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Differential-Algebraic Dynamic Logic for Differential-Algebraic Programs
"... Abstract. We generalise dynamic logic to a logic for differential-algebraic programs, i.e., discrete programs augmented with first-order differentialalgebraic formulas as continuous evolution constraints in addition to first-order discrete jump formulas. These programs characterise interacting discr ..."
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Cited by 41 (28 self)
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Abstract. We generalise dynamic logic to a logic for differential-algebraic programs, i.e., discrete programs augmented with first-order differentialalgebraic formulas as continuous evolution constraints in addition to first-order discrete jump formulas. These programs characterise interacting
MODEL THEORY AND DIFFERENTIAL ALGEBRA
"... I survey some of the model-theoretic work on differential algebra and related topics. 1 Introduction The origins of model theory and differential algebra, foundations of mathematics and real analysis, respectively, may be starkly different in character, but in recent decades large parts of these sub ..."
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I survey some of the model-theoretic work on differential algebra and related topics. 1 Introduction The origins of model theory and differential algebra, foundations of mathematics and real analysis, respectively, may be starkly different in character, but in recent decades large parts
Composition-Diamond Lemma for differential algebras
- Arabian Journal for Science and Engineering
, 2009
"... Abstract: In this paper, we establish the Composition-Diamond lemma for free differential algebras. As applications, we give Gröbner-Shirshov bases for free Lie-differential algebras and free commutative-differential algebras, respectively. ..."
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Cited by 5 (5 self)
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Abstract: In this paper, we establish the Composition-Diamond lemma for free differential algebras. As applications, we give Gröbner-Shirshov bases for free Lie-differential algebras and free commutative-differential algebras, respectively.
DIFFERENTIAL ALGEBRAS OF FINITE TYPE
, 2003
"... We study homological and geometric properties of differential algebras of finite type over a base field. The main results concern rigid dualizing complexes over such algebras. ..."
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We study homological and geometric properties of differential algebras of finite type over a base field. The main results concern rigid dualizing complexes over such algebras.
SUNDIALS: Suite of Nonlinear and Differential/ Algebraic Equation Solvers
- ACM Trans. Math. Software
, 2005
"... SUNDIALS is a suite of advanced computational codes for solving large-scale problems that can be modeled as a system of nonlinear algebraic equations, or as initial-value problems in ordi-nary differential or differential-algebraic equations. The basic versions of these codes are called KINSOL, CVOD ..."
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Cited by 162 (6 self)
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SUNDIALS is a suite of advanced computational codes for solving large-scale problems that can be modeled as a system of nonlinear algebraic equations, or as initial-value problems in ordi-nary differential or differential-algebraic equations. The basic versions of these codes are called KINSOL
Differential algebras in non-commutative geometry
- J. Geom. Phys
"... We discuss the differential algebras used in Connes ’ approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions ⊗ matrix are shown to be skew tensor products of differential forms with a specific matrix algebra. For th ..."
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Cited by 11 (2 self)
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We discuss the differential algebras used in Connes ’ approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions ⊗ matrix are shown to be skew tensor products of differential forms with a specific matrix algebra
Differentially Algebraic Gaps
, 2003
"... H-fields are ordered differential fields that capture some basic properties of Hardy fields and fields of transseries. Each H-field is equipped with a convex valuation, and solving first-order linear differential equations in H-field extensions is strongly affected by the presence of a "gap& ..."
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;gap" in the value group. We construct a real closed H-field that solves every first-order linear differential equation, and that has a differentially algebraic H-field extension with a gap. This answers a question raised in [1]. The key is a combinatorial fact about the support of transseries obtained from
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