Graphical representation of functions

Figure 3. Graphical representation of functional distance measure between two impedance spectra in a Nyquist plot. The bold connections represent examples of inner distances between impedance points...

As we saw above, one of the most convenient ways to represent the functional dependence of the variables of the system is by the use of coordinate systems. This is because each set of numbers is easily represented by a coordinate axis, and the graphs that result give an immediate visual representation of the behavior. In this section we shall explore several types of graphical representation of functions. We begin with functions that describe a linear dependence between the variables. 

In a mass spectrometer, the molecules, in the gaseous state, are ionized and fragmented. The fragments are detected as a function of their mass-to-charge ratio, m/e. The graphical representation of the ion intensity as a function of m/e makes up the mass spectrogram as illustrated In Figure 3.1. 

In the graphical representation of the integral shown above, a line represents the Mayer function f r.p between two particles and j. The coordinates are represented by open circles that are labelled, unless it is integrated over the volume of the system, when the circle representing it is blackened and the label erased. The black circle in the above graph represents an integration over the coordinates of particle 3, and is not labelled. The coefficient of is the sum of tln-ee tenns represented graphically as... 

The process and instrumentation (P I) diagram provides a graphical representation of the control configuration for the process. The P I diagrams illustrate the measurement devices that provide inputs to the control strategy, the actuators that will implement the results of the control calculations, and the function blocks that provide the control logic. 

Figure 27-10 provides a graphical representation of Eq. (27-32) showing the weight fraction of various products as a function of the chain growth parameter Ot. This figure shows that there is a particular Ot that will maximize the yield of a desired product, such as gasohne or... 

Fig. 1.10. Graphic representation of K-molecular orbitals of 1,3,5-hexatriene as combinations of 2p AOs. The sizes of the orbitals are roughly proportional to the coefficients of the Hiickel wave functions.

Serotoninergic System. Figure 1 Graphical representation of the current classification of 5-hydroxytryptamine (5-HT) receptors. Receptor subtypes represented by shaded boxes and lowercase designate receptors that have not been demonstrated to definitively function in native systems. Abbreviations 3-5r cyclic adenosine monophosphate (cAMP) phospholipase C (PLC) negative (-ve) positive (+ve)... 

Figure A2.1 is a graphical representation of the differences (790 — 768) (in Kelvins) or (f9o — t ) (in degrees Celsius) as a function of f9o (in degrees Celsius). The corrections in the region from about 500 to 1000 °C (773 to 1273 K) are seen to be substantial, varying all the way from about +0.35 to -0.20 °C.

Fig. 2.3a, b. Graphical representation of a the stable thickness of a lamella as a function of temperature T b The temperature above which a lamella of a given thickness would be unstable. Other notation in the Figure is defined in the text... 

As already described in part 2.3.2 for a set of pairs (R, a) (Fig. 3 a) the remaining geometric variables were optimized in keeping with a symmetry restriction (Fig. 3 b). The energy function E = f(R, a) obtained here in the gas phase is presented in Fig. 4 as a graphic representation of isoenergetic lines above the R-a-plane. Tire points marked by Roman numerals are minimas (educts I products III, IV, V) and the saddle... 

Figure 3.5 Graphical representation of the quantum mechanical tunnelling effect between tip and sample. The probability P of a particle with kinetic energy E tunnelling through a potential barrier cf> is shown as a function of sample-tip separation z.

Both the magnitude and the argument are functions of the frequency. The so-named Bode and Nyquist plots are nothing but graphical representations of this functional dependence. 

We know that both G(jco) and Z(G(jco)) are functions of frequency, co. We certainly would like to see the relationships graphically. There are three common graphical representations of the frequency dependence. We first describe all three methods briefly. Our introduction relies on the use the so-called Bode plots and more details will follow with respective examples. 

Figure 6.11 (Top) Plot showing chiral induction via sergeants and soldiers experiment, expressed in terms of Cotton effect (mdeg), as function of fraction of sergeants added. At higher concentrations maximum Cotton effect has been reached after addition of only 10% sergeant 22 to soldiers 20. (Bottom) Graphical representation of columns formed by 22 ( ) and 20 in hexane with 80-fold amplification of chirality and molecular dissolved nature in chloroform.

Graphical representation of a function of two variables reduced to a function of one variable by direct substitution. The unconstrained minimum is at (0,0), the center of the contours. 

The Kaplan-Meier estimates produce a step function for each group and are plotted over the lifetime of the animals. Planned, accidentally killed, and lost animals are censored. Moribund deaths are considered to be treatment related. A graphical representation of Kaplan-Meier estimates provide excellent interpretation of survival adjusted data except in the cases where the curves cross between two or more groups. When the curves cross and change direction, no meaningful interpretation of the data can be made by any statistical method because proportional odds characteristic is totally lost over time. This would be a rare case where treatment initially produces more tumor or death and then, due to repair or other mechanisms, becomes beneficial. 

Later, in Figure 3-22, we give a graphical representation of the principles of the truncated Taylor series expansion for a one-parameter function. 

Figure 5.13, which is a graphical representation of the ZND theory, shows the variation of the important physical parameters as a function of spatial... 

Graphic representation of cumulative frequency distribution of selected effects as a function of concentration is also prepared where ratio of median effective concentration is considered for drug selectivity using different endpoints. 

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