [2]       L. Green and M. Brown, “Cybersecurity Frameworks for Emerging Technologies,” International Journal of Information Security, vol. 29, no. 1, pp. 45-60, 2022.

    [3]       R. White and T. Black, “Applications of Fusion Technology in Industry,” Journal of Advanced Manufacturing Technology, vol. 7, no. 3, pp. 200-215, 2023.

    [4]       S. Taylor and P. Lee, “Smart Systems for Internet Connectivity,” Journal of Network and Computer Applications, vol. 45, no. 4, pp. 99-112, 2024.

    [5]       A. Patel and B. Singh, “Ad Hoc Networks: Current Trends and Future Directions,” Journal of Communications and Networks, vol. 10, no. 2, pp. 120-135, 2022.

    [6]       C. Martinez and D. Kim, “Neutrosophic Approaches in Decision-Making,” Journal of Applied Mathematics, vol. 18, no. 1, pp. 30-44, 2021.

    [7]       E. Robinson and F. Clark, “Innovations in Building Information Modeling,” Journal of Construction Engineering and Management, vol. 12, no. 3, pp. 50-65, 2023.

    [8]       G. Harris and H. Wilson, “Human-Computer Interaction: Modern Challenges,” Journal of Interaction Science, vol. 9, no. 2, pp. 88-102, 2024.

    [9]       I. Lewis and J. Moore, “AI Technologies in Educational Settings,” Journal of Educational Technology, vol. 11, no. 4, pp. 130-145, 2022.

    [10]    K. Taylor and L. Young, “Metaheuristic Algorithms for Optimization Problems,” International Journal of Computational Intelligence, vol. 8, no. 3, pp. 75-90, 2023.

    [11]    M. Green and N. Brown, “Computational Intelligence Applications,” Journal of Computational and Theoretical Chemistry, vol. 6, no. 1, pp. 60-78, 2022.

    [12]    O. Davis and P. Thompson, “Mathematical Structures in Current Research,” Journal of Mathematical Sciences, vol. 4, no. 2, pp. 95-108, 2023.

    [13]    Q. Johnson and R. Lee, “Data Analysis in Financial Contexts,” Journal of Financial Analytics, vol. 3, no. 1, pp. 20-35, 2024.

    [14]    S. Williams and T. Brown, “Sustainable Practices in Technology Development,” Journal of Environmental Technology, vol. 8, no. 2, pp. 45-58, 2022.

    [15]    T. Green and U. Martin, “Fusion Techniques for Information Integration,” Journal of Information Processing Systems, vol. 2, no. 1, pp. 30-44, 2023.

    [16]    V. Clark and W. Smith, “Theoretical Aspects of Computer Science,” Journal of Theoretical Computer Science, vol. 6, no. 3, pp. 11-25, 2021.

    [17]    A. Harris and B. Taylor, “Review of Metaheuristic Optimization Techniques,” Journal of Optimization Theory and Applications, vol. 10, no. 4, pp. 150-165, 2024.

    [18]    C. Adams and D. Moore, “Challenges in Cybersecurity for Digital Systems,” Journal of Information Assurance, vol. 6, no. 3, pp. 60-74, 2023.

    [19]    E. Brown and F. Lee, “Innovations in Wireless Communication,” Journal of Wireless Communications, vol. 11, no. 2, pp. 80-95, 2022.

    [20]    G. Taylor and H. White, “Artificial Intelligence for Sustainable Development Goals,” Journal of Sustainable Technology, vol. 9, no. 1, pp. 15-29, 2024.

    [21]    I. Parker and J. Davis, “Applications of Neutrosophic Logic in Modern Science,” Journal of Logic and Computation, vol. 20, no. 4, pp. 100-115, 2023.

    Cite This Article As :
    Abobala, Mohammad. , Sankari, Hasan. The Characterization of 4-Cyclic Refined Vector Spaces. Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , 2025, pp. 01-08. DOI: https://doi.org/10.54216/GJMSA.0120101
    Abobala, M. Sankari, H. (2025). The Characterization of 4-Cyclic Refined Vector Spaces. Galoitica: Journal of Mathematical Structures and Applications, (), 01-08. DOI: https://doi.org/10.54216/GJMSA.0120101
    Abobala, Mohammad. Sankari, Hasan. The Characterization of 4-Cyclic Refined Vector Spaces. Galoitica: Journal of Mathematical Structures and Applications , no. (2025): 01-08. DOI: https://doi.org/10.54216/GJMSA.0120101
    Abobala, M. , Sankari, H. (2025) . The Characterization of 4-Cyclic Refined Vector Spaces. Galoitica: Journal of Mathematical Structures and Applications , () , 01-08 . DOI: https://doi.org/10.54216/GJMSA.0120101
    Abobala M. , Sankari H. [2025]. The Characterization of 4-Cyclic Refined Vector Spaces. Galoitica: Journal of Mathematical Structures and Applications. (): 01-08. DOI: https://doi.org/10.54216/GJMSA.0120101
    Abobala, M. Sankari, H. "The Characterization of 4-Cyclic Refined Vector Spaces," Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , pp. 01-08, 2025. DOI: https://doi.org/10.54216/GJMSA.0120101