Point, imaginary

Now envision this lattice of imaginary points in the same space occupied by the crystal. For a small real unit cell, interplanar spacings dhkl are small, and hence the lines from the origin to the reciprocal lattice points are long. Therefore, the reciprocal unit cell is large, and lattice points are widely spaced. On the other hand, if the real unit cell is large, the reciprocal unit cell is small, and reciprocal space is densely populated with reciprocal lattice points. 

Scheme 4. Definition of the dihedral angle ZXSilSi2Si3. Imaginary point X is placed along the C3 axis of the SiaSi unit...

In thinking about crystals, it is often convenient to ignore the actual atoms composing the crystal and their periodic arrangement in space, and to think instead of a set of imaginary points which has a fixed relation in space to the atoms of the crystal and which may be regarded as a sort of framework or skeleton on which the actual crystal is built. 

The data set obtained for the electropherogram, which is represented in the time domain, is converted into a data set in the frequency domain using an FT. When the number of the data points is N, FT of the data in the time domain yields N/2 + 1 complex points that are pairs of real and imaginary points in the frequency domain. These complex data are represented in terms of their magnitude as follows ... 

The first equation gives real values of x if mless than, or both greater than, b/a, and hence one diameter meets the curve in real points and the other in imaginary points. It is not difficult to show, in a similar way to the above, that the sum of the squares of the conjugate semi-diameters is a2—b2, a constant. 

Figure 9.14b showed a non-simplex domain fitting well inside an inverted f/-simplex, but two of the corners of the simplex were not only outside the domain but outside the ternary diagram. They are "imaginary" points with negative amounts of two of the components. This also can give matrices with rather better properties than if the model is defined in terms of the pure components. Here also the coefficients have no direct physical significance and it is only the prediction of the response surface within the domain that is valid. 

The formal relation between a real and a reciprocal lattices is as follows. The reciprocal lattice is a set of imaginary points constructed in such a way that the direction of vectors in this lattice from one point to another coincides with the direction of normals to planes in the real crystal lattice. The magnitude of the reciprocal lattice vector g is equal to the reciprocal of the interplanar spacing 1/d in the real lattice multipUed by 2jt. 

The first step in the application of symmetry to molecular properties is therefore to recognize and organize all of the symmetry elements that the molecule possesses. A symmetry element is an imaginary point, line, or plane in the molecule about which a symmetry operation is performed. An operator is a symbol that tells you to do something to whatever follows it. Thus, for example, the Hamiltonian operator is the sum of the partial differential equations relating to the kinetic and... 

The Gaussian model is based on analytical solutions of the general transport equation for a point source. Steady continuous and instantaneous releases (plumes and puffs) can be modeled. For time-varying continuous releases, time-integrated puff models should be used. For area sources, such as a liquid pool, two approaches are possible. In the first approach, an imaginary point source is assumed upwind of the actual source, so that the width of the cloud matches the source dimensions at the site of the actual source. The second approach is based on an area integration of the point source equations over the source area. 

Single-electrode potentials are important for some fundamental but unmeasurable quantities. The problem has been discussed in literature [2, 3]. Relative potential values (not absolute values which refer to an imaginary point in the universe ) can be calculated. Also single-electrode entropy values can be calculated by means of non-isothermal cells, but it is necessary to make use of some non-thermodynamic assumptions. 

Note that, whereas the unshifted problem has pure imaginary points of degeneracy... 

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