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Pure and Applied Mathematics Journal

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Volume 10, Issue 5, October 2021

  • On Geodesic Flow and Energy Functional on Riemannian Manifolds

    Yang Liu

    Issue: Volume 10, Issue 5, October 2021
    Pages: 104-106
    Received: 20 August 2021
    Accepted: 2 September 2021
    Published: 12 October 2021
    DOI: 10.11648/j.pamj.20211005.11
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    Abstract: In this paper, we study the geodesic flow and the energy functional on a Riemannian manifold and show that the geodesics have minimal energy, in other words, are the minimizers of the energy functional, from the new perspective of involution, and that the geodesic flow is a Hamiltonian flow which has a close connection with the canonical symplectic... Show More
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  • Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System

    Magdy Salah El-Azab, Mohamed Shokry, Reham Emad Aly

    Issue: Volume 10, Issue 5, October 2021
    Pages: 107-120
    Received: 13 September 2021
    Accepted: 11 October 2021
    Published: 10 November 2021
    DOI: 10.11648/j.pamj.20211005.12
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    Abstract: The incorporation of many various and modern mathematical tools provides efficient and successful methods to model problems with uncertainty such as graph theory, Fuzzy sets, rough sets and soft sets. This powerful incorporation of the three different concepts rough sets, soft sets and graphs is known as soft rough graphs that is introduced previou... Show More
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