Results 131 to 140 of about 11,653 (147)
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The calculation of eigenvalues and eigenfunctions in an asymptotically Coulomb potential
Computer Physics Communications, 1976Abstract The calculation of eigenvalues in a central field involves the matching, by Newton-Raphson or otherwise, of forward and backward trial solutions of the radial Schrodinger equation; the backward integration is commenced in a region where the potential has assumed its asymptotic form.
I.H. Aldeen, A.C. Allison, M.J. Jamieson
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On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of Non-Self-Adjoint Elliptic Operators
Journal of Mathematical Sciences, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pyatnitskiĭ, A. L., Shamaev, A. S.
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Asymptotic eigenfunctions and eigenvalues of a homogeneous integral equation
IEEE Transactions on Information Theory, 1962Summary: The eigenfunctions and eigenvalues of a certain integral equation are of importance in the Karhunen-Loève expansion of second-order stationary random functions. In this note the asymptotic eigenfunctions and eigenvalues of this integral equation are derived for the case where the kernel is the Fourier transform of a rational function of ...
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Journal of Pseudo-Differential Operators and Applications, 2022
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Zhao, Yuan, Tang, Lin
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Zhao, Yuan, Tang, Lin
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Differential Equations, 2003
The authors consider the quasidifferential expression \[ L_{mn}(y) = \sum^{n}_{i=0}\sum^{m}_{j=0} (a_{ij}y^{(n-i)})^{(m-j)}, \quad m,n>0, \] on a finite interval \([a,b]\), where \(a_{00}\) is constant, \(a_{10}, a_{01} \equiv 0\), \(a_{i0}, a_{0j} \in L^{2}[a,b]\) and \(a_{ij}\) are derivatives of right continuous functions of bounded variation for ...
Makhnej, A. V., Tatsij, R. M.
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The authors consider the quasidifferential expression \[ L_{mn}(y) = \sum^{n}_{i=0}\sum^{m}_{j=0} (a_{ij}y^{(n-i)})^{(m-j)}, \quad m,n>0, \] on a finite interval \([a,b]\), where \(a_{00}\) is constant, \(a_{10}, a_{01} \equiv 0\), \(a_{i0}, a_{0j} \in L^{2}[a,b]\) and \(a_{ij}\) are derivatives of right continuous functions of bounded variation for ...
Makhnej, A. V., Tatsij, R. M.
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Differential Equations, 2002
Het, the authors extend two results on the boundary problem \[ z(x)=x-\int_{0}^{l}{\nu(x-t)z(t)}\,d(\sigma(t)+t\lambda), \quad x\in{[0,l]}, \quad z(l)=0, \] obtained by them in two previous papers [\textit{V. A.Vinokurov}, Dokl. Math., 57, No. 1, 43--46 (1998; Zbl 0989.34016) and Dokl. Math., 59, No. 2, 220--222 (1999; Zbl 0967.34076)]. In these papers,
Vinokurov, V. A., Sadovnichii, V. A.
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Het, the authors extend two results on the boundary problem \[ z(x)=x-\int_{0}^{l}{\nu(x-t)z(t)}\,d(\sigma(t)+t\lambda), \quad x\in{[0,l]}, \quad z(l)=0, \] obtained by them in two previous papers [\textit{V. A.Vinokurov}, Dokl. Math., 57, No. 1, 43--46 (1998; Zbl 0989.34016) and Dokl. Math., 59, No. 2, 220--222 (1999; Zbl 0967.34076)]. In these papers,
Vinokurov, V. A., Sadovnichii, V. A.
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Asymptotic Expressions for Eigenfunctions and Eigenvalues of a Dielectric or Optical Waveguide
IEEE Transactions on Microwave Theory and Techniques, 1969An asymptotic technique is presented, resulting in an analytically simple self-consistent description of the modes of a circular dielectric structure. When the dielectric difference between the rod and surrounding medium is small, the asymptotic expressions are valid for all frequencies.
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Journal of Engineering Physics and Thermophysics, 2008
Within the framework of the uncoupled thermoelasticity, using G. Weyl’s method, asymptotic formulas for eigenvalues and eigenfunctions of the first boundary-value problem have been obtained for cubically anisotropic bodies limited by a finite number of closed and nonclosed unintersecting Lyapunov surfaces.
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Within the framework of the uncoupled thermoelasticity, using G. Weyl’s method, asymptotic formulas for eigenvalues and eigenfunctions of the first boundary-value problem have been obtained for cubically anisotropic bodies limited by a finite number of closed and nonclosed unintersecting Lyapunov surfaces.
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Mathematical Notes, 2019
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Journal of Physics A: Mathematical and General, 1980
Asymptotic representations are obtained for the eigenfunctions of the differential equation describing scalar waves in a clad inhomogeneous planar waveguide, which has two turning points and finite boundaries. These representations are valid to all asymptotic orders in the large parameter, which is proportional to wavenumber.
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Asymptotic representations are obtained for the eigenfunctions of the differential equation describing scalar waves in a clad inhomogeneous planar waveguide, which has two turning points and finite boundaries. These representations are valid to all asymptotic orders in the large parameter, which is proportional to wavenumber.
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