Intermediate variable

The values of the intermediate variables a, b, c, etc. have no fundamental significance, of course, and are used simply to link experimental process output X to the corresponding input y. 

Many engineering problems involve several parameters, that impede the elaboration of the pi space. Fortunately, in some cases, a closer look at a problem (or previous experience) facilitates reduction of the number of physical quantities in the relevance list. This is the case when some relevant variables affect the process by way of a so-called intermediate quantity. Assuming that this intermediate variable can be measured experimentally, it should be included in the problem relevance list, if this facilitates the removal of more than one variable from the list. 

Here C is another integration constant to be determined from matching with the transition layer solution (5.5.20). This matching may be achieved, following the standard prescription of matched asymptotics [15], by introducing the intermediate variable... 

This mapping is to be combined with Eqs. (13.21), (13.22) fixing the uncritical manifold. A compact form results by introducing an intermediate variable w... 

Hip-flop inference rule is simple If a variable is assigned a value under the control of a clock edge, a flip-flop is generated an exception to this rule is when a variable is assigned and used only locally within an always statement as an intermediate variable. 

Because of the fact that the Nusselt number and the Peclet number are not simply expressed in terms of the particle diameter it is convenient to use them as intermediate variables in the calculation. Since the mass velocity is fixed, the Reynolds number and the Nusselt number are determined by the particle diameter. The calculation proceeds by finding the values of r2 from selected values of dp, as determined from ki, and fc2 separately. By inverse interpolation, the value of dp that makes the two values of r2 equal is found. 

Completion of a solution by matched asymptotic expansions entails employing matching conditions. Although there are many ways to effect matching, the most infallible approach currently available is to investigate a parametric limit in an intermediate variable [35]. Thus we consider oo with f]t held fixed, where t] = s(p)t]/t(p) = ( — o)/KPX with t(p) 0 and KP)/s(P) 00 in the limit. The general matching condition is then written as... 

In electrocatalysis, notable cases of formation of strongly bound species that are not, however, the kinetically involved intermediates in the main reaction pathway arise in the electrochemical oxidations of HCOOH, HCHO, and CH3OH at Pt anodes for those reagents, a self-poisoning intermediate, variably identified as chemisorbed CO, in bridged or linear double bonding to the electrode, or the species- C—OH, is involved (43) this species is not a principal kinetically involved intermediate in, for example, HCOOH oxidation, which proceeds at unpoisoned sites by the mechanism discussed in Section V,B,3. 

Identify all of the variables in Figure 51 as either input or output variables. (Do not include the intermediate variables F3, C 3, and Cg3 associated with stream... 

An intermediate variable in defining mixing rules for pressure reducing parameter. Heat flux. 

Appendices. Appendices contain details needed to support your results and to be used by people who may continue your work. Make it easy for them by organizing the material under subtitles or sub-appendices listed in the table of contents. Use enough words in appendices to define units and manipulations, but do not worry about smooth text with introductions and transitions. Include data sheets, sample calculations including error propagation, tables of intermediate variables in the calculations, working plots, calibration curves, and all the figures and tables that you did not include in the main body. 

The coordination numbers for the unknowns, N , are then calculated as N = B /S. The final values of the unknown coordination numbers are listed in Table I and also in Table IV with the values of intermediate variables B , S and B . 

In use, the left-hand sides of the three lines are used to find the value of the intermediate variable X corresponding to given A and T. The right-hand sides then give the Doppler width AA in A, for this value of x and the given M. 

The five coordinate spirophosphoranes have played an important role with respect to understanding the stereochemistry of four coordinate phosphorus reactions which proceed via phos-phorane intermediates. Variable temperature NMR studies have established the apicophilicities of a wide range of groups (i.e. relative preferences of a series of groups to occupy an apical position rather than an equatorial position of a trigonal bipyramidal (t.b.p.) conformation of a phosphorane). The spiro ring system has been used to stabilize transient reaction intermediates of acyclic compounds, for example hydrolysis intermediates such as hydroxyphosphoranes. 

Therefore, Overall = 3+2+1 - 6 intermediate variables (not including x04 since that s going to the dryer) = 0... 

This is all that is required from the UNIFAC tables. Below we summarize the results for the various intermediate variables (i = 1 refers to ethanol, i = 2 refers to acetonitrile) ... 

Step 3 Decomposition into component parts. It has been demonstrated that a first-order lag is a reasonable approximation for the dynamics of a distillation column (Skogestad, 1987). Thus, the LSF configuration is decomposed into two component parts, one for each column. Four intermediate variables are identified to model the information transfer between the component parts Xbh B, Tg, and Qch (= Qrl)- Note that both Tg and Qch are needed for the energy balance in the reboiler because partial vaporization occurs. 

The success of the matching is due to the existence of the overlapping region. In this overlapping region, one could define an intermediate variable as... 

This means that the overlapping region lies between the boundary layer (which has a thickness of order of e) and the outer region (which has a thickness of order of unity). In this overlapping region, the intermediate variable is of order of unity. Now, we write the outer variable x and the inner variable x in terms of this intermediate variable... 

Note, we previously obtained both the inner and the outer solutions for the zero order solutions. Hence, the composite solution obtained has an error of order of e. To find a composite solution, which has an error of the order of we need to find the first order inner solution, as we did for the outer solution (Eq. 6.61), and then we make use of the matching principle using the intermediate variable of Eq. 6.82 to achieve our goal of composite solution having an error of e. ... 

To solve for the constant Cj, we resort to the matching principle and utilize the intermediate variable Xg. The itmer and outer variables are related to this intermediate variable as shown in Eqs. 6.85 and 6.86. Thus, in the intermediate region, the inner solution (Eq. 6.89) and the outer solution (Eq. 6.59) behave like... 

We have shown the basic steps for the method of matched asymptotic expansion. The matching principle is based on the use of the overlapping region and an intermediate variable in that region. In what follows is another simple method of matching for a class of problems, which takes the following form... 

Between Parallel Plates. An exact solution of Eq. 11 can be written [7] for a pair of plates separated by a distance 2H and each held at a potential The origin z = 0 is chosen on one of the plates so that the second plate is located at z = 2H. It is convenient to introduce the intermediate variables k = exp( Z and O... 

Alpha du Centaur does not place the intermediate variables that result from localizing global operations in the same index space. This can be done with a re-indexing transformation after the localization step. The localization procedure could also be adapted so that this step is not necessary, as in the case of the localization of broadcast operations. 

In contrast, the output of a controlled source is algebraically related to its input. If the latter is not an output of an independent source or an energy store with integral causality, then it can be expressed by means of such outputs by back propagation of causal paths in the junction structure and by eliminating intermediate variables. 

Note, that if there are causal paths between resistor ports then impUcit, algebraic equations will result. This means, that the output of the resistor port at one end of the causal path cannot be computed without knowing the output of the resistive port at the other end of the causal path. In this case, intermediate variables cannot be eliminated and expressed by system inputs and state variables by back propagation along causal paths. The mathematical model will be of the form of a DAE system that can be transformed into an ODE system if the system of coupled algebraic equations can be solved symbolically. 

Using this form for calculating e removes the errors related to the storage of intermediate variables. 

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