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DifferentialAlgebraic Dynamic Logic for DifferentialAlgebraic Programs
"... Abstract. We generalise dynamic logic to a logic for differentialalgebraic programs, i.e., discrete programs augmented with firstorder differentialalgebraic formulas as continuous evolution constraints in addition to firstorder discrete jump formulas. These programs characterise interacting discr ..."
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Cited by 41 (27 self)
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Abstract. We generalise dynamic logic to a logic for differentialalgebraic programs, i.e., discrete programs augmented with firstorder differentialalgebraic formulas as continuous evolution constraints in addition to firstorder discrete jump formulas. These programs characterise interacting
MODEL THEORY AND DIFFERENTIAL ALGEBRA
"... I survey some of the modeltheoretic 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 modeltheoretic 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
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.
CompositionDiamond Lemma for differential algebras
 Arabian Journal for Science and Engineering
, 2009
"... Abstract: In this paper, we establish the CompositionDiamond lemma for free differential algebras. As applications, we give GröbnerShirshov bases for free Liedifferential algebras and free commutativedifferential algebras, respectively. ..."
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Cited by 5 (5 self)
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Abstract: In this paper, we establish the CompositionDiamond lemma for free differential algebras. As applications, we give GröbnerShirshov bases for free Liedifferential algebras and free commutativedifferential algebras, respectively.
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
Differential algebras in noncommutative geometry
 J. Geom. Phys
"... We discuss the differential algebras used in Connes ’ approach to YangMills 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 YangMills 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
DifferentialAlgebraic Equations
"... The current demand for more complex models has initiated a shift away from statespace models towards models described by differentialalgebraic equations (DAEs). These models arise as the natural product of objectoriented modeling languages, such as Modelica. However, the mathematics of DAEs is so ..."
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The current demand for more complex models has initiated a shift away from statespace models towards models described by differentialalgebraic equations (DAEs). These models arise as the natural product of objectoriented modeling languages, such as Modelica. However, the mathematics of DAEs
Using Linear Algebra for Intelligent Information Retrieval
 SIAM REVIEW
, 1995
"... Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical ..."
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Cited by 672 (18 self)
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Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higherorder structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented by 200300 of the largest singular vectors are then matched against user queries. We call this retrieval method Latent Semantic Indexing (LSI) because the subspace represents important associative relationships between terms and documents that are not evident in individual documents. LSI is a completely automatic yet intelligent indexing method, widely applicable, and a promising way to improve users...
Results 1  10
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