1966 ◽  
Vol 13 (4) ◽  
pp. 293-295
Author(s):  
Patricia M. Bergen

Division of fractions has caused confusion for pupils and irresolution in teachers for many years. Its rationalization in terms sixth-grade pupils will understand is difficult. Even the authorities on the teaching of arithmetic disagree on the best method of coping with this problem. Recommendations encompass the common denominator and inversion methods and, of late, the complex fraction (reciprocal) method.


2018 ◽  
Vol 2018 (1) ◽  
pp. 1-8
Author(s):  
J. Silic ◽  
R. Paterson ◽  
D. FitzGerald

Author(s):  
Liwei Wang ◽  
Henning Koehler ◽  
Ke Deng ◽  
Xiaofang Zhou ◽  
Shazia Sadiq

The description of the origins of a piece of data and the transformations by which it arrived in a database is termed the data provenance. The importance of data provenance has already been widely recognized in database community. The two major approaches to representing provenance information use annotations and inversion. While annotation is metadata pre-computed to include the derivation history of a data product, the inversion method finds the source data based on the situation that some derivation process can be inverted. Annotations are flexible to represent diverse provenance metadata but the complete provenance data may outsize data itself. Inversion method is concise by using a single inverse query or function but the provenance needs to be computed on-the-fly. This paper proposes a new provenance representation which is a hybrid of annotation and inversion methods in order to achieve combined advantage. This representation is adaptive to the storage constraint and the response time requirement of provenance inversion on-the-fly.


1962 ◽  
Vol 9 (1) ◽  
pp. 10-16
Author(s):  
Lelon R. Capps

For some time there has existed a difference of opinion with regard to the effectiveness of the common-denominator and inversion methods of teaching division of fractions.


Geophysics ◽  
2001 ◽  
Vol 66 (3) ◽  
pp. 973-975
Author(s):  
Adrianus T. de Hoop

Reciprocity is an important property of elastodynamic, electromagnetic, and acoustic wavefields. Combined with optimization techniques, reciprocity theorems can be regarded as providing the basic ingredients to imaging and inversion methods in geophysical exploration and remote sensing (de Hoop, M. V. and de Hoop, A. T., 2000). Furthermore, reciprocity serves as the basis for the elimination procedures of surface‐related multiples in marine seismic data processing (Fokkema and van den Berg, 1993). In view of all this, a thorough and elucidating discussion on the configurations to and the conditions under which reciprocity applies, and what reciprocity leads to, like the recent paper by Arnsten and Carcione (2000), serves a useful purpose. In this paper, also a number of interesting applications are worked out in detail. The aim of this discussion is to indicate briefly how some of the results obtained in that paper are related to the ones that the present author has presented in de Hoop (1995), a reference that does not appear in Arntsen and Carcione (2000).


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