Practical feasibility region

This equation means that when there is a free energy difference of a few fcs T the probability P( ) is reduced considerably, that is, those conformations with large A( ) are sampled very rarely. This is a very important observation in terms of numerical efficiency. At the transition region for example, the free energy is maximum and typically very few sample points are obtained during the course of molecular dynamics simulation. In turn this results in very large statistical errors. Those errors can only be reduced by increasing the simulation time, sometimes beyond what is practically feasible. 

A cast film of 28 also responded to the chirality of liquid and solid chiral amines, and exhibited an ICD in the UV-visible region. The observed Cotton effect patterns were similar to those of 28 induced by the chiral amines in solution [147]. These methods are more convenient and practically feasible to sense the chirality of chiral amines than the solution method, and may be applicable to other dynamic helical polyacetylenes. 

As seen above, the objective function is modified in a way that it increases quite significantly as the solution approaches the constraints but remains practically unchanged inside the feasible region. Inside the feasible region, i(ki) is small and results in a small contribution to the main diagonal element of matrix A. Consequently, will not be affected significantly. If on the other hand, the... 

The concept of convexity is fundamental in optimization. Many practical problems possess this property, which generally makes them easier to solve both in theory and practice. If the objective function in the optimization problem (1) and the feasible region are both convex, then any local solution of the problem is in fact a global solution. The term convex programming is used to describe a special case of the general constrained optimization problem in which ... 

In principle, the Synapt has sufficient activation/ dissociation regions to perform up to MS, although typically up to MS is practically feasible. 

Often, the space of practically feasible mixtures is smaller than the entire set of Xi, X2,...,Xp satisfying (4-15). (For example, in many contexts, pure mixtures do not produce viable product. Concrete made using only water and no sand or cement obviously is a useless building product. One common type of constraint on the proportions Xi, X2,...,Xp that produces quite simple experimental regions is that of lower bounds on one or more of the individual proportions. Cornell, for example, discusses a situation where the effectiveness in grease stain removal of a p = 3 bleach mixture was studied and past experience with the product indicated that the proportions by weight of bromine, Xi, of powder, X2, and of HCl, X3, needed to satisfy the following constraints ... 

Deuterated compounds have recently aroused interest not only for the laboratory use but also for practical application. Deuterium-labeled polymers are regarded as feasible materials for wave guides in optical communication, because of their transparency in the 500-800 nm infrared region [20], For this purpose greater distribution of deuterium atoms on the polymer is preferable. The preparation of... 

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