Other restraints

Here s is the standard uncertainty (default value is 0.02 or the first DBFS parameter). If s is negative, the absolute value is used as standard uncertainty and symmetry equivalent atoms are taken into account when deciding which atoms are connected (that can be interesting when the asymmetric unit contains fractions of a full molecule and bonds go through symmetry elements). 

The SUMP command allows to restrain the (weighted) sum of several free variables to assume a given target value (see Section 2.7 about free variables). This command can be used to refine disorders with more than two components (for details see Chapter 5) but is not limited to this application. Using the syntax 

DBFS globally changes the default standard uncertainties for the restraints CHiv, DANG, DELU, DFix, FLAT, SADI, SAME and SIMU, using the following syntax  

In parentheses are the default values, sd is the default for s in DFIX and SADI, and for si in the SAME instruction for DANG twice the value of sd is applied, sf is the default standard uncertainty for CHIV and FLAT, su is the default values for si and s2 in DELU, and ss is the default value for s in SIMU. As mentioned above, the default values for st in SIMU and ISOR, as well as s2 in SAME are calculated from the respective s or si values (unless specified differently by the 

As their name suggests, free variables can be used to refine a multitude of different parameters and facilitate the formulation of constraints and restraints. The first free variable is always the overall scale factor (osf), which is used to bring the reflections in the dataset to an absolute scale. The example in Section 4.4.3 shows the effects of incorrect scaling on the refinement. Additional free variables can be linked to the site occupancy factors (sof) of groups of disordered atoms (for details see Chapter 5), but can also be related to other atomic parameters (x, y, z, sof, U, etc.) and even interatomic distances, chiral volumes, and other parameters. 

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Table 10-56 gives values for the modulus of elasticity for nonmetals however, no specific stress-limiting criteria or methods of stress analysis are presented. Stress-strain behavior of most nonmetals differs considerably from that of metals and is less well-defined for mathematic analysis. The piping system should be designed and laid out so that flexural stresses resulting from displacement due to expansion, contraction, and other movement are minimized. This concept requires special attention to supports, terminals, and other restraints. 

The confusion which has resulted from Federal and State Air Quality laws has prevented electric utilities from making future commitments for coal. As a result, coal companies are not making the commitments to new coal mines either. Many of the new mines which are listed as planned in current forecasts ha e already been delayed due to environmental suits and other restraints. Examples are the Kaiparowitz project in Utah and a number of other Wyoming coal projects. 

There are no other restraint components which will give warning of T.C.U. seizure but the transducer clips give direct measurement which supplement... 

Printing presses shall be subject to no other restraint than liableness to legal prosecution for false facts printed and published. 

Other restraints in use of molasses include the pretreatment required to reduce mineral content and excess suspended matter, low cell yields of about 25% of the weight of molasses used, and seasonal availability of between 3 to 8 months per year. 

Dies should not close against stop blocks or other restraints. The blank must be the only stop the die sees when stamping. Safety stop blocks, used to prevent empty die halves from crashing against each other, should be designed to provide a 0.020-in. distance between die halves. 

Equation (30a) is more useful than Eq. (30b). The latter equation requires the determination of the eigenvectors of p. This is by no means a trivial task. Since the trace in Eq. (30a) is representation independent, it canbe evaluated by employing aity convenient representation satisfying the proper symmetry requirements and aity other restraints placed on the system. Note that Eq. (30b) assumes the form of a quantum average when the system has been prepared in a pure state. 

EQUILIBRIUM WITH OTHER RESTRAINTS, OTHER APPROACHES TO EQUILIBRIUM... 

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