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In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow water surfaces. It is particularly notable as the prototypical example of an integrable PDE and exhibits many of the expected behaviors for an integrable PDE, such as a large number of explicit solutions, in particular soliton solutions, and an infinite number of conserved quantities, despite the nonlinearity which typically renders PDEs intractable. The KdV can be solved by the inverse scattering method (ISM). In fact, Gardner, Greene, Kruskal and Miura developed the classical inverse scattering method to solve the KdV equation.
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- Aftereffect is an applied problem: it is well known that, together with the increasing expectations of dynamic performances, engineers need their models to behave more like the real process. Many processes include aftereffect phenomena in their inner dynamics. In addition, actuators, sensors, and communication networks that are now involved in feedback control loops introduce such delays. Finally, besides actual delays, time lags are frequently used to simplify very high order models. Then, the interest for DDEs keeps on growing in all scientific areas and, especially, in control engineering.
- Delay systems are still resistant to many classical controllers: one could think that the simplest approach would consist in replacing them by some finite-dimensional approximations. Unfortunately, ignoring effects which are adequately represented by DDEs is not a general alternative: in the best situation, it leads to the same degree of complexity in the control design. In worst cases, it is potentially disastrous in terms of stability and oscillations.
- Voluntary introduction of delays can benefit the control system.
- In spite of their complexity, DDEs often appear as simple infinite-dimensional models in the very complex area of partial differential equations (PDEs).
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In mathematics, the logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm. The logarithmic norm was independently introduced by Germund Dahlquist and Sergei Lozinskiĭ in 1958, for square matrices. It has since been extended to nonlinear operators and unbounded operators as well. The logarithmic norm has a wide range of applications, in particular in matrix theory, differential equations and numerical analysis. In the finite-dimensional setting, it is also referred to as the matrix measure or the Lozinskiĭ measure.
Steven Alan Orszag was an American mathematician.
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References
- 1 2 Johnson., Elgy S. (February 22, 1999). Properties of solutions of nonlinear differential equations (Book, 1979). OCLC 10472636 . Retrieved February 1, 2019– via WorldCat.org.
- ↑ "UDC Consolidation" (PDF). Maryland – D.C. – Virginia Section of the MAA Newsletter. Fall 1978. Retrieved 1 February 2019.
- ↑ "Roberson v. District of Columbia Bd. of Higher Ed". Justia Law. January 12, 2019. Retrieved January 1, 2019.
- 1 2 3 "ELGY SIBLEY JOHNSON, 74, RETIRED UDC PROFESSOR, DIES". Washington Post. March 12, 1987. Retrieved February 1, 2019.
- ↑ Shakil, M (2010). "African-Americans in mathematical sciences – a chronological introduction" (PDF). Polygon. 4 (Spring): 27–42. Retrieved 8 April 2017.
- ↑ "Notable Members of Mu Lambda". Alpha Phi Alpha Fraternity, Mu Lambda chapter. Archived from the original on 21 January 2012. Retrieved 26 February 2012.
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