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 measuring block 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 wetend chemistry, a polymer is often used to increase retention. We use the Britt britt n. Variant of brit. Noun 1. britt  the young of a herring or sprat or similar fish brit 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. fil·trate v. 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 totalsolids consistency of the furnish, retention is called totalsolids retention. In the mill, this is often called firstpass retention (FPR FPR Ford Performance Racing FPR Front Patriotique Rwandais (Rwanda Patriotic Front) FPR FloatingPoint 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. Surya is with OndeoNalco Pacific," you may him at email psurya@ondeonalco.com. Chua and Khoo are with the National University of Singapore The National University of Singapore (Abbreviation: NUS) is Singapore's oldest university. It is the largest university in the country in terms of student enrollment and curriculum offered. ; email Chua at stactc@nus.edu.sg; email Khoo at atfeio@singnet.com.sg. 

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