Left-Right Equivalence and Stability

2020 ◽  
pp. 45-96
Author(s):  
David Mond ◽  
Juan J. Nuño-Ballesteros
Keyword(s):  
Right Equivalence

LOCALCr-RIGHT EQUIVALENCE OFCr+1FUNCTIONS

2016 ◽  
Vol 59 (1) ◽  
pp. 265-272 ◽  
Author(s):  
PIOTR MIGUS
Keyword(s):  
Formula Group ◽  
Image Position ◽  
Right Equivalence

AbstractLetf,g:(ℝn, 0) → (ℝ, 0) beCr+1functions,r∈ ℕ. We will show that if ∇f(0)=0 and there exist a neighbourhoodUof 0 ∈ ℝnand a constantC> 0 such that$$\begin{equation*} \left|\partial^m(g-f)(x)\right| ≤ C \left|\nabla f(x)\right|^{r+2-|m|} \quad \textrm{ for } x\in U, \end{equation*} $$and for anym∈ ℕ0nsuch that |m| ≤r, then there exists aCrdiffeomorphism ϕ:(ℝn, 0) → (ℝn, 0) such thatf=g° ϕ in a neighbourhood of 0 ∈ ℝn.

scholarly journals CT-Right Equivalence Of Analytic Functions

2015 ◽  
Vol 48 (2) ◽  
Author(s):  
Piotr Migus
Keyword(s):  
Analytic Functions ◽  
Right Equivalence

AbstractLet ƒ, g : (ℝ

scholarly journals A note on right equivalence of module presentations

1992 ◽  
Vol 52 (1) ◽  
pp. 141-142
Author(s):  
M. J. Canfell
Keyword(s):  
Stable Range ◽  
Finitely Generated ◽  
Right Equivalence

AbstractIf R has 1 in the stable range, then any two presentations f, g: p→ M of an R-module M by a finitely generated projective p are right equivalent, that is, f = gh for some automorphism h of P. The convers is also true.

On right-equivalence

1985 ◽  
Vol 190 (2) ◽  
pp. 163-205 ◽  
Author(s):  
Andrew du Plessis ◽  
Leslie Wilson
Keyword(s):  
Right Equivalence

scholarly journals Strategies in Solving Equivalent-related Problems in Translation: Implications to Cross-cultural Understanding

2021 ◽  
Vol 9 (3) ◽  
pp. 8
Author(s):  
Rusdi Noor Rosa
Keyword(s):  
Cross Cultural ◽  
Target Language ◽  
Translation Process ◽  
Cultural Understanding ◽  
Source Language ◽  
Translation Practice ◽  
The Right ◽  
Right Equivalence ◽  
Equivalence Problems ◽  
Bahasa Indonesia

Any translation practice is intended to produce a text which is equivalent in meaning with its source text. However, to arrive at such equivalence is not an easy task due to a number of differences between the source language and the target language. Therefore, finding the right equivalence is a problem often encountered by translators, especially student translators. Suggested by such problem, a study on equivalence problems and possible strategies to solve the problems is obviously necessary. This article aims at finding out the problems of equivalence encountered and the strategies to solve such problems applied by student translators in translating a historical recount text. This is a descriptive study taking 10 student translators as the participants who were asked to translate a historical recount text from English into bahasa Indonesia. The data were collected using Translog that recorded all the translation process done by the student translators. The results of the study were: (i) the student translators encountered five equivalence problems while translating a historical recount text from English into bahasa Indonesia; and (ii) to solve such problems, they applied six strategies (naturalization, borrowing, description, deletion, addition and generalization). The findings imply that the problems were motivated by the student translators’ lack of cultural understanding of the source language.

A note on right-equivalence of map-germs

1979 ◽  
Vol 168 (2) ◽  
pp. 149-165
Author(s):  
Olaf von Grudzinski
Keyword(s):  
Right Equivalence

scholarly journals Lack of equivalence in the elemental and stable isotope chemistry within the sagittal otolith pair of the summer flounder, Paralichthys dentatus

2013 ◽  
Vol 71 (2) ◽  
pp. 356-364 ◽  
Author(s):  
Antranik Kajajian ◽  
Jason J. Schaffler ◽  
Cynthia M. Jones
Keyword(s):  
Stable Isotope ◽  
Growth Patterns ◽  
Summer Flounder ◽  
Paralichthys Dentatus ◽  
Chemical Signatures ◽  
Sagittal Otolith ◽  
The Us ◽  
Nursery Habitats ◽  
Left And Right ◽  
Right Equivalence

Abstract Kajajian, A., Schaffler, J. J., and Jones, C. M. 2014. Lack of equivalence in the elemental and stable isotope chemistry within the sagittal otolith pair of the summer flounder, Paralichthys dentatus. – ICES Journal of Marine Science, 71: 356–364. In fish that are not bilaterally symmetrical, the left and right sagittae are often not symmetrical, exhibiting divergent growth patterns and mass, and may have differences in chemical composition. We investigated this in the asymmetrical summer flounder Paralichthys dentatus, collected from different nursery habitats along the US east coast. Significant differences were detected in otolith mass, δ13C, δ18O, Li:Ca, Mg:Ca, and Sr:Ca, and overall chemical signatures. These results refute the hypothesis of left–right equivalence that is prevalent for bilaterally symmetrical fishes. We tested whether a specific side was better suited for classification. The best models differed between sagittae and resulted in different classification accuracies. The left otolith produced better classification accuracies. Simulated samples of randomized sets of left or right otoliths produced mean accuracies intermediate to classification and were often highly variable. We recommend that future otolith chemistry studies involving bilaterally asymmetrical species test the hypothesis of equivalence within the sagittae before randomly choosing an otolith for chemical analyses.

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