Strong form weight function

The weight function is identical in the Galerkin and tau methods (i.e. weight function is set equal to the basis function in the polynomial trial function expansion, see (12.405)-(12.408)). The essential difference between the Galerkin and the tau methods is the treatment of the boundary conditions (strong form). In the tau method, the boundary conditions are enforced as additional equations and in order to get a system of equations where the number of unknowns is identical to the number of equations, the equation system has to be relaxed such that n residual equations are replaced by the n boundary conditions. In the Galerkin method, some linear combinations of the polynomials that fulfill the boundary conditions must be performed. 

When concentrated sulphuric acid alone was used as the initiator, the polymerization was found to follow a different path. It is well known that Bronsted acids can function as cationic/pseudocationic initiators in the oligomerization of olifins [174]. If the counter ion has a higher nucleophilicity as it forms cation-conjugate pairs, which collapse rapidly, polymerization will not take place. As the counter ion in the case of sulphuric acid is not very strong compared to the cation, oligomerization can take place, but may not be to a very high molecular weight. This, however, depends on the nature of the... 

This area is a development in the usage of NDDO models that emphasizes their utility for large-scale problems. Structure-activity relationships (SARs) are widely used in the pharmaceutical industry to understand how the various features of biologically active molecules contribute to their activity. SARs typically take the form of equations, often linear equations, that quantify activity as a function of variables associated with the molecules. The molecular variables could include, for instance, molecular weight, dipole moment, hydrophobic surface area, octanol-water partition coefficient, vapor pressure, various descriptors associated with molecular geometry, etc. For example, Cramer, Famini, and Lowrey (1993) found a strong correlation (r = 0.958) between various computed properties for 44 alkylammonium ions and their ability to act as acetylcholinesterase inhibitors according to the equation... 

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