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FORMALIZATION OF HILBERT'S GEOMETRY OF INCIDENCE AND PARALLELISM
Synthese, 1997The author first describes how \textit{D. Hilbert} changed the phrasing of his axioms of incidence in the various early editions of his Grundlagen der Geometrie [(Teubner, Leipzig) (1899; JFM 30.0424.01); second edition (1903; JFM 34.0523.01); seventh edition (1930; JFM 56.0481.01)], in which ``bestimmen'' gave way to ``es gibt''.
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Left ventricular geometry and risk of incident hypertension
Heart, 2019Objective Left ventricular (LV) geometry change is an independent predictor for cardiovascular disease. However, data are equivocal on the association of echocardiographic parameters of LV geometry with incident hypertension.
Sung Keun Park +4 more
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Pumping geometry for a grazing-incidence dye laser
Applied Optics, 1992A new pumping geometry for longitudinal excitation of a grazing-incidenceg rating dye laser is proposeda nd experimentally demonstrated.
S R, Mishra, H S, Rawat, S C, Mehendale
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Incidence loops and their geometry
1992Publisher Summary This chapter discusses the concept of incidence loops and their geometry. An incidence group (P, L,·) is a group (P,·) together with a structure (P, L) of an incidence space such that both structures are compatible. The notion of incidence group can be generalized by weakening the assumptions concerning the algebraic structure of P;
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Preliminaries and Incidence Geometry (I)
2015This chapter contains a brief summary of several types of mathematical knowledge needed to read this book, including the elements of logic, set theory, mapping theory, and algebraic structures such as number systems and vector spaces. Definitions of basis, dimension, linear mappings, isomorphism, matrices and determinants are given; there is also ...
Edward John Specht +3 more
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Incidence problems in discrete geometry
2017Over the past decade, discrete geometry research has flourished with clever uses of algebraic methods. The polynomial method has had a deep impact on a wide collection of results in combinatorics, such as tight asymptotic lower bounds on finite field Kakeya and Nikodym sets, near optimal lower bound for Erdos' distinct distances problem, and improved ...
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