Design space exact

The DX6 program generates most of the symmetric designs, Taguchi orthogonal designs, and exact D-optimal designs for process, mixture, and process+mixture combined spaces. DX6 can also handle constrained mixtures. It can also produce the respective two- and three-dimensional-contour Descartes and mixture plots. There is considerable flexibility provided in model construction and their modification. 

The design space is explored using either an exact or a heuristic search of the assignments, using cost criteria that include area, interconnection, and delay. 

Using the conflict-free allocation as guideline, a set of resource allocations ai,...,afc is specified either by the user manually or by the system automatically. Hebe supports both exact and heuristic strategies to explore the design space they are summarized below. 

For some designs, exact exploration of the design space may be prohibitive due to its size. Hebe also supports heuristic strategies to explore the design space, where the resulting implementation is no longer guaranteed to be optimal. 

It applies for both formulations above that the expansion in principle contains an infinite number of terms. The convergence to a few lowest order terms relies on the ability to orderly separate influences of the dominant rf irradiation terms (through a suitable interaction frame) from the less dominant internal terms of the Hamiltonian. In principle, this may be overcome using the spectral theorem (or the Caley-Hamilton theorem [57]) providing a closed (i.e., exact) solution to the Baker-Campbell-Hausdorf problem with all dependencies included in n terms where n designates the dimension of the Hilbert-space matrix representation (e.g., 2 for a single spin-1/2, 4 for a two-spin-1/2 system) [58, 59]. 

Although each stack added to a series network would improve the system s efficiency, the incremental benefit obtained with each additional stack diminishes. A finite number of stacks could adequately, but not exactly, approach a reversible process. In a practical network, the number of stacks would be limited by economic, space, and design constraints. 

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