Representative sample defining

An important issue concerning reversible CA is their construction. In particular, we are interested in knowing if there is some systematic method by which reversible CA rules can be constructed from scratch. On the one hand - if the desire is to randomly choose a reversible rule out of the set of all possible rules, the outlook for success is very dim. Amoroso and Patt [amoro72], for example, had observed that, within the space of all possible rules, the set of nontrivial reversible rules appeared to be exceedingly small. Sears [sears71] had also shown that the set of invertible CA actually constitutes a vanishingly small subset. On the other hand, if the desire is to simply define some representative samples of reversible rules (or some set of rules that may also possess some additional special features), a number... 

A defined procedure whereby a part of a substance, material or product is taken to provide for testing or calibration a representative sample of the whole. Sampling may also be required by the appropriate specification for which the substance, material or product is to be tested or calibrated. 

Several soil-vapor monitoring techniques are currendy being used to define areas of volatile organic chemical contamination. These procedures usually involve the collection of representative samples of the soil gas for analysis of indicator compounds. Maps marked with concentration contours of these indicator compounds can be used to identify potential sources to delineate the contaminated area. Indicator compounds (usually the more volatile compounds) are selected for each specific situation. For gasoline contamination, the compounds are usually benzene, toluene, ethylbenzene, and total xylene (BTEX). In the case of a fuel oil spill, the most commonly used indicator is naphthalene. Some laboratories have adapted the laboratory procedures used for quality analysis of wellhead condensate (i.e., normal paraffins) to include light-end (<8 carbons) molecular analysis. 

The TOS defines as correct any sampling procedure which is accurate (property of the mean). If it is also reproducible (property of the variance) then it may be qualified as representative. The central issue is then that even for truly representative sampling, in practice any specific analytical result as is an estimate of the true (average) Al only. This is due to the influence of the fundamental sampling error (FSE), more of which below. 

In Ireland, compliance with toxicity limits for selected industries is ascertained by annual or biannual test on representative samples of effluent. The test species most commonly used is the rainbow trout (Salmo gairdneri). Control authorities normally require results from 96-hour tests. The toxicity values are expressed as the minimum acceptable proportion of effluent (as a percentage) in a test resulting in 50% fish mortality after 96 hours of exposure. The toxic units (TU) are defined as the maximum number of times an effluent may be diluted to produce the test criteria (TU = 100/96-hour LC50, with LC50 expressed as the percentage of effluent in the test) (Fig. 5). 

Define sample, representative sample, composite sample, selective sample, random sample, bulk sample, primary sample, secondary sample, subsample, laboratory sample, test sample. 

A representative sample is a sample taken using a clearly defined procedure in order to obtain information about a batch. 

Figure 8 is a plot of r89M4 vs. particle size. We define rlt j as the ratio of equivalent fissions of i to equivalent fissions of j. These ratios have several advantages (1) they are independent of the percent active particles, (2) they are independent of errors in weighing the samples, and (3) in a truly representative sample of weapon debris, rltj = 1 for all i and j. Figure 8 presents two surprises (1) for Zuni, r89,144 is generally lower in the more distant sample, and (2) the Zuni 85-km. curve below 150/x and the Bravo curve above 50/x have positive slopes (and appear to... 

It allows a representative sample of configurations on the dividing surface to be collected in a reasonable amount of computer time (the dividing surface is conveniently defined by r(q) = rmin, where rmin is the minimum of the bimodal distribution of p(r)... 

Recommendation 4-2. The Army should define the quantity and characteristics of anticipated nonprocess waste streams and evaluate options for the final disposition of each type of waste. On-site processes should be developed and demonstrated for treating all agent-contaminated wastes. Methods of representative sampling and characterization of wastes should be developed to verify that treated wastes are free of agent to below appropriate risk thresholds. 

Accuracy is often expressed inversely in terms of the standard deviation or variance and includes any systematic error or bias. Accuracy includes both the random error of precision and any systematic error. The effect of systematic error on the standard deviation is to inflate it. In the measurement of coal quality for commercial purposes, accuracy expressed in this manner is generally of less interest than is systematic error itself. When systematic error is reduced to a magnitude that is not of practical importance, accuracy and precision can become meaningful parameters for defining truly representative sampling and for interpretation of the results of various test methods. 

The definition of the term representative sample is given in Section 4.1. In each case the representativeness should be regarded as being defined for the specific purpose. In environmental investigations it is impossible in practice to obtain one representative sample, except for the case of a composite sample for bulk analysis. It is, however, possible to obtain representative samples with a properly designed and optimized sampling plan (see Section 4.5.3). 

Bulk crush strength is commonly measured by placing a representative sample in a cylinder, applying a constant force with a piston, and mesuring the amount of fines generated. Many different variants are possible and no generally accepted method is yet available. The bulk crush strength is defined empirically and the re-... 

The uniformity was assessed by selecting representative samples from the dyed lot and determining the color (tristimulus values) on a standard colorimeter (DIANO/LSCE Automate System). The difference in color of each specimen from the average color of all specimens was determined using the FMC II color difference formula (5J. In this system one unit of color difference is defined as the minimum perceptible difference in color. Thus spots or unlevel dyeing could be readily identified by variations in color difference between specimens from the same dyeing. 

Upon completion of the process, samples are taken to establish that the batch meets the final product specifications defined for release. Predefined sampling plans are utilized to obtain representative samples of the entire batch, the prior validation effort having assured through an expanded sampling effort that the process provides a uniform product. End-product sampling often suffers from the inability to link an anomalous result with a specific portion/segment of the batch. If the validation is insufficiently rigorous, an out-of-specification result will ordinarily result in rejection of the batch and little opportunity to take effective corrective action. 

Important trends of double-mesopore structural development resulting from the water-treatment are revealed in Figure 2 by the N2 adsorption-desorption isotherms and the corresponding BJH pore size distribution based on the desorption branch for the representative samples mentioned above. The isotherm of the normally synthesized DMS simple shows a typical irreversible type IV adsorption isotherm with two separate, well-expressed HI hysteresis loops as defined by lUPAC at relative pressures p/po of 0.2-0.45 and that of 0.8-1.0, respectively. The first condensation step on the isotherm at p/pQ=0.2-0.45 is similar to that for usual MCM-41 materials, however, obviously, this inflection at higher relative pressures differs completely from that of previously-synthesized mesoporous materials in the aspect of their effects on the mesoporous frameworks of the product, namely, this material is of a clear double mesopore size distribution. After 1 day of postsynthesis hydrothermal treatment, the properties of the samples changed dramatically. Compared with the normally synthesized DMS sample, the water-treated sample at 373K shows more steep adsorption steps at 0.25-0.4p/po and 0.8-1.0p/po, respectively, suggesting that double-... 

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