Uniform Asymptotic Research Articles

Uniform coordinates and spectral asymptotics for solutions of the scattering problem for the Schr�dinger equation

Uniform asymptotic formulas at large distances and for a large value of the spectral parameter are obtained for solutions of the scattering problem. The singularities of the scattering amplitude in the angular variables and its asymptotic expression in the spectral parameter are described.

Unusual Maneuvers on Nimbus and Landsat Spacecraft

References 1 Suzuki, M. and Miura, M., Feedback Controllers for Singularly Perturbed Linear Constant Systems, IEEE Transactions on Automatic Control, Vol. AC-21, 1976, pp. 123-124. 2 Porter, B., Singular Perturbations Methods in the Design of Stabilizing Feedback Controllers for Multivariable Linear Systems, International Journal of Control, Vol. 20, 1974, pp. 689-692. Kalman, R., and Bucy, R., New Results in Linear Flitering and Prediction Journal of Basic Engineering, Transactions of ASME, Ser. D., Vol. 83, 1961, pp. 95-108. Luenberger, D., Observing the State of a Linear System, IEEE Transactions on Military Electronics, Vol. 8, 1964, pp. 74-80. Klimushchev, A. and Krasovskii, N., Uniform Asymptotic of Systems of Differential Equations with Small Parameter in the Derivative Terms, Journal of Applied Mathematics and Mechanics, Vol. 25, 1961, pp. 1011-1025. Wonham, W., On Pole Assignment in Multi-input Controllable Linear Systems, IEEE Transactions on Automatic Control, Vol. AC-12, 1967, pp. 660-665. Kokotovic, P., O'Malley, R., and Sannuti, P., Singular Perturbations and Order Reduction in Control Theory—An Overview, Automatica, Vol. 12, 1976, pp. 123-132. Shensa, M., Parasitics and the of Equilibrium Points of Nonlinear Networks, IEEE Transactions on Circuit Theory, Vol. CT-18, 1971, pp. 481-484. Desoer, C. and Shensa, M., with Very Small and Very Large Parasitics: Natural Frequencies and Stability, Proceedings of the IEEE, Vol. 58, 1970, pp. 1933-1938. Wilde, R.R. and Kokotovic, P.V., Stability of Singularity Perturbed Systems and Networks with Parasitics, IEEE Transactions on Automatic Control, Vol. AC-17, 1972, pp. 245-246.

Spectral analysis of high‐frequency diffraction of an arbitrary incident field by a half plane—Comparison with four asymptotic techniques

The knowledge of high‐frequency diffraction of an arbitrary wave incident on an edge is important in many applications, such as antennas mounted on aircraft and reflector antennas illuminated by complex feeds. In this paper the problem of a half plane illuminated by a nonplanar wave is investigated using the concept of the plane wave spectral representation. For large wave number k, a new higher‐order asymptotic solution for the total field up to and including terms of order k−5/2 relative to the incident field is derived. The behavior of the solution for the observation points which coincide with shadow boundary directions of a multipole line source is discussed in detail. Furthermore, numerical solution of the field integral representation is constructed for the observation angles in the transition regions. The results are compared with those of the Geometrical Theory of Diffraction (GTD), the Uniform Asymptotic Theory (UAT), the Uniform Theory of Diffraction (UTD) and the Modified Slope Diffraction (MSD).

On the Uniform Asymptotic Stability of Certain Linear Nonautonomous Differential Equations

In this paper we give a simple characterization of the uniform asymptotic stability of equations $\dot x = - P(t)x$ where $P(t)$ is a bounded piecewise continuous symmetric positive semi-definite matrix. In the course of developing this characterization, a new and general sufficient condition is given for uniform asymptotic stability in terms of Lyapunov functions. The stability of this type of equation has come up in various control theory contexts (identification, optimization and filtering).

5.—The Uniform Asymptotic Stability of Certain Linear Differential-difference Equations

SynopsisA necessary and sufficient condition is developed for determination of the uniform stability of a class of non-autonomous linear differential-difference equations. This condition is the analogue of the Liapunov criterion for linear ordinary differential equations.

On Improved WKB (Uniform Asymptotic) Quantum Conditions, Dunham Corrections, the Langer Modification, and RKR Potentials

An improvement to the WKB quantum condition for the rotation-vibration levels of diatomic molecules, known empirically to give RKR potentials of increased accuracy and to account for the Dunham correction Y00, is derived using uniform asymptotic methods. The role of the Langer transformation in this problem is also discussed.

On the Uniform Asymptotic Stability of Functional Differential Equations of the Neutral Type

On the Uniform Asymptotic Stability of Functional Differential Equations of the Neutral Type

Eventual Uniform Asymptotic Stability of Control Systems

Mathematische NachrichtenVolume 48, Issue 1-6 p. 43-47 Article Eventual Uniform Asymptotic Stability of Control Systems Chris P. Tsokos, Chris P. Tsokos Blacksburg (Virginia)Search for more papers by this author Chris P. Tsokos, Chris P. Tsokos Blacksburg (Virginia)Search for more papers by this author First published: 1971 https://doi.org/10.1002/mana.19710480104Citations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume48, Issue1-61971Pages 43-47 RelatedInformation