An Efficient Method for Solving Regular Variable Fractional Sturm-Liouville Problems

2017 ◽  
Vol 3 (4) ◽  
pp. 305-321
Author(s):  
Muhammed I. Syam
Keyword(s):  
Efficient Method ◽  
Regular Variable ◽  
Sturm Liouville

scholarly journals Some notes on conformable fractional Sturm–Liouville problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wei-Chuan Wang
Keyword(s):  
Asymptotic Expansion ◽  
Eigenvalue Problem ◽  
Efficient Method ◽  
Sturm Liouville

AbstractThe conformable fractional eigenvalue problem $$\begin{aligned} -D_{x}^{\alpha }D_{x}^{\alpha }y+q(x)y=\lambda \rho (x)y \end{aligned}$$ − D x α D x α y + q ( x ) y = λ ρ ( x ) y is considered. We employ an easy and efficient method to derive its eigenvalue asymptotic expansion. On the basis of this result, we also investigate Ambarzumyan problems related to this eigenvalue problem as an application.

Polarimetric Observations of Red Variables: A Study of Gas and Particle Interactions

1979 ◽  
Vol 46 ◽  
pp. 386-408 ◽  
Author(s):  
G. V. Coyne ◽  
I. S. McLean
Keyword(s):  
Wavelength Dependence ◽  
Stellar Atmosphere ◽  
Molecular Absorption ◽  
Absorption Bands ◽  
Absorption And Emission ◽  
Mira Variables ◽  
Stellar Photosphere ◽  
Regular Variable ◽  
Red Supergiants ◽  
Balmer Lines

AbstractIn recent years the wavelength, dependence of the polarization in a number of Mira variables, semi-regular variables and red supergiants has been measured with resolutions between 0.3 and 300 A over the range 3300 to 11000 A. Variations are seen across molecular absorption bands, especially TiO bands, and across atomic absorption and emission lines, especially the Balmer lines. In most cases one can ignore or it is possible to eliminate the effects due to interstellar polarization, so that one can study the polarization mechanisms operating in the stellar atmosphere and environment. The stars Omicron Ceti. (Mira), V CVn (semi-regular variable) and Mu Cephei (M2 la), in addition to other stars similar to them, will be discussed in some detail.Models to explain the observed polarization consider that the continuum flux is polarized either by electron, molecular and/or grain scattering or by temperature variations and/or geometrical asymmetries over the stellar photosphere. This polarized radiation is affected by atomic and molecular absorption and emission processes at various geometric depths in the stellar atmosphere and envelope. High resolution spectropolarimetry promises, therefore, to be a power-rul tool for studying stratification effects in these stars.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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