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Showing 1 to 6 of 6 for “"differential algebra"”.
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Categorical Aspects of Differential Algebra
Made available in DSpace on 2014-12-11T18:24:07Z (GMT). No. of bitstreams: 1 7412062.pdf: 6201736 bytes, checksum: 686e1e23708b8de4b198311d75f77c14 (MD5) Previous issue date: 1973
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Rational matrix differential operators and integrable systems of PDEs
… of evolution PDEs ut = F(u), where F lies in a differential algebra of functionals V and u = (U1, ... , ul) depends on one space variable x and time t, is to be part of an infinite hierarchy of generalized symmetries. Recall that V carries a Lie algebra bracket {F, G} = XF(G) - XG(F), where XF …
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The Theory of Exponential Differential Equations
… thesis is a model-theoretic study of exponential differential equations in the context of differential algebra. I define the theory of a set of differential equations and give an axiomatization for the theory of the exponential differential equations of split semiabelian varieties. In particular, …
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Derivations on o-minimal fields
… we turn our attention to $T$-convex $T$-differential fields. These are models $K\models T$ equipped with a $T$-derivation which is continuous with respect to a $T$-convex valuation ring of $K$, as defined by van den Dries and Lewenberg. We show that if $K$ is a $T$-convex $T$-differential …
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Truncation in differential Hahn fields
… in the sense that it is preserved under various algebraic and transcendental extension procedures. Nevertheless, in Chapter 4 of this dissertation we show that generalized series fields with truncation as an extra primitive yields undecidability in several settings. Our main results, however, …
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On the Complexity of Computing Galois Groups of Differential Equations
<p>The differential Galois group is an analogue for a linear differential equation of the classical Galois group for a polynomial equation. An important application of the differential Galois group is that a linear differential equation can be solved by integrals, exponentials and algebraic …