Erratum to: Very ample but not normal lattice polytopes

Shoetsu Ogata

doi:10.1007/s13366-012-0136-0

Erratum to: Very ample but not normal lattice polytopes

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry ◽

10.1007/s13366-012-0136-0 ◽

2013 ◽

Vol 54 (2) ◽

pp. 769-770

Author(s):

Shoetsu Ogata

Keyword(s):

Lattice Polytopes ◽

Normal Lattice

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Very ample but not normal lattice polytopes

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry ◽

10.1007/s13366-011-0077-z ◽

2011 ◽

Vol 54 (1) ◽

pp. 291-302 ◽

Cited By ~ 3

Author(s):

Shoetsu Ogata

Keyword(s):

Lattice Polytopes ◽

Normal Lattice

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Defects in Crystals

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100100962 ◽

1968 ◽

Vol 26 ◽

pp. 244-245

Author(s):

Kenneth R. Lawless

Keyword(s):

Electron Microscope ◽

Point Defects ◽

Surface Defects ◽

Chemical Properties ◽

Material Point ◽

Crystal Defects ◽

Defects In Crystals ◽

Irradiation Effects ◽

Normal Lattice ◽

Line Defects

One of the most important applications of the electron microscope in recent years has been to the observation of defects in crystals. Replica techniques have been widely utilized for many years for the observation of surface defects, but more recently the most striking use of the electron microscope has been for the direct observation of internal defects in crystals, utilizing the transmission of electrons through thin samples.Defects in crystals may be classified basically as point defects, line defects, and planar defects, all of which play an important role in determining the physical or chemical properties of a material. Point defects are of two types, either vacancies where individual atoms are missing from lattice sites, or interstitials where an atom is situated in between normal lattice sites. The so-called point defects most commonly observed are actually aggregates of either vacancies or interstitials. Details of crystal defects of this type are considered in the special session on “Irradiation Effects in Materials” and will not be considered in detail in this session.

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Polytopes and 𝐾-Theory

Georgian Mathematical Journal ◽

10.1515/gmj.2004.655 ◽

2004 ◽

Vol 11 (4) ◽

pp. 655-670

Author(s):

W. Bruns ◽

J. Gubeladze

Keyword(s):

Lattice Polytopes ◽

Unit Simplex

Abstract This is an overview of results from our experiment of merging two seemingly unrelated disciplines – higher algebraic 𝐾-theory of rings and the theory of lattice polytopes. The usual 𝐾-theory is the “theory of a unit simplex”. A conjecture is proposed on the structure of higher polyhedral 𝐾-groups for certain class of polytopes for which the coincidence of Quillen's and Volodin's theories is known.

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