Trial error

The procedure recommended by Reference [18] is based on the conventional gas flow equations, writh some slight modifications. The importance in final line size determination is to determine w hat is a reasonable pressure loss at the absolute pressure required and the corresponding pipe size to balance these. In some cases a trial/error approach is necessary. 

R. Edse, ZElektrochem 49, 178(1943) (Determination of temp of deton by systematic graphical procedure, which in the case of homogeneous gas equilibria, reduced considerably the trial-error work) 11a) M.R. von Stein, ForschGebietelngenieum 14, 113... 

When doing experimental research, one should distinguish several kinds of errors measurement error, trial error and experiment error. These errors will be analyzed in detail in a subsequent chapter. 

We can with 95% confidence assert that value yu is between 30.96 and 31.44. From the same section and formula (2.26), we may determine for the given confidence the necessary number of replicate trials so that the trial error be lower than a beforehand established value. In practice, it is often possible to use a smaller number of replicate trials than those defined in Table 2.11. Initially, in the phase of the... 

Unfortunately, in a large portion of our research, differences in response values for various trials of a design of experiments amount to for example, 1-3%, and the trial error standard deviation amounts to 5%. Experimental research in such cases makes no sense. 

Statistical significance of differences yu, for known values of a trial error are established by expression (1.72) ... 

Assume that the difference between response averages for two different trials is Pmax — Imin = 4.2, for ni=2 and n2=2. Trial errors are the same S=2. Determine the statistical significance of trial value differences. 

Assume this situation the basic design half-replica, linear model, is inadequate, the method of steepest ascent proved to be inefficient, the optimum area is close by. The system response is the product yield. Maximal possible yield is 100%. The best yield in realizing half-replica is 80%. Trial error is 1%. 

When selecting factor-variation intervals Xj X2 and X3, one should know that on approaching an optimum the values of associated regression coefficients become comparable to the replicated trial errors, while at the same time effects of square members grow. An increase in factor-variation intervals will diminish the first but augment the second problem. 

No one herbicide will do the job and control all of the many weeds in most fields. Farmers require combinations of effective and dependable herbicides that will work under a wide variety of weed species and densities, soil types, and climatic conditions. Many years of research, trial, error, and experience have been required for farmers to arrive at the greater than 22% of all corn acreage in no-till, and 112.6 million A (45.6 million ha) or more than 40% of our total United States cropland acres in some form of conservation tillage systems in 2004 (CTIC, 2004). Table 33.1 shows the trend toward various types of conservation tillage in recent years. 

Success or failure in resolution by the diastereomeric salt formation method is not determined only by the molecular structures of compounds used and physical properties of the salt crystals but also by the resolution environment such as solvent. Therefore, the proposed working hypothesis may not always be effective in all combinations of the resolution system. However, this idea will be helpful in minimizing tedious trial error experimental efforts in the laboratory. 

CRF audits should also be conducted on a draft version, just before finalization of the CRF. As the CRF is the data collection tool in a clinical trial, errors and inconsistencies in its contents and design and inconsistencies with the trial protocol may lead to serious problems if they are not identified prior to the CRF being used. This holds true for paper CRFs and electronic CRFs, as well as the use of remote data entry (RDE) or web-based data collection and transmission tools. The latter requires careful consideration of related guidelines (FDA 21 CFR Part 11 FDA Guidance for Industry, 1999). 

Figure 3 -Percent of gold leached from a calcined ore in a solution composed of lOOmM CaS203 + 0.5mM CuS04 at pH 8.5 and 50°C. The leach solution also contained OpM DMSA (blue bars - single trial)and 5 pM DMSA (red bars - two trials). Error bars represent thestandarddeviation across 2 independent runs.

Very few nonlinear equations yield analytical solutions, so graphical or trial-error solution methods are often used. There are a few nonlinear finite difference equations, which can be reduced to linear form by elementary variable transformation. Foremost among these is the famous Riccati equation... 

We rearrange the recurrence formula for the backward Euler formula (Eq. 7.44) to the following standard format, suitable for the application of the Newton-Raphson trial-error technique... 

In the previous three chapters, we described various analytical techniques to produce practical solutions for linear partial differential equations. Analytical solutions are most attractive because they show explicit parameter dependences. In design and simulation, the system behavior as parameters change is quite critical. When the partial differential equations become nonlinear, numerical solution is the necessary last resort. Approximate methods are often applied, even when an analytical solution is at hand, owing to the complexity of the exact solution. For example, when an eigenvalue expression requires trial-error solutions in terms of a parameter (which also may vary), then the numerical work required to successfully use the analytical solution may become more intractable than a full numerical solution would have been. If this is the case, solving the problem directly by numerical techniques is attractive since it may be less prone to human error than the analytical counterpart. 

Extensive tests were carried out over parts with a wide range of surface finish (roughness) and chip-removal processes. An in-depth study of the test results allowed for finding the main parameters that relates the contact profilometer measurement and the optoelectronic profilometer measurement. Operation time savings, avoiding trial error tests for finding the optimum setup of a particular measurement, justifies the importance of this study. In fact, for this profilometer, almost all processes can be fitted to an exponential curve (quality behavior curve), as shown in Fig.5. 

The variational method is used in everyday life. Usually we determine the target (say, cleaning the car), and then by trial, errors and corrections we apptoaeh the ideal, but never fully achieve it. 

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