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Reduction to a First Order System
In the previous chapter we constructed complete asymptotic expansions of solutions to equation (11.1) assuming that the coefficients also admit certain asymptotic expansions. The asymptotic procedures used were direct and rather simple. If one is interested in asymptotic formulae which are valid under weak restrictions to the coefficients, the same ...
Vladimir Kozlov, Vladimir Maz’ya
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Analysis of a First-Order System
In this chapter we investigate the properties of solutions to a system of partial differential equations motivated by the Navier-Stokes equations and ramifications of these which arise in various thermal convection contexts. In addition to studying blow-up (or non-existence) we also examine when the solution will remain bounded for all time, or even ...
Brian Straughan
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The SVD System for First-Order Linear Systems
IEEE Transactions on Control Systems Technology, 2015This brief presents theoretical guarantees for stability and performance for the singular value decomposition (SVD) system with subsystems that are linear and first order. The SVD system reduces the dimension of the control input. It is used to meet the rank-one input constraint imposed by the row–column structure.
Winck, Ryder, Book, W.K.
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Forced oscillations in first order systems
2003 European Control Conference (ECC), 2003Forced oscillations is a phenomenon in which a nonlinear closed loop system is forced to operate at the same frequency as the external forcing sinusoid. This paper derives the necessary and sufficient conditions for which forced oscillations can be achieved when a first order linear system is placed in a closed loop relay feedback configuration.
A. P. Loh, J. Fu
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Emmetropization as a first-order feedback system
Vision Research, 1993The existence of a regulatory mechanism that controls the growth of the eye toward emmetropia is generally agreed upon, but such an emmetropization mechanism has never been verified experimentally. This report supports the hypothesis that emmetropization can be described as a feedback process with a first-order equation and establishes a theoretical ...
A, Medina, E, Fariza
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First-order sources in first-order systems: second-order correlations
Applied Optics, 1991The laws of propagation of the second-order correlation of a generalized Gaussian Schell-model source in first-order systems are deduced from the canonical operator formalism. A far-reaching generalization of Kogelnik's q parameter is derived, valid in n dimensions, for misaligned, lossy, and anisotropic sources and systems. Even in one dimension these
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A first order logic classifier system
Proceedings of the 7th annual conference on Genetic and evolutionary computation, 2005Motivated by the intention to increase the expressive power of learning classifier systems, we developed a new Xcs derivative, Fox-cs, where the classifier and observation languages are a subset of first order logic. We found that Fox-cs was viable at tasks in two relational task domains, poker and blocks world, which cannot be represented easily using
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Systems of first order equations
2014In this preliminary section we recall some facts from Linear Algebra, mainly concerning matrices and vectors. We limit ourselves to discuss only the topics that will be used in this book. For more details and further developments we refer to any book on Linear Algebra, such as the one by H. Anton and C. Rorres (see References).
Shair Ahmad, Antonio Ambrosetti
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First-Order Logic and Numeration Systems
2018The Buchi-Bruyere theorem states that a subset of \(\mathbb {N}^d\) is b-recognizable if and only if it is b-definable. This result is a powerful tool for showing that many properties of b-automatic sequences are decidable. Going a step further, first-order logic can be used to show that many enumeration problems of b-automatic sequences can be ...
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1998
In order to keep this book to a reasonable size we have decided not to give an extensive treatment of subjects that can be found elsewhere and that are somewhat peripheral to our primary interests. That policy begins to have an effect now. Proving completeness of first-order axiomatizations can be quite complex—see (Garson, 1984) for a full discussion ...
Melvin Fitting, Richard L. Mendelsohn
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In order to keep this book to a reasonable size we have decided not to give an extensive treatment of subjects that can be found elsewhere and that are somewhat peripheral to our primary interests. That policy begins to have an effect now. Proving completeness of first-order axiomatizations can be quite complex—see (Garson, 1984) for a full discussion ...
Melvin Fitting, Richard L. Mendelsohn
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