A differentially algebraic replacement theorem, and analog computability
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- by Leonard Lipshitz and Lee A. Rubel PDF
- Proc. Amer. Math. Soc. 99 (1987), 367-372 Request permission
Corrigendum: Proc. Amer. Math. Soc. 104 (1988), 668.
Abstract:
A theorem is proved that enables one to replace a ${C^n}$ solution of a system of algebraic differential equations by analytic solutions nearby, such that each satisfies its own algebraic differential equation. As an application, we emend a proof of the Shannon-Pour-E1 thesis relating the outputs of analog computers to solutions of algebraic differential equations.References
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- Lee A. Rubel, An elimination theorem for systems of algebraic differential equations, Houston J. Math. 8 (1982), no. 2, 289–295. MR 674043
- Claude E. Shannon, Mathematical theory of the differential analyzer, J. Math. Phys. Mass. Inst. Tech. 20 (1941), 337–354. MR 6251, DOI 10.1002/sapm1941201337
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 367-372
- MSC: Primary 12H05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0870803-1
- MathSciNet review: 870803