Modelle ebener metrischer ringgeometrien

Schröder, Eberhard M.

doi:10.1007/bf02941298

Cited by 9 publications

(5 citation statements)

References 6 publications

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“…Examples for algebras with involution over a commutative ring can be obtained similarly to the cases above: As for algebras over fields (see [1], [6], [7]) also for algebras over tings one can show that, e.g., two-dimensional algebras (cp. [18]), quaternion algebras, orthe algebras M(2 × 2, R) of 2 × 2-matrices have an involution.…”

Section: (7) N(ab) = Ab[a = An(b)a = Aan(b) = N(a)n(b) (8) a E A* =mentioning

confidence: 99%

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A quadric model for Klingenberg chain spaces

Blunck

1995

Geom Dedicata

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Abstract. Consider a finite-dimensional algebra with involution over a commutative local ring. The chain geometry over this algebra is a Klingenberg chain space. We embed this structure into a projective Klingenberg space, such that the points are identified with points of a quadric and the chains with plane sections.Mathematics Subject Classifications (1991): 51 C05, 51B05.For the classical chain geometries over the real algebras C of complex numbers, D of dual numbers, and A of double numbers, one has in a natural way a 'projective embedding', where the points are identified with certain points of a quadric in the three-dimensional real projective space and the chains with plane sections of the quadric (see [1]). For example, the real MSbius plane can be interpreted as the geometry of circles on the 2-sphere. In [4] and [5], Hotje generalized this to the case of chain geometries over so-called kinematic algebras over fields (see below). Now Hotje's results shall be carried over to 'Klingenberg chain spaces' belonging to certain algebras over local rings.

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Section: (7) N(ab) = Ab[a = An(b)a = Aan(b) = N(a)n(b) (8) a E A* =mentioning

confidence: 99%

“…Now we look for a quadric model of ~(R, A). For special cases also compare [17] (Section 3.3, where A = R + Ri, i 2 = -1, and _R is the ring of dual numbers) and [18] (where R is an arbitrary, not necessarily local, commutative ring and A is 2-dimensional over R).…”

Section: Projective Klingenberg Spaces: the Embeddingmentioning

confidence: 99%

A quadric model for Klingenberg chain spaces

Blunck

1995

Geom Dedicata

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“…where we checked the d-dimensional expression for a 1 (ǫ) in [23], b 1 (ǫ) is from [11], b 2 (ǫ = 0) from [24], and v can be obtained from [25]. However, in the present work, we shall use this result only for a rough estimate.…”

Section: Potentialsmentioning

confidence: 99%

Third-order non-Coulomb correction to the S-wave quarkonium wave functions at the origin

2008

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We compute the third-order correction to the S-wave quarkonium wave functions |ψ n (0)| 2 at the origin from non-Coulomb potentials in the effective non-relativistic Lagrangian. Together with previous results on the Coulomb correction and the ultrasoft correction computed in a companion paper, this completes the thirdorder calculation up to a few unknown matching coefficients. Numerical estimates of the new correction for bottomonium and toponium are given.

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“…A complete definition can be found in (Schröder et al, 1999). Figure (1) outlines the overall architecture of the system consisting of a lexicon component, ontologies and other external shallow parsing components, all of which are accessed via constraints affecting the internal constraint network as far as variables are in their scope.…”

Section: Weighted Dependency Parsingmentioning

confidence: 99%

Dynamic dependency parsing

Daum

2004

Proceedings of the Workshop on Incremental Parsing Bringing Engineering and Cognition Together - IncrementParsing '04

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The inherent robustness of a system might be an important prerequisite for an incremental parsing model to the effect that grammaticality requirements on full sentences may be suspended or allowed to be violated transiently. However, we present additional means that allow the grammarian to model prefix-analyses by altering a grammar for non-incremental parsing in a controlled way. This is done by introducing underspecified dependency edges that model the expected relation between already seen and yet unseen words during parsing. Thus the basic framework of weighted constraint dependency parsing is extended by the notion of dynamic dependency parsing.

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Modelle ebener metrischer ringgeometrien

Cited by 9 publications

References 6 publications

A quadric model for Klingenberg chain spaces

A quadric model for Klingenberg chain spaces

Third-order non-Coulomb correction to the S-wave quarkonium wave functions at the origin

Dynamic dependency parsing

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