Minimization comparison

Nanias M et al (2005) Protein structure prediction with the UNRES fOTce-field using replica-exchange Monte Carlo-with-minimization comparison with MCM, CSA, and CFMC. J Comput Chem 26 1472-1486... 

In many cases, the methods used to solve identification problems are based on an iterative minimization of some performance criterion measuring the dissimilarity between the experimental and the synthetic data (generated by the current estimate of the direct model). In our case, direct quantitative comparison of two Bscan images at the pixels level is a very difficult task and involves the solution of a very difficult optimization problem, which can be also ill-behaved. Moreover, it would lead to a tremendous amount of computational burden. Segmented Bscan images may be used as concentrated representations of the useful... 

For sensitivity detection the standard defectometers were used. Relative sensitivity comparison at steel objects radiographic control by radiation with energy of 25 and 45 MeV shows that sensitivity minimum for 45 MeV energy is very displaced towards the big thickness and has not yet reached its minimal meaning at 500mm thickness. 

A systematic comparison of two sets of data requires a numerical evaluation of their likeliness. TOF-SARS and SARIS produce one- and two-dhnensional data plots, respectively. Comparison of sunulated and experimental data is accomplished by calculating a one- or two-dimensional reliability (R) factor [33], respectively, based on the R-factors developed for FEED [34]. The R-factor between tire experimental and simulated data is minimized by means of a multiparameter simplex method [33]. 

By using this approach, it is possible to calculate vibrational state-selected cross-sections from minimal END trajectories obtained with a classical description of the nuclei. We have studied vibrationally excited H2(v) molecules produced in collisions with 30-eV protons [42,43]. The relevant experiments were performed by Toennies et al. [46] with comparisons to theoretical studies using the trajectory surface hopping model [11,47] fTSHM). This system has also stimulated a quantum mechanical study [48] using diatomics-in-molecule (DIM) surfaces [49] and invoicing the infinite-onler sudden approximation (lOSA). 

The inequality like (1.59) is called a variational inequality. It was obtained from a minimization problem of the functional J over the set K. In the sequel we will look more attentively at a connection between a minimization problem and a variational inequality. Now we want to underline one essential point. We see that the problem (1.58) is more general in comparison with the minimization problem on the whole space V. It is well known that the necessary condition in the last problem coincides with the Euler equation. The variational inequality (1.59) generalizes the Euler equation. Moreover, ior K = V the Euler equation follows from (1.59). To obtain it we take U = Uq +u and substitute in (1.59) with an arbitrary element u gV. It gives... 

Concern for personnel exposure to hydrazine has led to several innovations in packaging to minimize direct contact with hydrazine, eg, Olin s E-Z dmm systems. Carbohydrazide was introduced into this market for the same reason it is a soHd derivative of hydrazine, considered safer to handle because of its low vapor pressure. It hydrolyzes to release free hydrazine at elevated temperatures in the boiler. It is, however, fairly expensive and contributes to dissolved soHds (carbonates) in the water (193). In field tests, catalyzed hydrazine outperformed both hydrazine and carbohydrazide when the feedwater oxygen and iron levels were critical (194). A pubUshed comparison is available (195) of these and other proposed oxygen scavengers, eg, diethyUiydroxylarnine, ydroquinone, methyethylketoxime, and isoascorbic acid. 

Figure 5 A comparison of steepest descent (SD) minimization and conjugated gradients (CG) minimization of the same protein.

Hartree-Fock MO approach, the minimization of energy should provide the most accurate description of the electronic field. The mathematical problem is to define each of the terms, with being the most challenging. The formulation carmot be done exactly, but various approaches have been developed and calibrated by comparison with experimental data. The methods used most frequently by chemists were developed by A. D. Becke. " This approach is often called the B3LYP method. The computations can be done with... 

Table 3 Elastic constants and bulk moduli for hexagonal close-packed elements. Comparison is made between the results of our tight-binding parametrization (TB) and experiment (Exp). The tight-binding results include internal relaxation. Calculations were performed at the experimental volume, but at the c/a ratio which minimized the energy for that volume. Note that in a hexagonal crystal, Cee = (Ch - Ci2)/2.

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