Space original

If we were to define the operations of the point group as also rotating and reflecting the (p.q.r) axis system (in which case the axes would be tied to the positions of the nuclei), we would obtain a different multiplication table. We could call this the nuclear-fixed axis convention. To implement this the protons in the o, O2 and planes in figure Al.4.2 would be numbered H, H2 and respectively. With this convention the operation would move the a plane to the position in space originally occupied by the 02 plane. If we follow such a C3 operation by the reflection (in the plane containing Ft ) we find that, in the nuclear-fixed axis convention ... 

Suppose that the waves reaching some point in space originate from two i different sources. The principle of superposition states that the total wave displacement at that point is the sum of those caused by each individual wave. As a first example, consider the situation where a wave is reflected back on itself. The reflected wave has an equation similar to eqn 1.3, but with j the sign of x changed, corresponding to a reverse direction of travel. The combined (forward plus reflected) wave displacement is therefore... 

In other words, the entire space originally spanned by the orbitals ipm is represented as the direct sum of orthogonal subspaces serving as the carrier subspaces to different groups, but the numbers of residing electrons are not fixed for each carrier subspace and all their possible distributions enter the expansion. In the expansion eq. (1.214) each distribution a of electrons among the groups satisfies the condition ... 

The incoming states planar wave states sustained by the Rubidium atom. The collimators allow separation in space base states 10) and 20) propagate along channels 1 and 2 < i(x) and 02(x) are the scattered states at DS-1 and, as the source state is the same and we take identical slit interaction potentials, these functions differ only in space origin. After interaction with the laser beam the base states label from 1) to 10> are sufficient for discussing several possibilities... 

Hybrids constructed from hydrogenic eigenfunctions are examined in their momentum-space representation. It is shown that the absence of certain cross-terms that cause the breaking of symmetry in position space, cause inversion symmetry in the complementary momentum representation. Analytical expressions for some simple hybrids in the momentum representation are given, and their nodal and extremal structure is examined. Some rather unusual features are demonstrated by graphical representations. Finally, special attention is paid to the topology at the momentum-space origin and to the explicit form of the moments of the electron density in both spaces. 

The inversion can be done more compactly by computing the inverse in the space originally occupied by A. Simple changes in steps 2 and 3 will accomplish this ... 

Greenburg J. M. (1984) Chemical evolution in space. Origins Life 14, 25-36. 

The ELF defined in equation 14 is a local function which describes to what extent the Pauli repulsion is efficient at a given point of the molecular space. Originally, the ELF was derived from the Laplacian of the conditional probability [V Pcondiri, r2)]ri=r2- An... 

Figure 9.1 Reciprocal space construction for a powder diffraction experiment. The myriad reciprocal lattice points for the crystallites combine to form nested spherical shells centered at the reciprocal space origin.

If a solute coming from a solution at constant concentration penetrates into a limited space originally empty and moves in that space by a diffusion process, the amount of solute q present in that space at time t is given by... 

It has recently been observed [22,26] that the stockholder principle of equation (91b) in fact states the equality between the local conditional probabilities (D°(r) = p°(alr) = p°(r) and Da(r) = p(alr) = p(r), that an electron found at a given location in space originates from the specified free or bonded subsystem. Thus, a restatement of the information principle, more appropriate to justify the stockholder rule, should be in terms of these conditional probabilities. Indeed, for a given location in space the following local variational principle is satisfied [26] ... 

Fig. 10 Photomicrographs of paragon-stained sections of (a) CaP-coated, (b) chitosan-coated, and (c) uncoated titanium pins after 12 weeks in rabbit tibia. A mixture of mature lamellar and new bone was observed around all implanted pins, (d) Good bone formation was also observed around a chitosan-coated titanium pin that had migrated toward the rabbit tibial marrow space (original magnification 2x). Reprinted with kind permission from Bumgardner et al. [62], Wolters Kluwer Health/Lippincott Williams Wilkins, 2007...

Tables 7.1 and 12. present some toxic compounds that can be found in indoor spaces originating mainly from construction materials (Table 7.1) as well as their possible effects on humans (Table 12).

Under the assumption of a monoclinic cell, which gave the best fit of the data, a calculation of representative spectra lead to lattice plane distances and indexes of the reflexes. A recalculation of the spectra for the different lots showed slightly different d-spacings (original data in Ref [29]). 

The microstmcture of Portland-slag cement pastes is not too different from that of plain Portland cement. The main difference consists in a reduced amount of free Ca(OH) 2- Just as with clinker grains, layers of reaction products formed in situ are also present at the boimdaries of the slag grains, in addition to the hydrated material formed within the space originally filled with water. 

Topochemical reaction—a chemical reaction, such as a hydration, taking place in a suspension in which the product of reaction occupies the space originally occupied by one of the reactants, rather than being precipitated randomly from the liquid phase. 

Swinne made a theoretical study of the variation of various properties of radioelements and, in particular, half-lives. He came to the conclusion that the elements directly following uranium had to have short half-lives. But the elements with the numbers in the ranges between 98 and 102 and between 108 and 110 could be expected to have sufficiently long half-lives. Where to look for them Swinne suggested that the best bet would be not terrestrial minerals but space objects. This is why he studied the dust of space origin collected in Greenland. All this was quite fascinating but not substantiated and therefore looked like doomed for oblivion. 

FIGURE 15.9 Activity landscape constracted from a data set of cyclooxygenase-2 inhibitors. The chemical space depicted is the 2D projection of the original, multidimensional space. (Original figure provided courtesy of Prof. Dr. Jiirgen Bajorath see [156]). 

A centric scan SPRITE acquisition samples the central point of k-space first, such that no T1 weighting is introduced at the k-space origin. The local image intensity at any point in the image is thus given by... 

---