C2 of A3 (degrees) and a dihedral angle with the fluorine atom of 180.0. All parameters given lettered variable names (LI, A1 ete) will be optimized the dihedral angles are given explieitly as these are fixed by synnnetry (the moleeiile is planar). Simple eonstraints ean be imposed by removing parameters from the optimization list. [Pg.2343]

In order to Introduce thermal effects into the theory, the material balance equations developed in this chapter must be supplemented by a further equation representing the condition of enthalpy balance. This matches the extra dependent variable, namely temperature. Care must also be taken to account properly for the temperature dependence of certain parameters In... [Pg.156]

In the extreme case where both solvents B and S are completely insoluble, then there are only four variables, namely, T, P, and and the more familiar equilibrium curve illustrated in Figure 44 can be constructed. [Pg.322]

The followingset of commands shows us the variable names used to this point in the notebookandthattheyareindeedremovedbytheRemovecommand. [Pg.318]

This review is structured as follows. In the next section we present the theory for adsorbates that remain in quasi-equilibrium throughout the desorption process, in which case a few macroscopic variables, namely the partial coverages 0, and their rate equations are needed. We introduce the lattice gas model and discuss results ranging from non-interacting adsorbates to systems with multiple interactions, treated essentially exactly with the transfer matrix method, in Sec. II. Examples of the accuracy possible in the modehng of experimental data using this theory, from our own work, are presented for such diverse systems as multilayers of alkali metals on metals, competitive desorption of tellurium from tungsten, and dissociative... [Pg.440]

The most widely used method for fitting a straight line to integrated rate equations is by linear least-squares regression. These equations have only two variables, namely, a concentration or concentration ratio and a time, but we will develop a more general relationship for use later in the book. [Pg.41]

When only one parameter follows a variable name, that variable is held fixed throughout the entire scan. When all three parameters are included, that variable will be allowed to vary during the scan. Its initial value will be set to initial-value this value will increase by increment-size at each of number-of-points subsequent points. [Pg.171]

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). ... [Pg.291]

Integer—Variable names starting with I-N, unless otherwise dedaied. [Pg.114]

Type declaration—Specifies data type to be represented by a variable name (overrides defaults), e.g.,... [Pg.115]

Equivalence statement—Assigns two or more variable names to the same memory location... [Pg.116]

In general, because the noise in the concentration data is independent from the spectral noise, each optimum factor, W, will lie at some angle to the plane that contains the spectral data. But we can find the projection of each W, onto the plane containing the spectral data. These projections are called the spectral factors, or spectral loadings. They are usually assigned to the variable named P. Each spectral factor P, is usually organized as a row vector. [Pg.140]

We conclude this section by deriving an important property of jointly gaussian random variables namely, the fact that a necessary and sufficient condition for a group of jointly gaussian random variables 9i>- >< to be statistically independent is that E[cpjCpk] = j k. Stated in other words, linearly independent (uncorrelated),46 gaussian random variables are statistically independent. This statement is not necessarily true for non-gaussian random variables. [Pg.161]

Thus, the self information of a sequence of N symbols from a discrete memoryless source is the sum of N independent random variables, namely the self informations of the individual symbols. An immediate consequence of this is that the entropy of the sequence, ff(Ujr), is the average value of a sum of random variables so that... [Pg.198]

The random variable p with the probability density shown above is the sum of 2 independent random variables, namely the input a> with variance Aa2 and the noise with variance a2. Thus, Pr( y) satisfies... [Pg.243]

Whenever one property is measured as a function of another, the question arises of which model should be chosen to relate the two. By far the most common model function is the linear one that is, the dependent variable y is defined as a linear combination containing two adjustable coefficients and X, the independent variable, namely. [Pg.94]

All setup data and results are stored in Data Resource Files rather than standard sequential or random access files. This has turned out to be a key feature contributing to a flexible and low maintenance system. These are ASCII files which can be typed to the screen, printed, or edited with a word processor. They contain information organized by variable name, value, and units. The following is an example of a data resource file ... [Pg.13]

In the snail preceedlng example it can be seen that each data set consists of three fields enclosed by square brackets. The first field is the variable name, the second is the value for that variable, and the third is an optional units field. All fields are read as string variables and the value field is changed to a numeric variable when necessary. The order in which the data sets appear is not Important, nor is their position in... [Pg.15]

The flexibility of data resource files also facilitate dynamic storage so that the user can generate variable names and values during program operation. This is done in the Identify section in which the user can save and later access data under improvised names. [Pg.15]

This information is saved under any name desired by the user. It is thereafter accessible through the report generator. If the user frequently saves data, the variable names can be permanently stored and accessed from the identify setup data resource file. [Pg.18]

The table below illustrates these issues by comparing how a recursive subroutine must handle data which is available from a database, such as the cost of a raw material, data that is calculated for the formulated product, such as PBR, and data for intermediate products. (The variable names shown in the table are part of the example procedure given in the appendix.) Compare with the previous table for a non-recursive modelling procedure s data structure. [Pg.58]

Source and use of data within recursive modelling procedure Examples of variable names shown in ITALICS ... [Pg.58]

Data is passed between levels of recursive procedures in variables cited in the CALL statement for the procedure. As indicated in the section on programming issues, care must be taken in assigning names to the data variables so that values returning from a recursive CALL do not overwrite the values in variables within the calling procedure. Note the difference between the variable names in the SUBROUTINE statement of... [Pg.59]

The variable names listed below are used as ISIM system variables and can not be used for any other purpose. [Pg.674]

A variable named in a VAL command does not appear in the symbol table. [Pg.687]

For illustration, we consider some examples involving only one variable, namely, the cartesian coordinate x, for which w x) = 1. An operator that results in multiplying by a real function /(x) is hermitian, since in this case fix) = fix) and equation (3.8) is an identity. Likewise, the momentum operator p = (i)/i)(d/dx), which was introduced in Section 2.3, is hermitian since... [Pg.70]

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