Lumping notation

The total number of bits set on A is a + c. and the total number of bits set on B is b + c. These totals form the basis of an alternative notation that uses a instead of a + c, and b instead oib + c [16]. This notation, however, lumps together similarity and dissimilarity components" - a disadvantage when interpreting a similarity measure. 

Be that as it may, in either case (lumping or overall) the procedure can be followed regardless of whether the system is discrete or continuous. Lumping a continuous system onto a finite dimensional subspace can give good approximations or even be exact in some cases. Our notation is summarized in Table I. 

We will assume that all the tubes behave in a similar fashion, and so may lump them together for the purposes of calculation. Let us introduce the following subscripts t to denote tube fluid, tw to denote tube wall and twt to denote a transfer from tube wall to tube fluid. The inside diameter of the tube will be written D,i (the subscripts denoting tube and inside ). Using this notation, the heat flux per unit length, from tube wall to tube fluid is the product of the heat transfer coefficient, ATn,-, the temperature difference, (Tn,. — T,) and the tube-wall surface area per unit length, N,nD,j, where N, is the number of tubes ... 

Lumping of single hydrocarbons to pseudo-components (PC, for S3unbols see notation) is a possible way to simplify and to manage the obscure reaction network of complex multi-component systems. As expected, the selective n-heptane cracking was... 

Fig. 14.4. Reentry distribution at the undeformed state of polyethylene as a function of reentry orientation at two temperatures light bar 350K, dark bar 450K. The last entry rest lumps together all the remaining loops not explicitly considered in the other sets. The shortest reentry vector length in a particular direction increases from left to right. See text for notation. Reproduced from [29] with written permission from ACS Publications...

The average collision density in an absorbing lump imbedded in an absorbing moderator e qpressed in the notation of Nordheim is... 

Metabolic networks can be analysed using 2D [ C, H] COSY (NMR) measurements of C-labeled metabolites. A framework is presented whereby the steady state reaction rates are deduced from conventional isotopomer balances. This model is reduced by removing redundant nodes and lumping equilibrium pools. Conversion of the balances to the recently introduced bondomer notation further reduces the complexity. When the reduction approaches are applied to the glycolysis and pentose phosphate pathway, the number of equations is reduced by a factor of three without loss of information. 

Here the several kinetic parameters vere lumped into the constants Kt, K, and K according to Eqs. (71)-(73), to allow for a more concise notation. 

These are to be added to V(q). The otj take the place here of the Morse steepness parameter. Because in the empirical approach one does not compute the corresponding hindered rotor eigenvalues exactly but rather by interpolation, one lumps all the Uj together into one a and uses the interpolation formula (110) for channel eigenvalues (see Figure 3 for the notation). 

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