Variable nested

I don t claim to have done this yet. But I do believe that I have stumbled upon an intellectual avenue that could be followed to achieve this understanding. The key lies in cycles of temporal variables nested in hierarchical structures, which generate various kinds of fractal relationships unfolding toward often surprising kinds of closure. 

The NSS concept corresponds to an operator attached to an arbitrary number of nested sums. In other words, a NSS represents a set of summation symbols where the number of them can be variable. In a general notation one can write a NSS as E (j=i,f,s,L) where the meaning of this convention corresponds to perform all the sums involved in the generation of all the possible values of the index vector j under the fulfillment of the set of logical expressions collected in the components of the vector L. The elements of the vector j have the following limits ... 

In standard high level language programming the dimension of the NSS n, signals the number of nested do loops which are necessary to reproduce the structure in a computational environment. But the mathematical usefulness of this entity can be easily recognized when the particular characteristic of this symbolic unit is analyzed the involved vector parameters could be chosen with arbitrary and variable dimensions. There are many scientific and mathematical formulae which will benefit of this property, when written in a paper or computationally implemented. 

Perhaps this is valid SAS code, but there is no code documentation to tell the user what any of those macro variables or macro calls actually do. Upon further investigation, we may find that the %MAKECOD macro calls six other SAS macros in a nested fashion. Also, is a %RUN really necessary, or has the programmer developed one too many macros ... 

A complete list of the reaction conditions tested for this response surface design can be found in [76], The center point reaction condition was repeated six times. This was done to measure the variability of the reaction system. Also, the space velocity is kept constant, as it was the least important factor predicted by screening design, for all the reaction conditions. The purpose of this nested response surface design was to develop an empirical model in the form of Eqn (5) to relate the five reaction condition variables and the three catalyst composition variables to the observed catalytic performance. 

Fig. 8.6. Representation of 14 multivariately characterized objects in a two-dimensional space of variables where the clusters are connected into four groups (a) and classified into two differently chosen groups (b,c), respectively d shows a nested clustering of B within A... 

Some recent applications have benefited from advances in computing and computational techniques. Steady-state simulation is being used off-line for process analysis, design, and retrofit process simulators can model flow sheets with up to about a million equations by employing nested procedures. Other applications have resulted in great economic benefits these include on-line real-time optimization models for data reconciliation and parameter estimation followed by optimal adjustment of operating conditions. Models of up to 500,000 variables have been used on a refinery-wide basis. 

Filling Conveyor. Filling line transfer system is an automatic, nonsynchronus, variable-speed drive unit complete with filling pallets and nests for the five different munitions filled and closed on the line. This unique system moves work pallets from station to station and provides accurate shot pin alignment for the work piece as various operations are performed, and features automatic acceleration and deceleration of the filling pallets. Operation is unusually smooth, quiet and safe. 

They think locally and act locally, but their collective action produces global behavior. Take the relationship between foraging and colony size. Harvester ants constantly adjust the number of ants actively foraging for food, based on a number of variables overall colony size (and thus mouths needed to be fed) amount of food stored in the nest amount of food available in the surrounding area even the presence of other colonies... 

D Monte Carlo A kind of nested Monte Carlo simulation in which distributions representing both incertitude and variability are combined together. Typically, the outer loop selects random values for the parameters specifying the distributions used in an inner loop to represent variability. 

As already discussed in Chapter 1, this kind of mixed valence salt becomes conductive due to the transfer of one electron from two BEDT-TTF molecules to the anion layers. However, at the surface, the charge can become unbalanced, resulting is an incomplete CT. This leads to differentiated surface vs. bulk nesting vectors and to the existence of surface CDWs (Ishida et al, 1999). The Peierls transition has also been observed on the a -planes of single crystals of TTF-TCNQ with a variable temperature STM (Wang et al, 2003) and will be discussed in Section 6.1. 

Notice that two values are displayed in the Simulation Status window. The bottom line changes quickly and is the main sweep variable, Vs. The line second to the bottom is the nested sweep variable, BV. Notice that for each value of BV, Vs is swept from -15 to +15. Logically, the primary sweep loop executes inside the secondary sweep loop. That is, BV is set to 1 and Vs is swept from -15 to +15. Then BV is set to 2, and Vs is swept from —15 to +15. Then BV is set to 3, and Vs is swept from -15 to +15, and so on. When the analysis is finished, Probe will run. Add the trace V(VL) (press the INSERT key) ... 

The simulation status window indicates the progress of each loop. Notice that for each value of the nested variable, the main variable is swept from 0 to 15 volts. When the simulation is finished, the Probe window will display a blank window. I W N switch Probe to occupy the entire window. Press the INSERT key and add the trace IC (Ql) ... 

For each value of VGS, we want to sweep VDS from 0 to 15 volts. Thus, we want VGS to be our nested sweep variable and VDS to be our main sweep variable. Note also that for jFETs we must sweep VGS from zero to a negative value. Fill in the DC Sweep and Secondary Sweep dialog boxes as shown ... 

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