Hardness criteria

Once the analyst is satisfied that the model provides an adequate fit to the model building data set, further validation techniques that test the quality of the model may then be applied. Most validation methods are based on a comparison between predictions or simulated data under the observed model and its associated data set to some other set of data. Thus the conclusions drawn from these methods are based on the concept of similarity, i.e., the results are similar between two different data sets. The problem is that no hard criteria exists for what constitutes similar and may become almost uninterpretable. This leads to a fundamental difference between the developer of the model and the end user of the model. To the analyst, the definition of validation then becomes one of shades of gray, whereas the user wants a dichotomous outcome, i.e., the model is validated or it is not validated. It then becomes paramount for the modeler to be able to effectively communicate to the user why validation isn t a yes/no outcome, but an outcome of degrees. Usually to a naive-user, if validation... 

From the bonding perspective all discussed bases originate in hard-hard acid-base interactions in accordance with the introduced maximum hardness criteria. 

Only subalignments of length >100 nucleotide above 99% sequence identity and with > 15 exact matches at both ends were considered. This is a hard criterion for excluding paralogs and other unreliable candidates. 

Zhou and Navangul calculated MNDO hardnesses for 14 benzenoid hydrocarbons and showed it to be a good indicator for their aromaticity.Using the hardness criterion, kekulene, coronene, and the corannulene tetraanion were all predicted to be superaromatic, also confirmed by calculations of Babic and Trinajstic and Cioslowski, O Connor, and Fleischmann in the case of kekulene. " Jiao and Schleyer, however, concluded, based on geometrical, energetic, and magnetic criteria of aromaticity, that kekulene is not superaromatic. ... 

Free ionic silver readily forms soluble complexes or insoluble materials with dissolved and suspended material present in natural waters, such as sediments and sulfide ions (44). The hardness of water is sometimes used as an indicator of its complex-forming capacity. Because of the direct relationship between the availabiUty of free silver ions and adverse environmental effects, the 1980 ambient freshwater criterion for the protection of aquatic life is expressed as a function of the hardness of the water in question. The maximum recommended concentration of total recoverable silver, in fresh water is thus given by the following expression (45) in Fg/L. 

For sieve plates, thickness is usually in the lO-to-14 U.S. standard gauge range of 3.58 to 1.98 mm, or 0.141 to 0.078 in. Hardness of metal, size of die, and hmits on hole size (for process reasons) lead to the following thickness criterion ... 

The hardness of a mineral as measured by the Mohs scale is a criterion of its resistance to crushing [Fahrenwald, Trans. Am. In.st. Min. Metall. Pet. Eng., 112, 88 (1934)]. It is a fairly good indication of the abrasive character of the mineral, a factor that determines the wear on the grinding media. Arranged in increasing order or hardness, the Mohs scale is as fohows 1, talc 2, gypsum 3, calcite 4, fluoride 5, apatite 6, feldspar 7, quartz 8, topaz 9, corundum and 10, diamond. 

The surface water runoff from paved/hard standing areas also depends on rainfall intensity calculated from the geographical locations of the site and storm-return period. However, the return period for a site will be far higher than for a building in order to ensure prevention of persistent flooding of the site. In many instances the local authority may specify the storm-return period as the design criterion. 

Fig. 12b). Since practically the same spectral shape is obtained at Q-band (35 GHz) (Fig. 12c), the commonly used criterion stating that the shape of an interaction spectrum is frequency-dependent fails to apply in this case. Actually, outer lines arising from the exchange interaction are visible on the spectrum calculated at Q-band (Fig. 12c), but these lines would be hardly detectable in an experimental spectrum, because of their weak intensity and to the small signal-to-noise ratio inherent in Q-band experiments. In these circumstances, spectra recorded at higher frequency would be needed to allow detection and study of the spin-spin interactions. 

Most substances which appear in the examples of this chapter are analysed In Part Two and their enthalpy of decomposition determined experimentally. This is because most of them are considered hardly stable. This is one of the reasons for assigning no Tow risk in the suggested classifications. But it is also indisputable that criterion Cf overestimates the instability risk. It is the case for all aromatic compounds that are generally very stable. In the examples above, N-methylaniline, dichlorobenzene... 

We present an improved model for the flocculation of a dispersion of hard spheres in the presence of non-adsorbing polymer. The pair potential is derived from a recent theory for interacting polymer near a flat surface, and is a function of the depletion thickness. This thickness is of the order of the radius of gyration in dilute polymer solutions but decreases when the coils in solution begin to overlap. Flocculation occurs when the osmotic attraction energy, which is a consequence of the depletion, outweighs the loss in configurational entropy of the dispersed particles. Our analysis differs from that of De Hek and Vrij with respect to the dependence of the depletion thickness on the polymer concentration (i.e., we do not consider the polymer coils to be hard spheres) and to the stability criterion used (binodal, not spinodal phase separation conditions). 

Another criterion for catalyst selection is relative comonomer incorporation. The proposed material design is one in which the soft segment (SS) is amorphous and the hard segment (HS) contains as little comonomer as possible. To achieve this combination, the chain shuttling catalysts must have very different reactivity ratios. 

Different measures of the quality of the solution can be used for scheduling problems. However, the criterion selected to be optimized usually has a direct effect on the model computational performance. In addition, some objective functions can be very hard to implement for some event representations, requiring additional variables and complex constraints. 

A theoretical analysis of the stability of such colloidal crystals of spherical latex particles has been carried out by Marcel ja et al (28.). They employ the Lindemann criterion that a crystal will be stable if the rms thermal displacement of the particles about their equilibrium positions is a small fraction f of the lattice spacing R. Comparison with Monte Carlo simulations shows that f is about 0.1 for "hard crystals, and 0.08 for "soft crystals stabilized by long-ranged electrostatic forces. This latter criterion translates into a critical ratio... 

When in solution, both substances will cause an increase in boiling point. At the same concentration this increase will, for a low-molecular substance, be considerably higher than for a polymer (readily a factor 100 of 1000 times greater), since the increase in boiling point is proportional to the number of molecules solved. An even simpler criterion is the viscosity of the solution with a low-molecular substance hardly any change is noticed, where a polymer solution exhibits a significant increase in viscosity. 

In order to define a ionic/nonionic surfactant solution with high salinity/hardness tolerance, the following criterion should be followed. The mixed micelle should have as large of a negative deviation from ideality as possible. Surfactant mixture characteristics which result in this have already been discussed. The nonionic surfactant should have a high cloud point. Otherwise the amount of nonionic surfactant which can be added to the system is limited to low levels before phase separation occurs. If possible, a mixed ionic surfactant should be used for reasons Just discussed. There is no such benefit to using mixed nonionic surfactants, although this is not necessarily detrimental either. 

One of the drawbacks of sequential optimization methods is that optimizing two or more criteria at the same time is hard, if not impossible. If the two or more criteria are combined in one overall criterion, which is advocated sometimes, then ambiguous results are obtained. This is shown in Chapter 4. There are ways to overcome this ambiguity to some extent [21]. Another drawback of a sequential procedure is that it gives not much information on the dependence of the criterion on the design variables. In the context of robustness this is a very serious drawback. This is one of the reasons why the use of sequential optimization methods is not present in this book. 

Failure to meet an acceptance criterion for appearance, physical attribute, or functionality test (e.g., color, phase separation, resuspendibility, caking, hardness, or dose delivery per actuation). However, some changes in physical attributes (e.g., softening of suppositories, melting of creams) may be expected under accelerated conditions. 

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