Linear transformation, its application in the paper industry.
Application: Linear transformation simplifies data analysis. Mills can use the methods described here to simplify and improve drainage analysis.
Change of measuring unit Noun 1. measuring unit - a unit of measurement
unit, unit of measurement - any division of quantity accepted as a standard of measurement or exchange; "the dollar is the United States unit of currency"; "a unit of wheat is a bushel"; "change is often encountered in daily life. For example, length is expressed in nanometer (nm) rather than in meter (m); this is a simple change in scale. Similarly, temperature can be expressed in degrees Celsius rather than in degrees Fahrenheit. In this second case, the scale is changed and the origin is shifted. That is, the new units are obtained by a linear transformation of the original units.
What is linear transformation? It is a way to express one variable (y) in a different variable (y') such that the relationship between y and y' can be expressed as y' = [a.sub.0] + [a.sub.1]y where [a.sub.0] and [a.sub.1] are constants. Examples of descriptive measures are mean and variance.
In wet-end chemistry, a polymer is often used to increase retention. We use the Britt britt
Variant of brit.
Noun 1. britt - the young of a herring or sprat or similar fish
young fish - a fish that is young
2. dynamic drainage jar (DDJ DDJ Dr. Dobb's Journal
DDJ Data Dependent Jitter
DDJ Dell Disc Jockey (Mp3 Player) ) to measure filtrate filtrate /fil·trate/ (fil´trat) a liquid or gas that has passed through a filter.
To put or go through a filter.
n. consistency and retention The filtrate consistency should decrease with the addition of the polymer (retention aid). So, for a given polymer dosage, a convenient and commonly used definition of retention is y' = 100% * (b - y) / b where y' is retention, y is filtrate consistency and b is the reference point, as defined below. Thus, we can think of the amount of polymer added as our independent variable x, the filtrate consistency as our basic dependent variable y, and the retention as a transformation y' of y. Note that y' is a linear transformation of y (let [a.sub.0] be 1 and [a.sub.1] be -1/b). This is significant because it allows us alternative ways to define the reference point b. If the reference point is the total-solids consistency of the furnish, retention is called total-solids retention. In the mill, this is often called first-pass retention (FPR FPR Ford Performance Racing
FPR Front Patriotique Rwandais (Rwanda Patriotic Front)
FPR Floating-Point Register (CPU architecture)
FPR Fuel Pressure Regulator (automotive) ). If the reference point is the fines consistency of the furnish, retention is called fines retention.
We also show an example where apparent linear transformation is not. In this case, if we choose to express our result in drainage rate rather than in drainage time, the mean, the variance, and the regression coefficient Regression coefficient
Term yielded by regression analysis that indicates the sensitivity of the dependent variable to a particular independent variable. See: Parameter.
regression coefficient of determination (obtained through linear regression Linear regression
A statistical technique for fitting a straight line to a set of data points. ) will not be likely the same.
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