Frames representation

Figure Bl.15.7. Transient EPR. Bottom time-resolved EPR signal of the laser-flash-indueed triplet state of pentaeene in /j-terphenyl. BpO.085 mT. Top initially, the transient magnetization M is aligned along B z. In the presenee of a MW magnetie field B the magnetization preeesses about BJ x (rotating frame representation).

Figure Bl.15.10. FT EPR. (A) Evolution of the magnetization during an FT EPR experiment (rotating frame representation). (B) The COSY FT EPR experiment.

Figure Bl.15.11. Fomiation of electron spin echoes. (A) Magnetization of spin packets i,j, /rand / during a two-pulse experiment (rotating frame representation). (B) The pulse sequence used to produce a stimulated echo. In addition to this echo, which appears at r after the third pulse, all possible pairs of the tluee pulses produce primary echoes. These occur at times 2x, 2(x+T) and (x+2T).

Figure 6. Spin frame representation of a spin-vector by flagpole normalized pair representation a,b over the Poincare sphere in Minkowski tetrad (l,x,y,z) form (n representation) and for three timeframes or sampling intervals providing overall (t]. r ) a Cartan-Weyl form representation. The sampling intervals reset the clock after every sampling of instantaneous polarization. Thus polarization modulation is represented by the collection of samplings over time. Minkowski form after Penrose and Rindler [28]. This is an SU(2) Gd hx) m C over it representation, not an SO(3) Q(to, 8) in C representation over 2it. This can be seen by noting that an b or bt-z a over it, not 2n, while the polarization modulation in SO(3) repeats at a period of 2it.

Scheme 1 is an example of the frame representation (written in PROLOG) for one particular experiment relative to the alkylation of toluene with isopropanol to produce cymene with mordenite as catalyst taken from reference [23]. 

Fig. 14.2. Sizing the nanospheres is possible. Top polyhedral representations of the clustertype [(pent)i2(link)3o] = (Mo)Mo5 i2 linl< 30 (linkers Mo 2 and Fe " type units, indicated by arrows) showing a size-comparison of the two clusters Mo72Fe3o (a) and M0132 (b). Middle size-comparison of the two clusters via wire-frame representation of the metal skeletons. Note in (a) the size- shrinking as the dinuclear Mo 2 ...

Figure 2.6. The laboratory and rotating frame representations. In the laboratory frame the co-ordinate system is viewed as being static, whereas in the rotating frame it rotates at a rate equal to the applied rf frequency, vq. In this representation the motion of one component of the applied rf is frozen whereas the other is far from the resonance condition and may be ignored. This provides a simplified model for the description of pulsed NMR experiments.

Figure 6. Wire frame representation of the layer structure of linked Mo72Feioj units with emphasized Fe-O-Fe bridges along the a axis in 8 (only the metal atoms are shown Fe centers, black spheres). The unit cell is also depicted, showing the approximate face-centered cubic packing of the cluster spheres.

Figure 8. Demonstration of the structure of the building block of iO with the capsule (host) and encapsulated Keggin-type cluster nucleus (guest) the metal Mo72Fejo)capsule is shown in wire frame representation -with the 30 Fe " centers (highlighted as spheres) linking the 12 (Mo)Mo5) pentagons - and the Keggin nucleus in polyhedral representation.

If we apply a magnetic field rotating at the Larmor frequency in the plane perpendicular to the static field, we can cause the individual nuclear moments to flip with the result that the entire macroscopic magnetization may be turned towards or away from the static field. In order to understand this and other more complicated operations, we now discuss the rotating frame representation of pulse NMR. The major problem in trying to visualize the motion of the magnetization in a static magnetic field is the fact that all motions towards... 

Figure 6.6 shows a wire-frame representation of the heart (right) and the resulting 3D visualization (left). Original data were acquired by cardiovascular MRI. 

Winograd, T. Frame representations and the declarative rocedural controversy. Li D. G. Bobrow A. Collins (Eds.), Representation and understanding. Studies in cognitive science (pp. 185-210). New York Academic Press. 1975. 

The wire-frame representation of a three-dimensional object consists of a three-dimensional vertex point list and an edge list of vertex pairs. Although this representation is very simple, it is an ambiguous representation for determining such quantities as surface area and volume of an object. Wire-frame... 

Regarding the use of upper and lower case subscripts it must be borne in mind that in some instances it is not without ambiguity, as in the case of displacements. Strictly speaking, the distinction is mandatory only for the coordinates themselves in combination with the comma notation for derivatives. In all other contexts upper case indices serve as a useful reminder that a material frame representation is used. This reminder, of course, is superfluous if only Unear effects are considered. 

Molecular structures are commonly drawn in the form of lines representing the bonds between atomic centers. The atoms are only represented as junctions of these lines. These drawings may be referred to as line models, Dreiding models, or wire-frame representations. The bonds of the molecules can be color coded, for example, by the atom types, and single, double, or triple bonds can be represented by one, two, or three lines, respectively. Smooth lines on computer displays can be achieved by using a method called antialiasing . A wire-frame representation of a tryptophane molecule is shown in Figure 1(a). 

Figure 41 VRML scene of the mutated p53 DNA complex. The DNA fragment is shown in wire frame representation, the backbone of the protein in ribbon representation with the mutation hotspots in capped sticks (magenta, mutated amino acid ARG248 > GLN248). The space button in the lower left comer leads to a lower quality representation of this scene...

To describe the motion of spins under the influence of a resonant rf field, Hj, it is conventional in magnetic resonance to transform to a rotating frame representation. In the rotating fr me, the spins are subject to an effective field,... 

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