On Geodesic Flow and Energy Functional on Riemannian Manifolds
Issue:
Volume 10, Issue 5, October 2021
Pages:
104-106
Received:
20 August 2021
Accepted:
2 September 2021
Published:
12 October 2021
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 structure on the tangent bundle of a Riemannian manifold.
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...
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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
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 previously by Noor et al. The aim of this paper is to propose new concepts of linking soft set, rough set and graph theory in order to create new types of sub-graphs according to properties on the original graph by using generalized relationship through the out-link vertices or directed cycle. Our approach is based on introducing new structure for the roughness of the soft graphs by defining new types of operators by using closed paths. Then, it applies all of these concepts to the cardiovascular system in the human body in order to explain some phenomena and medical facts in a mathematical style. Finally, it discusses the comparison properties and containment relationships between various kinds of new approximation soft subgraph.
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...
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