SEPARATING SETS OF HYPERRECTANGLES

1993 ◽  
Vol 03 (02) ◽  
pp. 155-165 ◽  
Author(s):  
FABRIZIO D’AMORE ◽  
PAOLO GIULIO FRANCIOSA
Keyword(s):  
Upper Bound ◽  
Time And Space ◽  
Separator Theorem

We consider the problem of separating a set of d-dimensional non-overlapping isothetic hyperrectangles by means of one cutting isothetic hyperplane. If the cutting hyperplane crosses one hyperrectangle this is split into two non-overlapping hyperrectangles. We show that it always exists a cutting hyperplane that separates n given hyperrectangles into two sets each containing no more than [αd · n] hyperrectangles, where αd=(2d−1)/2d. Also, we show that there are instances for which it is not possible to do better. An optimal O(d · n) time and space algorithm for finding this cutting hyperplane is presented. An upper bound to the number of intersected hyperrectangles is also given, thus proving a separator theorem for hyperrectangles.

Economy as an Organism

2011 ◽  
pp. 140-151
Author(s):  
A. Golubev
Keyword(s):  
Time And Space

Practicability of viewing economy not as a mechanism but as an organism is grounded. The concept of "genetic economics" that is considered in time and space is defined. The orders of economic constancy are recommended. "Genetic economics" axiomatic statements are formularized.

Fictive Mode, ‘Journey to the West’, and Transformation of Space: ‘Ali Mubarak’s Discourses of Modernization

2007 ◽  
Vol 4 (3) ◽  
pp. 331-358
Author(s):  
WEN-CHIN OUYANG
Keyword(s):  
Cultural Transformation ◽  
Recent History ◽  
Theoretical Principle ◽  
Time And Space ◽  
The West ◽  
Arab Culture ◽  
History Of ◽  
Journey To The West

I begin my exploration of ‘Ali Mubarak (1823/4–1893) and the discourses on modernization ‘performed’ in his only attempt at fiction, ‘Alam al-Din (The Sign of Religion, 1882), with a quote from Guy Davenport because it elegantly sums up a key theoretical principle underpinning any discussion of cultural transformation and, more particularly, of modernization. Locating ‘Ali Mubarak and his only fictional work at the juncture of the transformation from the ‘traditional’ to the ‘modern’ in the recent history of Arab culture and of Arabic narrative, I find Davenport's pronouncement tantalizingly appropriate. He not only places the stakes of history and geography in one another, but simultaneously opens up the imagination to the combined forces of time and space that stand behind these two distinct yet related disciplines.

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