Representation definition

An alternative and commonly used representation of the range of reserves is the proven, proven plus probable, and proven plus probable plus possible definition. The exact cumulative probability which these definitions correspond to on the expectation curve... 

This makes it desirable to define other representations in addition to the electronically adiabatic one [Eqs. (9)-(12)], in which the adiabatic electronic wave function basis set used in the Bom-Huang expansion (12) is replaced by another basis set of functions of the electronic coordinates. Such a different electronic basis set can be chosen so as to minimize the above mentioned gradient term. This term can initially be neglected in the solution of the / -electionic-state nuclear motion Schrodinger equation and reintroduced later using perturbative or other methods, if desired. This new basis set of electronic wave functions can also be made to depend parametrically, like their adiabatic counterparts, on the internal nuclear coordinates q that were defined after Eq. (8). This new electronic basis set is henceforth refened to as diabatic and, as is obvious, leads to an electronically diabatic representation that is not unique unlike the adiabatic one, which is unique by definition. 

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). 

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. 

This eommutation relation is easily verified in the eoordinate representation leaving x untouehed (x = x ) and using the above definition for p. In the momentum representation... 

Extensive discussions have focused on the conformation of the alkyl chains in the interior ". It has been has demonstrated that the alkyl chains of micellised surfactant are not fully extended. Starting from the headgroup, the first two or three carbon-carbon bonds are usually trans, whereas gauche conformations are likely to be encountered near the centre of tlie chain ". As a result, the methyl termini of the surfactant molecules can be located near the surface of the micelle, and have even been suggested to be able to protrude into the aqueous phase "". They are definitely not all gathered in the centre of tire micelle as is often suggested in pictorial representations. NMR studies have indicated that the hydrocarbon chains in a micelle are highly mobile, comparable to the mobility of a liquid alkane ... 

Definition 2 is phrased in terms of knowledge-based systems rather than expert systems. No reference is made to expert human problem solvers. Definition 2 captures the sense that the representation and manipulation of knowledge is the source of such a system s power, whether or not that knowledge is dkecdy eHcited from a human expert. 

Contracts with the federal government require compliance with Executive Order Nos. 11625 and 12138 to utilize small and small disadvantaged businesses. The contractor/subcontractor must complete a copy of the representations and certifications providing self-certification of business classification under existing federal definitions. The representations and certifications also provide tax identification information required by the Internal Revenue Service. The original of the representation and certification form should be sent to regional purchasing and a copy included in the project file. 

Thus, the conversion from a logical representation to a probability representation follows naturally from superposition and the von Misesian definition of probability. Simply replace tlie component identifier by its failure probability and combine probabilities according to the logical operations. 

The user must have experience in airflow and indoor air quality analysis and be familiar with the theoretical principles and details upon which indoor air quality analysis is based. Engineering judgment will have to be used for the setup of the building representation and the definition of the input parameters. 

The preceding biaxial failure criteria suffer from various inadequacies in their representation of experimental data. One obvious way to improve the correlation between a criterion and experiment is to increase the number of terms in the prediction equation. This increase in curvefitting ability plus the added feature of representing the various strengths in tensor form was used by Tsai and Wu [2-26]. In the process, a new strength definition is required to represent the interaction between stresses in two directions. 

In order to find the effect of broadening of the surface on the structure parameters H and K, we first study the ordered phases with the diffusive interfaces. The ordered phases can be described by the periodic surfaces (0(r)) = 0 and we can compare and with H and K. The numerators in the definitions (76) and (77) in the Fourier representation assume the forms [68]... 

PROBLEM DEFINITION, QUALITATIVE ERROR PREDICTION AND REPRESENTATION. The recommended problem definition and qualitative error prediction approach for use with SLIM has been described in Section 5.3.1 and 5.3.2. The fact that PIFs are explicitly assessed as part of this approach to qualitative error prediction means that a large proportion of the data requirements for SLIM are already available prior to quantification. SLIM usually quantifies tasks at whatever level calibration data are available, that is, it does not need to perform quantification by combining together task element probabilities from a data base. SLIM can therefore be used for the global quantification of tasks. Task elements quantified by SLIM may also be combined together using event trees similar to those used in THERP. 

OH molecules, reaction between, 282 Oil-drop experiment, 241 Oil of wintergreen, 346 Oleomargarine, 407 Open hearth furnace, 404 Operational definition, 195 Orbital representation of chemical bonding, 278 Orbitals atomic, 262, 263 dand/, 262... 

Serotoninergic System. Figure 1 Graphical representation of the current classification of 5-hydroxytryptamine (5-HT) receptors. Receptor subtypes represented by shaded boxes and lowercase designate receptors that have not been demonstrated to definitively function in native systems. Abbreviations 3-5r cyclic adenosine monophosphate (cAMP) phospholipase C (PLC) negative (-ve) positive (+ve)... 

We now introduce a second complete orthonormal set of functions v, which we shall take to be functions of t, vt(t). First, however, we merely consider the set (0). Since they are by definition constant in time, they behave like the u, and all preceding equations can be written in the v(0)-representation. A transformation of the functions has the form... 

It is to be remarked that these operators can act only on states of the system expressed in occupation number representation, as explicitly appearing in the definitions, Eqs. (8-105), (8-106), (8-112), and (8-114). We can multiply any one of these operators by a scalar factor, so that we can also define the following operators ... 

Fock Space Representation of Operators.—Let F be some operator that neither creates nor destroys particles, and is a known function in configuration space for N particles. In symbols such an operator must by definition have the following matrix elements in Fock space ... 

With this definition, the classical entropy per system equals the ensemble average of the expectation value of 8 in occupation number representation. 

We have carried out tins discussion in occupation number representation or coordinate representation each with a definite number N of particles. Similar results follow for the Fock space representation and the properties of grand ensembles. Averages over grand ensembles are also independent of time when the probabilities > are independent of time, whether the observable commutes with H or not. 

One of the principal reasons for the usefulness of these definitions lies in the fact that they are invariant under a change of representation. One verifies that under a change of representation wherein... 

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