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Sharp Bounds on the Minimum M -Eigenvalue of Elasticity M -Tensors

Author

Listed:
  • Ying Zhang

    (School of Basic Teaching, Shandong Water Conservancy Vocational College, Rizhao 276800, China)

  • Linxuan Sun

    (School of Management Science, Qufu Normal University, Rizhao 276800, China)

  • Gang Wang

    (School of Management Science, Qufu Normal University, Rizhao 276800, China)

Abstract

The M -eigenvalue of elasticity M -tensors play important roles in nonlinear elastic material analysis. In this paper, we establish an upper bound and two sharp lower bounds for the minimum M -eigenvalue of elasticity M -tensors without irreducible conditions, which improve some existing results. Numerical examples are proposed to verify the efficiency of the obtained results.

Suggested Citation

  • Ying Zhang & Linxuan Sun & Gang Wang, 2020. "Sharp Bounds on the Minimum M -Eigenvalue of Elasticity M -Tensors," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:250-:d:320562
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    References listed on IDEAS

    as
    1. Gang Wang & Linxuan Sun & Lixia Liu, 2020. "M -Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors," Complexity, Hindawi, vol. 2020, pages 1-8, January.
    2. Lijun Gao & Meng Zhang & Xiuming Yao, 2019. "Stochastic input-to-state stability for impulsive switched stochastic nonlinear systems with multiple jumps," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(9), pages 1860-1871, July.
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