Molecular velocity distributions and generalized scale invariance in the turbulent atmosphere

2005 ◽  
Vol 130 ◽  
pp. 181 ◽  
Author(s):  
Adrian F. Tuck ◽  
Susan J. Hovde ◽  
Erik C. Richard ◽  
Ru-Shan Gao ◽  
T. Paul Bui ◽  
...  
Keyword(s):  
Turbulent Atmosphere ◽  
Scale Invariance ◽  
Molecular Velocity

D-test: A New Test for Analyzing Scale Invariance Using Symbolic Dynamics and Symbolic Entropy

Methodology ◽  
2011 ◽  
Vol 7 (3) ◽  
pp. 88-95 ◽  
Author(s):  
Jose A. Martínez ◽  
Manuel Ruiz Marín
Keyword(s):  
Symbolic Dynamics ◽  
Scale Invariance ◽  
Rating Scales ◽  
Rating Scale ◽  
Marketing Research ◽  
Response Patterns ◽  
Measurement Scales ◽  
Improve Measurement ◽  
Entropy Measures ◽  
The Difference

The aim of this study is to improve measurement in marketing research by constructing a new, simple, nonparametric, consistent, and powerful test to study scale invariance. The test is called D-test. D-test is constructed using symbolic dynamics and symbolic entropy as a measure of the difference between the response patterns which comes from two measurement scales. We also give a standard asymptotic distribution of our statistic. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. We applied D-test to a real marketing research to study if scale invariance holds when measuring service quality in a sports service. We considered a free-scale as a reference scale and then we compared it with three widely used rating scales: Likert-type scale from 1 to 5 and from 1 to 7, and semantic-differential scale from −3 to +3. Scale invariance holds for the two latter scales. This test overcomes the shortcomings of other procedures for analyzing scale invariance; and it provides researchers a tool to decide the appropriate rating scale to study specific marketing problems, and how the results of prior studies can be questioned.

Fluid membranes in the “semi-rigid regime”: scale invariance

1991 ◽  
Vol 1 (9) ◽  
pp. 1121-1132 ◽  
Author(s):  
M. Skouri ◽  
J. Marignan ◽  
J. Appell ◽  
G. Porte
Keyword(s):  
Scale Invariance ◽  
Fluid Membranes
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