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FIELD EXTENSION
"... Let G be a differential field of characteristic zero with the commuting derivations d ί9 — 9dm. If F is a differential subfield of G, the algebraic and differential degrees of transcendence of G over F, denoted respectively by d(G/F) and d.d(G/F) are numerical invariants of the extension. Unlike th ..."
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Let G be a differential field of characteristic zero with the commuting derivations d ί9 — 9dm. If F is a differential subfield of G, the algebraic and differential degrees of transcendence of G over F, denoted respectively by d(G/F) and d.d(G/F) are numerical invariants of the extension. Unlike
Spheres of quadratic field extensions
"... The concepts of the geometry of field extensions can be found in the book of W.!BENZ [2]. There it is shown that the geometry arising from the real quaternions and the complex numbers has a point model, namely the 2spheres on a ..."
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Cited by 3 (3 self)
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The concepts of the geometry of field extensions can be found in the book of W.!BENZ [2]. There it is shown that the geometry arising from the real quaternions and the complex numbers has a point model, namely the 2spheres on a
On Duality for Skew Field Extensions
, 1986
"... In this paper a duality principle is formulated for statements about skew field extensions of finite (left or right) degree. A proof for this duality principle is given by constructing for every extension L/K of finite degree a dual extension LJK,. These dual extensions are constructed by embedding ..."
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In this paper a duality principle is formulated for statements about skew field extensions of finite (left or right) degree. A proof for this duality principle is given by constructing for every extension L/K of finite degree a dual extension LJK,. These dual extensions are constructed by embedding
Shallow Parsing with Conditional Random Fields
, 2003
"... Conditional random fields for sequence labeling offer advantages over both generative models like HMMs and classifiers applied at each sequence position. Among sequence labeling tasks in language processing, shallow parsing has received much attention, with the development of standard evaluati ..."
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Cited by 581 (8 self)
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evaluation datasets and extensive comparison among methods. We show here how to train a conditional random field to achieve performance as good as any reported base nounphrase chunking method on the CoNLL task, and better than any reported single model. Improved training methods based on modern
COMBINATORIAL GEOMETRIES OF THE FIELD EXTENSIONS
"... Abstract. We classify projective planes in algebraic combinatorial geometries in arbitrary fields of characteristic zero. We investigate the firstorder theories of such geometries and pregeometries. Then we classify the algebraic combinatorial geometries of arbitrary field extensions of the transce ..."
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Cited by 3 (0 self)
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Abstract. We classify projective planes in algebraic combinatorial geometries in arbitrary fields of characteristic zero. We investigate the firstorder theories of such geometries and pregeometries. Then we classify the algebraic combinatorial geometries of arbitrary field extensions
An invariant for difference field extensions
, 902
"... A difference field is a field with a distinguished endomorphism σ. In this short note, we introduce a new invariant for finitely generated difference field extensions of finite transcendence degree, the distant degree. If (K, σ) is a difference field, and a a finite tuple in some difference field ex ..."
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A difference field is a field with a distinguished endomorphism σ. In this short note, we introduce a new invariant for finitely generated difference field extensions of finite transcendence degree, the distant degree. If (K, σ) is a difference field, and a a finite tuple in some difference field
Valuations in algebraic field extensions
, 2008
"... Let K → L be an algebraic field extension and ν a valuation of K. The purpose of this paper is to describe the totality of extensions {ν′} of ν to L using a refined version of MacLane’s key polynomials. In the basic case when L is a finite separable extension and rk ν = 1, we give an explicit descri ..."
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Cited by 7 (2 self)
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Let K → L be an algebraic field extension and ν a valuation of K. The purpose of this paper is to describe the totality of extensions {ν′} of ν to L using a refined version of MacLane’s key polynomials. In the basic case when L is a finite separable extension and rk ν = 1, we give an explicit
Toward the next generation of recommender systems: A survey of the stateoftheart and possible extensions
 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
, 2005
"... This paper presents an overview of the field of recommender systems and describes the current generation of recommendation methods that are usually classified into the following three main categories: contentbased, collaborative, and hybrid recommendation approaches. This paper also describes vario ..."
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Cited by 1490 (23 self)
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This paper presents an overview of the field of recommender systems and describes the current generation of recommendation methods that are usually classified into the following three main categories: contentbased, collaborative, and hybrid recommendation approaches. This paper also describes
On the Geometry of Field Extensions
 Aequat. Math
, 1993
"... Summary. We investigate the spread arising from a field extension and its chains. The major tool in this paper is the concept of transversal lines of a chain which is closely related with the CartanBrauerHua theorem. Provided that one chain has a "sufficiently large " number of such line ..."
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Cited by 5 (4 self)
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Summary. We investigate the spread arising from a field extension and its chains. The major tool in this paper is the concept of transversal lines of a chain which is closely related with the CartanBrauerHua theorem. Provided that one chain has a "sufficiently large " number
On Density of Primitive Elements for Field Extensions
, 2004
"... This paper presents an explicit bound on the number of primitive elements that are linear combinations of generators for field extensions. ..."
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Cited by 3 (0 self)
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This paper presents an explicit bound on the number of primitive elements that are linear combinations of generators for field extensions.
Results 1  10
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