Scale-Invariance of the Pi-Space – The Foundation of the Scale-Up

Aluminum additions to conventional 18Cr-8Ni austenitic stainless steel compositions impart excellent resistance to high sulfur environments. However, problems are typically encountered with aluminum additions above about 1% due to embrittlement caused by aluminum in solid solution and the precipitation of NiAl. Consequently, little use has been made of aluminum alloy additions to stainless steels for use in sulfur or H2S environments in the chemical industry, energy conversion or generation, and mineral processing, for example.A research program at the Albany Research Center has concentrated on the development of a wrought alloy composition with as low a chromium content as possible, with the idea of developing a low-chromium substitute for 310 stainless steel (25Cr-20Ni) which is often used in high-sulfur environments. On the basis of workability and microstructural studies involving optical metallography on 100g button ingots soaked at 700°C and air-cooled, a low-alloy composition Fe-12Cr-5Ni-4Al (in wt %) was selected for scale up and property evaluation.

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

Methodology ◽

10.1027/1614-2241/a000026 ◽

2011 ◽

Vol 7 (3) ◽

pp. 88-95 ◽

Cited By ~ 2

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.

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