Figures definition

Observe Figure 1.2. This figure definitely shows some form of pattern, but is not of such a character that meaningful values can be obtained directly for design purposes. If enough data of this pattern is available, however, they may be subjected to a statistical analysis to predict design values, or probability distribution analysis, which uses the tools of probability. Only two rules of probability apply to our present problem the addition rule and the multiplication rule. 

The area can be measured from a map. Figure 6.1 clarifies some of the reservoir definitions used in reserves estimation. 

Figure 2 Scatter plot of clustering results Figure 3 Definition of Damage Stages...

In this figure the next definitions are used A - projection operator, B - pseudo-inverse operator for the image parameters a,( ), C - empirical posterior restoration of the FDD function w(a, ), E - optimal estimator. The projection operator A is non-observable due to the Kalman criteria [10] which is the main singularity for this problem. This leads to use the two step estimation procedure. First, the pseudo-inverse operator B has to be found among the regularization techniques in the class of linear filters. In the second step the optimal estimation d (n) for the pseudo-inverse image parameters d,(n) has to be done in the presence of transformed noise j(n). 

Figure 2 represents the main view of the model, including all the objects and relationships, the detailed definition of which is given in the standard draft ( 8.2.1 - cf table I). fhe object groups of figure 1 have also been represented on figure 2, for an easier comprehension. This main view is common to all the NDT methods. 

This definition causes the wavefiinction to move with the molecule as shown for the X direction in figure Al.4,3. The set of all translation synnnetry operations / constitiites a group which we call the translational group G. Because of the imifomhty of space, G is a synnnetry group of the molecular Hamiltonian //in that all its elements commute with // ... 

Figure Al.4.4. The definition of the Euler angles (0, ( ), x) that relate the orientation of the molecule fixed (x, y, z) axes to the (X, Y, Z) axes. The origin of both axis systems is at the nuclear centre of mass O, and the node line ON is directed so that a right handed screw is driven along ON in its positive direction by twisting it from Z to z through 9 where 0 < 9 < n. ( ) and x have the ranges 0 to In. x is measured from the node line.

Consider, Figure Al.6.32 in which a system is initially populated with an incoherent distribution of populations with Boltzmaim probabilities, = 1. The simple-minded definition of cooling is to... 

Finally the concept of fields penults clarification of the definition of the order of transitions [22]. If one considers a space of all fields (e.g. Figure A2.5.1 but not figure A2.5.3, a first-order transition occurs where there is a discontinuity in the first derivative of one of the fields with respect to anotlier (e.g. (Sp/S 7) = -S... 

The slopes of the fimctions shown provide the reaction rates according to the various definitions under the reaction conditions specified in the figure caption. These slopes are similar, but not identical (nor exactly proportional), in this simple case. In more complex cases, such as oscillatory reactions (chapter A3.14 and chapter C3.6). the simple definition of an overall rate law tluough equation (A3.4.6) loses its usefiilness, whereas equation (A3.4.1) could still be used for an isolated system. 

For tire purjDoses of tliis review, a nanocrystal is defined as a crystalline solid, witli feature sizes less tlian 50 nm, recovered as a purified powder from a chemical syntliesis and subsequently dissolved as isolated particles in an appropriate solvent. In many ways, tliis definition shares many features witli tliat of colloids , defined broadly as a particle tliat has some linear dimension between 1 and 1000 nm [1] tire study of nanocrystals may be drought of as a new kind of colloid science [2]. Much of die early work on colloidal metal and semiconductor particles stemmed from die photophysics and applications to electrochemistry. (See, for example, die excellent review by Henglein [3].) However, the definition of a colloid does not include any specification of die internal stmcture of die particle. Therein lies die cmcial distinction in nanocrystals, die interior crystalline stmcture is of overwhelming importance. Nanocrystals must tmly be little solids (figure C2.17.1), widi internal stmctures equivalent (or nearly equivalent) to drat of bulk materials. This is a necessary condition if size-dependent studies of nanometre-sized objects are to offer any insight into die behaviour of bulk solids. 

Figure C3.4.4. Definition of the dimer transition dipole moments and p on tire basis of tire monomer transition dipole moments p and P2-...

Figure 5. Definition of the normal mode coordinates for a Dyi X3 molecule.

Depending on the application, models of molecular surfaces arc used to express molecular orbitals, clcaronic densities, van dor Waals radii, or other forms of display. An important definition of a molecular surface was laid down by Richards [182] with the solvent-accessible envelope. Normally the representation is a cloud of points, reticules (meshes or chicken-wire), or solid envelopes. The transparency of solid surfaces may also be indicated (Figure 2-116). 

Solvent-excluded surfaces correlate with the molecular or Connolly surfaces (there is some confusion in the literature). The definition simply proceeds from another point of view. In this c ase, one assumes to be inside a molecaile and examines how the molecule secs the surrounding solvent molecules. The surface where the probe sphere does not intersect the molecular volume is determined. Thus, the SES embodies the solvent-excluded volume, which is the sum of the van der Waals volume and the interstitial (re-entrant) volume (Figures 2-119. 2-120). 

The most well-known and at the same time the earliest computer model for a molecular structure representation is a wire frame model (Figure 2-123a). This model is also known under other names such as line model or Drciding model [199]. It shows the individual bonds and the angles formed between these bonds. The bonds of a molecule are represented by colored vector lines and the color is derived from the atom type definition. This simple method does not display atoms, but atom positions can be derived from the end and branching points of the wire frame model. In addition, the bond orders between two atoms can be expressed by the number of lines. 

Figure 5-16. Structure editor of the CrossFire ComiTiander V6, showing the definition ofan atom list (consisting of hydrogen and chlorine atoms) for polychlorinated biphenyls.

Figure 10.3-54 illustrates how the reaction center is derived from the disconnection of the strategic bond and which additional bond spheres are considered in the definition of the reaction substructure search queiy. 

Equation (9.23) is to be compared with the Feng and Stewart relations (9.4) which describe the fluxes in the same system under non-reactive conditions, The factor (BA coth BA - 1) has the form sketched in Figure 9.2. From the definition of B given by equation (9.19) it is seen chat 9- 0 as and each tend to zero, their ratio remaining equal to Che... 

Various other ways to incorporate the out-of-plane bending contribution are possible. For e3plane bend involves a cakulation of the angle between a bond from the central atom and the plane defined by I he central atom and the other two atoms (Figure 4.10). A value of 0° corresponds to all four atoms being coplanar. A third approach is to calculate the height of the central atom above a plane defined by the other three atoms (Figure 4.10). With these two definitions the deviation of the out-of-plane coordinate (be it an angle or a distance) can be modelled Lt ing a harmonic potential of the form... 

---