Graphics smooths

Fig. 16. Graphically smoothed data for calculated ternary diffusion coefficients in a system with a uniform concentration of dextran T500 (Hw 500,000) with an imposed 5 kg m-3 concentration gradient of PVP 360 the dextran concentration is varied...

The low temperature heat capacity was taken from Westrum (jJL ). The intermediate heat capacity (300-1650 C) was obtained from McDonald and Stull (1 ). The high temperature Cp was taken from Prophet and Stull (13). The heat capacities in the three temperature ranges were plotted and then graphically smoothed. Dworkin et al. (J ) also reported that heat capacity (50-300 K) not employed in this table. 

The heat capacity employed In this table was obtained by graphically smoothing the summation of the heat capacities for B20g and PbO. 

The enthalpy measurements of Smith (3) in the range 298 to 973 K were graphically smoothed and used to determine Cp. Above this range Cp is extrapolated. 

The number of discrete points of /cicc( ) determines the resolution of the chirality code is a smoothing factor which in practice controls the width of the peaks obtained by a graphical representation versus u. An example of a chir-... 

Obviously the regularity expressed in the qualitative form (a) is far less informative than any one of the quantitative presentations, (b), (c), or (d). The relative merits of the expressions (b), (c), and (d) depend upon the use. Table l-II tells in most detail exactly how much is known about the pressure-volume behavior of oxygen gas (from this experiment). In the graphical presentation of Figure 1-8 the trend of the data is shown by the smooth curve drawn to pass near as many points as possible. Uncertainties caused... 

We have found that data interpretation other than simple plotting from texture studies requires a sophisticated array of software tools. These include least squares curve resolving, non-linear least squares fitting, 2-dimensional data smoothing, numerical quadrature, and high-speed interactive graphics, to mention only a few. 

In experimental kinetics studies one measures (directly, or indirectly) the concentration of one or more of the reactant and/or product species as a function of time. If these concentrations are plotted against time, smooth curves should be obtained. For constant volume systems the reaction rate may be obtained by graphical or numerical differentiation of the data. For variable volume systems, additional numerical manipulations are necessary, but the process of determining the reaction rate still involves differentiation of some form of the data. For example,... 

Table 11,1.1 contains a workup of the data in terms of the above analysis. In the more general case one should be sure to use appropriate averaging techniques or graphical integration to determine both F(t) and T. When there is an abundance of data, plot it, draw a smooth curve, and integrate graphically instead of using the strictly numerical procedure employed above. 

In addition to the Premium Excel Solver and Optquest, there are many other software systems for constrained global optimization see Pinter (1996b), Horst and Pardalos (1995), and Pinter (1999) for further information. Perhaps the most widely used of these is LGO (Pinter, 1999), (Pinter, 2000), which is intended for smooth problems with continuous variables. It is available as an interactive development environment with a graphical user interface under Microsoft Windows, or as a callable library, which can be invoked from an application written by the user in... 

The graphical method has the advantage of smoothing the data if the other methods are used it may be necessary to smooth the data first. Application of the difference method directly to the data in the above table will show good agreement in the lower part of the range but oscillations will be observed towards the top of the range. 

SWV experiments are usually performed on stationary solid electrodes or static merciuy drop electrodes. The response consists of discrete current-potential points separated by the potential increment AE [1,20-23]. Hence, AE determines the apparent scan rate, which is defined as AE/t, and the density of information in the response, which is a number of current-potential points within a certain potential range. The currents increase proportionally to the apparent scan rate. For better graphical presentation, the points can be interconnected, but the fine between two points has no physical significance, as there is no theoretical reason to interpolate any mathematical function between two experimentally determined current-potential points. The currents measured with smaller A are smaller than the values predicted by the interpolation between two points measured with bigger AE [3]. Frequently, the response is distorted by electronic noise and a smoothing procedure is necessary for its correct interpretation. In this case, it is better if AE is as small as possible. By smoothing, the set of discrete points is transformed into a continuous current-potential curve. Care should be taken that the smoothing procedttre does not distort the square-wave response. 

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