### Table 1. The generalized results of quantum-chemical calculations for some molecules in HClO4 solution

"... In PAGE 17: ...onformer is more stable than the axial form, whereas for the thietane...HCl complex, opposite trend is observed ( Table1 ). Two low-frequency motions transfer one form of the complex to the other: the four-membered ring-puckering and the HCl inversion.... In PAGE 17: ... The shape of the potentials with respect to the both motions was studied in details and will be presented in the poster. Table1 . The MP2/6-311++G** energy differences for the complexes studied.... In PAGE 89: ... The latter values were further corrected for the basis set superposition error. Results and Discussion Table1 lists selected characteristics of some dihydrophenazine derivatives calculated at the applied level of the theory as well as those of anthracene and its methyl or ethyl derivatives. 1, shown in Fig.... In PAGE 90: ...Current Trends in Computational Chemistry 2001 270 Table1 . Total energies (Etot, au), HOMO and LUMO values (au), non-planarities (f, degree) and dipole moments (D, debye) calculated at the B3LYP/6-31G* level of theory for dihydrophenazine and anthracene derivatives.... In PAGE 90: ...2 0.70 An analysis of the data in Table1 show that, in contrast to the completely planar structure of anthracene and its methyl or ethyl derivatives, dihydrophenazines adopt mainly non-planar, propeller twist structures. As a measure of non-planarity, we choose an angle f formed between the two aromatic rings of dihydrophenazine moiety.... ..."

### TABLE 6: Self-Consistent Calculation of Liberation Energy for Perturbed Hard-Sphere Fluida

### Table 2: The energy levels in atomic units obtained by our calculations (C6), a larger cycle expansion (cycle) and quantum solutions (QM). The cycle and QM columns are taken from [1]

### Table 1. Classification of global optimization methods based on the degree of history dependence.

"... In PAGE 2: ... Finally, the small energy difference between the correct and incorrect minima and the exponential growth of the density of the non-native states with energy impose strict requirements on the accuracy of energy evaluation (less than about 1 kcal/mol)5. Numerous approaches have been used to attack the global optimization problem in protein structure prediction, with some success1-8 ( Table1 ). These methods are initially classified according to whether they are deterministic or not; stochastic methods are further subdivided according to the degree of similarity between conformations generated in consecutive iterations of the search algorithm.... In PAGE 3: ... Most of the MC-like stochastic global optimization strategies employ a three-step iteration: (i) modify the current conformation by means of a random move; (ii) evaluate its energy; (iii) accept or reject the new conformation according to an acceptance criterion. The random moves can be ranked by magnitude of change with respect to the current conformation ( Table1 ). The first group contains algorithms in which the generated conformations do not depend on the previous ones.... ..."

### Table 1. Effects of Cutout

1983

"... In PAGE 5: ...ffected by the cutout algorithm. Note that, with a 20.1 m/s (45 mph) cutout, almost all of the available energy is captured while a substantial fraction of the fatigue damage is still eliminated. Table1 lists the blade fatigue life expectancy and annual energy capture associated with edf apos;s and ddf apos;s for the blade-to-tower joints on the DOE 100-kW turbine at Bushland, TX, shown in Figures 5 and 4, respectively. Control Algorithm Effects The purpose of the cutout algorithm is therefore to balance the extension of fatigue life with the reduction in the annual energy capture, both of which result from shutting down the turbine in high winds.... ..."

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### Table 1. Ground state energies of a hydrogenic impurity in spherical quantum dot of in nite depth with a radius (R). (a) exact calculation [38, 39] (b) variational calculation [38], (c) QGA based on parameter optimization and (d) QGA based on wave function optimization.

"... In PAGE 10: ...2. Results and Discussion The results obtained from the calculations are presented comparatively in Table1 along with the exact results.... In PAGE 10: ....2. Results and Discussion The results obtained from the calculations are presented comparatively in Table 1 along with the exact results. The rst column in Table1 corresponds to the radius of the well, i.e.... ..."

### Table 3 n distinct eigenvalues bifurcations iterations/eigenvalue

"... In PAGE 21: ...meet and bifurcate into a complex conjugate pair. The second column of Table3 indi- cates that the likelihood of having bifurcations increases with the size of the problem. However, even for problems of small size, e.... In PAGE 21: ... When, in spite of the complex perturbation of the last re ection coe cient, we were unable to compute all eigenvalues accurately by the continuation method, the de ation scheme of Section 4 delivered the remaining eigenvalues. Table3 summarizes our experience using the continuation scheme for real re ec- tion coe cients for computing the zeros of 1000 Szeg}o polynomials of even degree between 4 and 18. The degree of the Szeg}o polynomials, n, is listed in the rst col- umn.... In PAGE 21: ... Starting from each eigenvalue of Hn(0), we track the eigenvalue paths using Algorithm 3 until either the endpoints of the paths are reached, or the algorithm stops after reaching the maximum number of iterations. Column 2 of Table3 shows how many times out of 1000 runs the algorithm reached the endpoint of all continuation paths and determined... In PAGE 22: ... The numbers listed in Column 2 shows that the continuation algorithm for real re ection coe cients almost always computes all eigenvalues correctly. The third column of Table3 , labeled \bifurcations quot;, counts the total number of bifurcations which occurred in the course of the 1000 experiments, i.e.... In PAGE 22: ... As we would expect, the number of bifurcations increases with the degree of the Szeg}o polynomial. The last column of Table3 , labeled \iterations/eigenvalue quot; reports the average num- ber of Newton steps needed for the computation of each eigenvalue. We remark that the value reported is the average over the computation of 1000n eigenvalues.... ..."

### TABLE II. X-Ray Crystal Structure Coordinates Used in Docking Experiments, Their Brookhaven Protein Data Bank Accession Codes and Resolution, Number of Rotatable Bonds in the Ligand, Number of Torsional Degrees of Freedom, Total Number of Degrees of Freedom, and Energy of Crystal Structure Using the Empirical Force Field Presented Here.

in Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function

1998

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### Table 3: Finite sample e ciencies of the SCM eigenvector and standardized eigenvalue estimates (reported between parentheses) relative to eigenvector and standardized eigen- value estimates based on the sample covariance matrix. Samples were generated from a k-variate t-distribution with degrees of freedom and = diag(1; : : : ; k).

2003

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