Description of the algorithm

The RG algorithm for hard-core chains is described in detail in ref. [111]. Here we discuss extensions of this algorithm for continuous potentials. In what follows we describe the RG scheme for canonical MC in which M chains of length N cire sampled. It is straightforward to extend this algorithm to other ensembles [29,32]. 

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The next section will highlight these features of the branch-and-bound framework, within the context of the flowshop scheduling problem. Then we will give an abstract description of the algorithm, followed by the... 

A brief description of the algorithm (as usual, everything is based on Y=CA) ... 

Then, one applies the procedure smoothing the fields of F in order to ensure stability of calculations. The detailed description of the algorithm can be found... 

Frequency domain resampling is attractive in the present context because the timescaling and the resampling operations can be performed in a single phase-vocoder analysis, thus reducing the computational cost. The interested reader may consult [Moulines and Laroche, 1995] for a complete description of the algorithm. 

The estimation of parameters D, b, s, a, a2 in model (11) - (17) of the hydrogen transfer in stainless steel was made by the identification algorithm based on the Fourier series. The detailed description of the algorithm is in [3, 4]. The experimental data got by the concentration pulses method were used for identification. In addition the estimations of s, X = Db1/2 were received by isotherms for the permeability method [3, 4]. Below we describe the identification algorithm based on the Fourier series. 

Figure 1.3 Topological equivalence of symmetry-related atoms used by CSDSymmetry for the first step of automated symmetry detection. A full description of the algorithm used to partition the groups is given in Cole et al. [29]...

As mentioned, the proposed methodology will be illustrated by the systematic derivation of a variety of regular processor arrays implementing 1-D convolution. The initial description of the algorithm in nested loop form [8] can be represented as follows ... 

Figure 4 shows a screen dump that gives a flavor of Amical at work. The right-hand window shows a Vhdl description of the algorithm being synthesized. The top window contains the transition table generated by the scheduler. The middle window shows the data-path, as synthesized by Amical. The bottom window provides information on the current status of Amical. We make use of concepts similar to those used in CORAL II [1] in order to link the behavior and structure. In this way, Amical is able to maintain the coherence... 

A description more suitable for formal verification is a combination of boolean equations and state registers (see the BCD recognizer example in section 4). To derive such a description from layout is not a trivial task, however, and is the topic of this section. A more extensive description of the algorithms described can be found elsewhere [3]. 

As one can see from the description of the algorithm for the P M method, it is very close to the one presented for the PME method in the previous section. The PME differs in the final steps, in which the potential is first interpolated onto the particles and the resulting potential is differentiated with respect to the particle positions to give the electric field and forces. The PME uses half as many FFTs as P M it is more efficient where the cost of the FFT becomes an issue, such as in the parallel implementations. The number of FFT transformations in the P M method can be reduced by first... 

The CSDW calculations described above require substantial computer resources. A description of the algorithms and structure of the five programs that comprise the CSDW suite can be found in Ref. [16], which also reports the effect of basis set variation on CPU times for CDC 76(X), CDC Cyber 176, CDC Cyber 205, Cray X-MP and Cray-2 computers. 

An illustration of the integrated circuit design process is shown in Figure 1-1. At the top, a behavioral description of the algorithm to be... 

The Behavioral Domain describes the behavior, or functionality, of the design, either as a complete, program-like description, or as set of behavioral descriptions. For example, at the Algorithmic level, the Behavioral Domain might be represented by a description of the algorithm to be implemented. Variables and the operations on them... 

There are many algorithms that are able to solve this kind of problems (see, e.g., Liu and Der Kiureghian 1991). The most common algorithm used in structural reliability is the one developed by Rackwitz and Flessler (1978). A comprehensive description of the algorithm and relevant examples can be found in Pinto et al. (2007), while a first review of the efficiency of the available algorithms was presented in Liu and Der Kiureghian (1991). Once P is determined, the probability of failure can be approximated by Eq. 8. 

The main algorithmic contributions of this research are described in the next four chapters. Ch ter 6 presents the relative scheduling formulation that includes description of the algorithms and analysis of their prqterties. Chapto 7 describes conflict resolution under timing constraints. Chapter 8 describes the generation of the control circuit from a relative schedule. Chapter 9 describes the control resynchronization optimization that reduces the area of the control implementation under timing and synchronization constraints. 

Now we return to the description of the algorithm. If in the first part available capacity is not allocated entirely, we come to this second part to consider the effect of the aggregated action Because we have taken already some decisions about the production in the first part, we do not have to consider all possible values for If in the first part capacity has been allocated m k different types and the remaining available capacity is C i, then the lower value we have to consider for a, written as Umiii is the sum of the actions taken in the first part ... 

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