The present paper deals with non-real eigenvalues of regular nonlocal indefinite Sturm-Liouville problems. The existence of non-real eigenvalues of indefinite Sturm-Liouville differential equation with nonlocal potential K(x, t) associated with self-adjoint boundary conditions is studied. Furthermore, a priori upper bounds of non-real eigenvalues for a class of indefinite differential equation involving nonlocal point interference potential function is obtained.
The present paper deals with non-real eigenvalues of singular indefinite Sturm–Liouville problems with limit-circle type endpoints. A priori bounds and the existence of non-real eigenvalues of the problem associated with a special separated boundary condition are obtained.
The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems. The bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation involving complex nonlocal potential terms associated with nonlocal boundary conditions are obtained in terms of the integrable conditions of coefficients and the real part of the eigenvalues.
Linear expansion coefficient (CTE) is one of the important thermal parameters for materials, which has a great influence on the thermal deformation analyzing. Thermal Mechanical Analysis (TMA) is adopted to measure the CTE of pre-stretched aluminum alloy sheet 7050-T7451 in three vertical directions. The mathematical functions of CTE of aluminum alloy 7050-T7451 are established, which is with three directions and reflect the influence of the temperature. A comparison between the accurate CTE data and the CTE from reference is carried out .The reason of the CTE variation of aluminum 7050-T7451 with temperature also been explained qualitatively.
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