Examination of Parameters

Raupp, J. (1996). Fertilization effects on product quality and examination of parameters and methods for quality assessment. Publications of the Istitute for... 

The suggested simulations and the systematic examination of parameters vs. catalyst properties in point 4 have yet to be done. However, for the first time, such studies are now possible at reasonable cost. 

In the maximum-likelihood method used here, the "true" value of each measured variable is also found in the course of parameter estimation. The differences between these "true" values and the corresponding experimentally measured values are the residuals (also called deviations). When there are many data points, the residuals can be analyzed by standard statistical methods (Draper and Smith, 1966). If, however, there are only a few data points, examination of the residuals for trends, when plotted versus other system variables, may provide valuable information. Often these plots can indicate at a glance excessive experimental error, systematic error, or "lack of fit." Data points which are obviously bad can also be readily detected. If the model is suitable and if there are no systematic errors, such a plot shows the residuals randomly distributed with zero means. This behavior is shown in Figure 3 for the ethyl-acetate-n-propanol data of Murti and Van Winkle (1958), fitted with the van Laar equation. 

In many process-design calculations it is not necessary to fit the data to within the experimental uncertainty. Here, economics dictates that a minimum number of adjustable parameters be fitted to scarce data with the best accuracy possible. This compromise between "goodness of fit" and number of parameters requires some method of discriminating between models. One way is to compare the uncertainties in the calculated parameters. An alternative method consists of examination of the residuals for trends and excessive errors when plotted versus other system variables (Draper and Smith, 1966). A more useful quantity for comparison is obtained from the sum of the weighted squared residuals given by Equation (1). 

As discussed in more detail elsewhere in this encyclopaedia, many optical spectroscopic methods have been developed over the last century for the characterization of bulk materials. In general, optical spectroscopies make use of the interaction of electromagnetic radiation with matter to extract molecular parameters from the substances being studied. The methods employed usually rely on the examination of the radiation absorbed. 

We first examine how chaos arises in tire WR model using tire rate constant k 2 as tire bifurcation parameter. However, another parameter or set of parameters could be used to explore tire behaviour. (Independent variation of p parameters... 

The text form for parameters uses white space or commas to separate the fields (columns) of the parameter tiles. They can be read by ordinary text editors, w ord processors, etc. In the text form, param eters are easy to m odify but not easy to com pare, stn dy, etc. Many database program s are capable of reading column s of text as a database, h owever. Wh ile spreadsheets are n ot. per se, databases, they can be useful for examining parameter sets. Microsoft Excel, for example, can read the text form of a param eter file and pn t the data in a form easily manipulated as a matrix or a database. The text form of parameters are stored, by default only, in Tart files. 

Traditionally, least-squares methods have been used to refine protein crystal structures. In this method, a set of simultaneous equations is set up whose solutions correspond to a minimum of the R factor with respect to each of the atomic coordinates. Least-squares refinement requires an N x N matrix to be inverted, where N is the number of parameters. It is usually necessary to examine an evolving model visually every few cycles of the refinement to check that the structure looks reasonable. During visual examination it may be necessary to alter a model to give a better fit to the electron density and prevent the refinement falling into an incorrect local minimum. X-ray refinement is time consuming, requires substantial human involvement and is a skill which usually takes several years to acquire. 

If considering transferring parameters from one force held to another, examine the parameters for an atom that is in both force helds already. If the two sets of parameters are not fairly similar, do not use parameters from that force held. 

In computational chemistry it can be very useful to have a generic model that you can apply to any situation. Even if less accurate, such a computational tool is very useful for comparing results between molecules and certainly lowers the level of pain in using a model from one that almost always fails. The MM+ force field is meant to apply to general organic chemistry more than the other force fields of HyperChem, which really focus on proteins and nucleic acids. HyperChem includes a default scheme such that when MM+ fails to find a force constant (more generally, force field parameter), HyperChem substitutes a default value. This occurs universally with the periodic table so all conceivable molecules will allow computations. Whether or not the results of such a calculation are realistic can only be determined by close examination of the default parameters and the particular molecular situation. ... 

In Chaps. 5 and 6 we shall examine the distribution of molecular weights for condensation and addition polymerizations in some detail. For the present, our only concern is how such a distribution of molecular weights is described. The standard parameters used for this purpose are the mean and standard deviation of the distribution. Although these are well-known quantities, many students are familiar with them only as results provided by a calculator. Since statistical considerations play an important role in several aspects of polymer chemistry, it is appropriate to digress into a brief examination of the statistical way of describing a distribution. 

Examination of the graph shows that the line is characterized by the following parameters ... 

The means by which high current densities are obtained can be understood from an examination of the electrolyte conductivity and the interelectrode gap width. These parameters are related to the current through Ohm s law, which states that the current I fiowing in a conductor of resistance Ris directly proportional to the appHed voltage IN... 

Sample quantity to estimate moisture for specific material is influenced to various levels of significance by properties such as particle-size range as well as relative amounts or moisture distributed among denoted forms of retention. Practical sample size estimates require background knowledge of parameters derived from experience for specific materials. More detailed examination of moisture-sampling aspects is provided in reference texts (Pitard). 

Bradshaw and his coworkers have listed several motivations for their explorations in this area. One objective of [the] research program is to prepare and study a series of multi-dentate compounds which resemble naturally occurring macrocyclic compounds . Further, Bradshaw and his coworkers have said that it is our hope that we can prepare macrocycles to mimic the selectivities of the naturally occurring cyclic antibiotics and thereby make available models for the investigation of biological cation transportation and selectivity processes . These workers have presented a number of comparisons with valinomy-cin . The other expressly stated goal of their research is to prepare molecules which will allow us to systematically examine the parameters which affect complex stability and to understand that stability in terms of AH and TAS values for complex formation . 

Preparation methods for PCNTs have been reviewed in the context of parameters which may lead to large-scale MWCNT synthesis free of by-products. It is noteworthy that the formation of aligned CNTs is currently an active area of research in conjunction with PCNT preparation. The use of SWCNTs and/or MWCNTs in electronic devices are being developed. As yet it has not proved possible to produce CNTs with diameters and helicities to order. The formation of SWCNTs by the PCNT process has not yet been reported and it is of interest to examine whether this process can be used to prepare them. 

The information on life-cycle costs gained with certain items of plant and equipment need not be true for a similar item in another location, as specific details on operating hours, and maintenance attendance can vary markedly. Also, it may be an auxiliary part (e.g. an electric motor) of a major component. Therefore, it may have an entirely different set of parameters. An important element that must be examined in detail when establishing life-cycle costs of a specific item of plant and equipment is the demand placed on energy resources by them. 

The products of the thermal transformation of PAN were used for the examination of the effect of stereoregularity of the initial polymer on the CTC properties. At equal transformation degrees, the concentration of complete charge transfer states in a bromine-complexed PCS, obtained on the basis of PAN-c (t e., a polymer with elevated content of isotactic sequences), exceeds by two orders of magnitude this parameter in the polymer obtained on the basis of PAN-r. 

The Avrami—Erofe ev equation, eqn. (6), has been successfully used in kinetic analyses of many solid phase decomposition reactions examples are given in Chaps. 4 and 5. For no substance, however, has this expression been more comprehensively applied than in the decomposition of ammonium perchlorate. The value of n for the low temperature reaction of large crystals [268] is reduced at a 0.2 from 4 to 3, corresponding to the completion of nucleation. More recently, the same rate process has been the subject of a particularly detailed and rigorous re-analysis by Jacobs and Ng [452] who used a computer to optimize curve fitting. The main reaction (0.01 < a < 1.0) was well described by the exact Avrami equation, eqn. (4), and kinetic interpretation also included an examination of the rates of development and of multiplication of nuclei during the induction period (a < 0.01). The complete kinetic expressions required to describe quantitatively the overall reaction required a total of ten parameters. 

It is apparent, from the above short survey, that kinetic studies have been restricted to the decomposition of a relatively few coordination compounds and some are largely qualitative or semi-quantitative in character. Estimations of thermal stabilities, or sometimes the relative stabilities within sequences of related salts, are often made for consideration within a wider context of the structures and/or properties of coordination compounds. However, it cannot be expected that the uncritical acceptance of such parameters as the decomposition temperature, the activation energy, and/or the reaction enthalpy will necessarily give information of fundamental significance. There is always uncertainty in the reliability of kinetic information obtained from non-isothermal measurements. Concepts derived from studies of homogeneous reactions of coordination compounds have often been transferred, sometimes without examination of possible implications, to the interpretation of heterogeneous behaviour. Important characteristic features of heterogeneous rate processes, such as the influence of defects and other types of imperfection, have not been accorded sufficient attention. 

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