Constants, variability

This file introduces the concept of variables within the molecule specification. Here, variables are simply named constants variable names are substituted for literal values within the Z-matrix, and their values are defined in a separate section following it. The two sections are separated by a blank line, or a line with a blank in the first column and the label Variables placed elsewhere on it (this is one exception Gaussian makes in its requirement for completely blank lines). ... 

The Swung-Lo plant, located in the Far East, is a relatively new plant with an improved reactor/recycle design. This plant can be operated between 80 X 106 and 120 X 106 lb/year and has a constant variable cost of 5.00/100 lb. 

PCA is successful for data sets with correlating variables as it is often the case with data from chemistry. Constant variables or highly correlating variables cause no problems for PCA however, outliers may have a severe influence on the result, and also scaling is important. 

Density variable variable variable/ constant variable variable N/A constant variable variable... 

The dielectric constant of polyimide films in the wet condition (50% RH atmosphere) is higher than in the dry condition. This is attributed to water absorption by the polyimides. Figure 15.5 also shows the water absorption of die polyimides, which is due to the presence of imide groups in the polymer and decreases widi increasing fluorine content because of the hydrophobic effect of fluorine atoms. The water absorption is related to the stability of the dielectric constant. The dielectric constant variability between the dry and wet conditions of highly fluorinated polyimides, P3FDA/TFDB and P6FDA/TFDB, is smaller than... 

As one can see in (1.14a), the variables (x, y, z) are cycled in the three derivatives, each appearing once in the numerator, once in the denominator, and once as the constant variable. The cyclic symmetry makes it easy (and advisable) to commit this identity to memory, even if it can be easily rederived from (1.10) for use as needed. 

Figure 7. Temperature variations of the two constant variables A(T) and B(T) defined in Eqs. 5 and 6 (see text).

Define all symbols for mathematical constants, variables, and unknown quantities the first time you use them in the text. If you use them in the abstract, define them there and then again at their first appearance in text. Do not define standard mathematical constants such as n, i, and e. 

Even when you use mathematical constants, variables, and unknown quantities in adjective combinations, retain the italic type. 

Figure 4.4 illustrates a radial basis function solution to the hypothetical depression classification problem. The algorithm that implemented the radial basis function application determined that seven cluster sites were needed for this problem. A constant variability term, a2 =. 1, was used for each hidden unit. Shown in the diagram are the two central parameters (because there are two input units) for each of the seven Gaussian functions. 

Equations 5 have been used with the variable pressure data to determine the constants. Variable pressure data were determined at 460°, 480°, and 499°F. Negative values of the adsorption constants were obtained... 

A stepwise selection procedure is performed to search for QSPR/QSAR models after the preliminary exclusion of - constant and near-constant variables. The - pair correlation cutoff selection of variables is then performed to avoid highly correlated descriptor variables within the model. 

Connoiiy surface area - molecular surface (O solvent-accessible molecular surface) constant interval reciprocal indices -> distance matrix constant and near-constant variables variable reduction constitutional descriptors... 

A preliminary approach to variable reduction consiting in the elimination of all the variables that take the same value for all the objects in the data set. Near-constant variables, i.e. variables that assume the same value except in one or very few cases, would also be excluded. A good measure for evaluating near-constant variables is the -> standardized Shannon s entropy the entropy of a variable with one different value over 10 objects is 0.141, over 20 objects is 0.066, and with two different values over 100 objects is 0.024. 

Properties White, gelatinous precipitate. Constants variable with the composition, d approx 2.4. Insoluble in water and alcohol, soluble in acid and alkali. Noncombustible. 

PTGL-technology can only be succesful if practical solutions are found for problems such as refuse handling and feeding, maintenance of stable operating conditions with a constantly variable feedstock, smooth elimination of residue and proper treatment of reaction products. Quite normally process developers center all their energy on the design,construction and demonstration of their plant and equipment. 

The initial discovery and description of the constant, variable, and hypervariable domains and elucidation of the primary structures of the immunoglobulins was made possible because of the disease multiple myeloma. In multiple myeloma, a single B-cell clone (mono-clone) synthesizes large quantities of structurally identical or monoclonal antibody molecules. Isolation of immunoglobulin from multiple myeloma patients who were producing structurally different immunoglobulins... 

Short variable names are convenient and appropriate to hold temporary or intermediate values, such as counters in conditional loops. However, it is recommended that meaningful names be used even for counters. The code in Code Block 1 (Figure 2.1) provides examples of descriptive names for constants, variables, and temporary counters in conditional loops. Although this is a trivial example, the benefits of using descriptive counter variable names increase as the number of statements and nesting levels in the conditional block increase. 

An important partition function can be derived by starting from Q (T, V, N) and replacing the constant variable AT by fi. To do that, we start with the canonical ensemble and replace the impermeable boundaries by permeable boundaries. The new ensemble is referred to as the grand ensemble or the T, V, fi ensemble. Note that the volume of each system is still constant. However, by removing the constraint on constant N, we permit fluctuations in the number of particles. We know from thermodynamics that a pair of systems between which there exists a free exchange of particles at equilibrium with respect to material flow is characterized by a constant chemical potential fi. The variable N can now attain any value with the probability distribution... 

Finally, we mention the chain rule for differentiation for instance, if we have the derivative of pA with respect to the density pA at some set of constant variables C, we now want the derivative of pA with respect to, say, the mole fraction xA, at the same set of constant variables C. We have... 

Assuming constant variability for the disturbances when the analysis is specified and having this assumption correct are not enough to make the long-run size of all residuals the same. If, for instance, we fit a straight line by equally weighted least squares to five equally spaced points and the model applies precisely, we find the following ... 

Figure 4.8 Scatter plot of simulated data from a Michaelis-Menten model with Vmax — 100 and Km — 20 (top) and Lineweaver-Burke transformation of data (bottom). Stochastic variability was added by assuming normally distributed constant variability with a standard deviation of 3.

The precursor should be either a liquid or a solid with sufficient vapor pressure and mass transport at the desired temperature, preferably below 200°C. Liquids are preferred to solids owing to the difficulty of maintaining a constant flux of source vapors over a non-equilibrium percolation (solid) process. Such nonbubbling processes are a function of surface area, a non-constant variable with respect to both time and particle size. The upper temperature limit is not dictated by chemical factors rather it is a limitation imposed by the stability of the mass flow controllers and pneumatic valves utilized in commercial deposition equipment. It must be stressed that while the achievement of an optimum vapor pres-... 

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