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Patterson and molecular replacement techniques, and the use of noncrystallographic symmetry in phasing
Tong, L., Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2010). Vol. B, ch. 2.3, pp. 244-281 [ doi:10.1107/97809553602060000765 ]
... as The Patterson coefficients then become The normalized structure factors, E (see Chapter 2.2 ), which are used in crystallographic direct methods ... the structure factors of the trial point Patterson. (The symbol E is used here because of its close relation to normalized ... for discriminating correct solutions, is a unit vector density criterion (Arnold et al., 1987)where is the number of vectors ...

Perspectives for the future
Arnold, E., Rossmann, M.G., Himmel, D.M., Spence, J.C.H. and Sun, S.  International Tables for Crystallography (2012). Vol. F, ch. 1.4, pp. 39-44 [ doi:10.1107/97809553602060000807 ]
... microscopy in structure determination. 1.4.1. Gazing into the crystal ball (E. Arnold) We live in an era when there are many wonderful ... on Gazing into the crystal ball (M. G. Rossmann) | | Eddy Arnold and I had planned to write a joint commentary ...

Recent salient examples in low-symmetry cases: multidomain averaging and systematic applications of multiple-crystal-form averaging
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.13, pp. 360-361 [ doi:10.1107/97809553602060000842 ]
... al., 1995), in some cases with dramatically improved diffraction resolution. Arnold and coworkers have applied multidomain and multiple-crystal-form averaging ... Kroeger Smith, M. B., Michejda, C. J., Hughes, S. H. & Arnold, E. (1996). Crystal structure of 8-Cl and 9- ...

Ab initio phasing starts
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.12, p. 360 [ doi:10.1107/97809553602060000842 ]
... too far in resolution can also lead to analogous problems (Arnold et al., 1987). Similar errors can occur due to ... determination frequently provides data points for the equivalent resolution. References Arnold, E., Vriend, G., Luo, M., Griffith, J. P., Kamer, G., ...

Convergence
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.11, pp. 359-360 [ doi:10.1107/97809553602060000842 ]
... Various weighting schemes are generally used (Sim, 1959; Rayment, 1983; Arnold et al., 1987; Arnold & Rossmann, 1988). As mentioned above, the rate of convergence ... error in the final phasing has been shown to be (Arnold & Rossmann, 1986) proportional to where N is the NCS ...

Phase extension and refinement of the NCS parameters
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.10, p. 359 [ doi:10.1107/97809553602060000842 ]
... be constantly improved and updated to match the improved resolution. Arnold & Rossmann (1986, 1988) discussed phase error as a function of ... References Abad-Zapatero, C., Abdel-Meguid, S. S., Johnson, J. E., Leslie, A. G. W., Rayment, I., Rossmann, M. G., Suck ... mosaic virus at 2.8 resolution. Nature (London), 286, 33-39. Arnold, E. & Rossmann, M. G. (1986). Effect of errors, ...

Combining different crystal forms
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.9, p. 358 [ doi:10.1107/97809553602060000842 ]
... Liu, J., Rodgers, D. W., Garlick, R. L., Tarr, G. E., Husain, Y., Reinherz, E. L. & Harrison, S. C. (1990). Atomic structure of a ...

Interpolation
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.8, p. 358 [ doi:10.1107/97809553602060000842 ]
... D. A second linear interpolation then determines the density at E (from densities at A and B) and at F (from ... interpolation determines the density at G from the densities at E and F. [Reproduced with permission from Rossmann et al. (1992 ... Then, it is possible to calculate an approximate density at E from with a similar expression for . Finally, the ...

Finding the averaged density
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.7, pp. 357-358 [ doi:10.1107/97809553602060000842 ]
... varphi]X174 structure determination. is proportional to the mean density (e-3) based on eight-point interpolation; n is number of ...

Determining the molecular envelope
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.6, pp. 356-357 [ doi:10.1107/97809553602060000842 ]
... Dai, J.-B., Wu, H., Choi, H.-K. & Lynch, R. E. (1992). Molecular replacement real-space averaging. J. Appl. Cryst. ...

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