On the algebra of intervals and convex bodies

Journal of Universal Computer Science

Volumn 4, Issue 1, 1998, Pages 34-47

  Markov, Svetoslav M ^a  

^a BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

Author keywords

Commutative semigroups; Convex bodies; Interval arithmetic; Isomorphic embedding; Minkowski operations; Quasilinear space

Indexed keywords

EID: 0009360250     PISSN: 0958695X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. [Hadwiger 1957] Hadwiger, H.: "Vorlesungen über Inhalt, Oberfäache und Isoperimetrie"; Springer (1957).
2. [Kaucher 1977] Kaucher, E.: "Algebraische Erweiterungen der Intervallrechnung unter Erhaltung der Ordnungs- und Verbandstrukturen"; Computing Suppl., 1 (1977), 65-79.
3. [MacLane and Birkhoff 1979] MacLane, S.; Birkhoff, G.: "Algebra", 2nd Ed.; Macmillan, New York (1979).
4. [Markov 1977] Markov, S.: "A non-standard subtraction of intervals"; Serdica, 3 (1977), 359-370.
5. [Markov 1995] Markov, S.: "On Directed Interval Arithmetic and its Applications"; J. UCS, 1, 7 (1995), 510-521.
6. [Markov 1996] Markov, S.: "On the Foundations of Interval Arithmetic"; Scientific Computing and Validated Numerics (G. Alefeld et al., eds.); Mathematical Research, 90, Akademie Verlag (1996), 307-313.
7. [Markov 1997] Markov, S.: "Isomorphic Embedding of Abstract Interval Systems"; Reliable Computing, 3 (1997), 199-207.
8. [Markov 1997a] Markov, S.: "On the Algebraic Properties of Convex Bodies"; submitted to Serdica.
9. [Mayer 1968] Mayer, O.: "Über Eigenschaften von Intervallprozessen,"; ZAMM, 48 (1968), T86-T87.
10. [Mayer 1970] Mayer, O.: "Algebraische und metrische Strukturen in der Intervallrechnung und einige Anwendungen"; Computing 5 (1970), 144-162.
11. [Popova 1997] Popova E.: "Algebraic Solutions to Some Interval Equations"; submitted to J. UCS (1997).
12. [Rådström 1952] Rådström, H.: "An Embedding Theorem for Spaces of Convex Sets"; Proc. Amer. Math. Soc. 3 (1952), 165-169.
13. [Ratschek 1975] Ratschek, H.: "Nichtnumerische Aspekte der Intervallmathematik"; Interval Mathematics (Ed. K. Nickel, Lecture Notes in Computer Science, 29, Springer, 1975.
14. [Ratschek and Schröder 1977] Ratschek, H.; G. Schröder: "Representation of semigroups as systems of compact convex sets"; Proc. Amer. Math. Soc. 65 (1977), 24-28.
15. [Schneider 1993] Schneider, R.: "Convex Bodies: The Brown-Minkowski Theory"; Cambridge Univ. Press (1993).