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*SAYRE* *EQUATION*, TANGENT FORMULA AND SAYTAN

"... V the volume of a unit cell r real-space positional vector defined within a unit cell ρ (r) electron density function with r as argument h reciprocal-lattice vector, which corresponds to the diffraction index hkl Fh the structure factor with h as argument; the Fourier transform of ρ (r) Fsq h the Fo ..."

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corresponding to Fh Eh the magnitude of Eh σn = Σj (Zj)n, Zj is the atomic number of the jth atom in the unit cell, n is an integer 2.

*Sayre*’s*equation*The*Sayre**equation*[1] is an exact*equation*linking structure factors. It holds under the following conditions: i) positivity; ii) atomicity; iii) equal### Direct Methods in Superspace. I. Preliminary Theory and Test on the Determination of Incommensurate Modulated Structures

, 1987

"... The validity of the Sayre equation [Sayre (1952). Acta Cryst. 5, 60-65] for (3+n)-dimensional periodic structures i examined. A practical procedure is pro-posed for the determination of incommensurate modulated structures; this is an extension of the direct method previously proposed for solving sup ..."

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The validity of the

*Sayre**equation*[*Sayre*(1952). Acta Cryst. 5, 60-65] for (3+n)-dimensional periodic structures i examined. A practical procedure is pro-posed for the determination of incommensurate modulated structures; this is an extension of the direct method previously proposed for solving### Integration of Direct Methods With Macromolecular Crystallographic Techniques

"... The role of direct methods in macromolecular crystallography is discussed. The common belief that such methods will still remain marginal is rejected. Different sectors are analyzed. A direct procedure for phasing reflections when diffraction data of one isomorphous derivative are available is brief ..."

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several years ago. It was soon realized that

*Sayre**equation*, tangent formula, Karle-Hauptman d...###
Choosing integration methods when solving differential *equations*

"... Abstract: There are two common types of solution methods for solving simple integrals: using integration constants or using limits of integration. We use the resources framework to model student solution methods. Preliminary results indicate both problematic and meaningful intersections of physical ..."

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meaning and mathematical formalism when solving linked integrals. Students solving separable first order differential

*equations*in typically use two methods: an integration constant (“+C”) or limits of integration. The two methods are similar, involving anti-derivatives and boundary conditions. But, we### Surface structure solution by X-ray diffraction: structure completion with positivity and atomicity constraints

, 2002

"... We propose a method for the solution of surface structures from X-ray diffraction based on the phasing of measured structure factor amplitudes in two stages. First, incorporation of calculated amplitudes and phases of the structure factors of the known underlying bulk structure, together with an ite ..."

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with an iterative algorithm that ensures the positivity of the electron density enables the determination of the amplitudes and phases of the surface structure factors contributing to the crystal truncation rods. Second, inclusion of these structure factors in an iterative algorithm based on

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