Standard functions

MeutralSoluble Salts. So dium sulfate [7757-82-6] and, to a considerably lesser extent, sodium chloride [7647-14-5] are the principal neutral soluble salts used in laundering compositions. They are often considered to be fillers although they perform an important standardizing function enabling the formulator to manufacture powders of a desired, controlled density. Sodium sulfate, in addition, lowers the critical micelle concentration of organic surfactants and thus the concentration at which effective washing can be achieved. 

The compounds considered in this work are shown in Table 1. These particular siloxane compounds have been described elsewhere [42]. A system of abbreviation already in use for these compounds is given in the same table. Their abbreviated formulas are expressed on a standard functional basis in Table 1 along with the name of the compound. An explanation of the units in the abbreviated formulas is given below ... 

To examine the fitness of the kinetic model CAER used for study of the water effect, we conducted model discrimination using the kinetic data of 15% Co/Si02 by comparing values of the standard function of mean absolute relative residual (MARR), which is simply defined as... 

In exceptional circumstances analytic solutions exist that are expressible in terms of standard functions. Although numerical methods must be used to obtain solutions in general, it is useful nonetheless to briefly review analytic methods. 

In a ternary system the property we are seeking is the standard function (Y) of transfer of an electrolyte (E) from water (W) to a mixed solvent of a nonelectrolyte in water (W + N). This function is defined by... 

Many standardized functional property tests have been published. Standardized methods are available from many organizations, including the American Association of Cereal Chemists, American Oil Chemists Society, and International Dairy Federation. Generally, these methods have been tested in collaborative studies by several laboratories and found to be repeatable. Therefore the use of standardized methods may facilitate comparison of results between laboratories. Even though a method has been standardized, there is no guarantee that the test results will relate to protein functionality in a particular product or product application. Another problem is that most of the standardized tests are empirical. If any step in the procedure is changed or equipment is substituted, comparisons between laboratories may not be possible. 

Rather than work with (3.3) directly, the MATLAB m function solveadiabxy. m above evaluates the associated standard function... 

In connection with studies on structure-property relationships with dermal penetration enhancers, substituted azepinone derivatives (e.g., 74, R = Me and 75, R = Me) were made by Kim et al. from the 3-aminoazepanone 71 via 72 and 73 using standard functional group manipulations (Scheme 8) <2001MI183>. 

In QM calculations, pM is the sum of the nuclear contribution (a linear combination of point charges located inside C) and of a regular function (the electronic density), that, in this section, is assumed to be supported in C. It then follows from standard functional analysis results [3] that for such pM, the limits V, VR e, 3yfi/3u , and dVR/dn e defined by Equations (1.17) and (1.18) exist, and VR is continuous across T. We thus infer from the representation formula (1.19) that... 

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