REAL EXPRESSION

A REAL entity represents a real value in the form of an entity It may be referenced from other entities, it may have an index entry and a real expression associated. 

A REAL EXPRESSION property indicates that the referenced real entity is in fact the value of an arithmetic expression. 

The consistency attribute indicates whether that value is consistent with the present expression the update mode indicates when updating of value is to occur Updating may occur whenever the expression (the construct) is 

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In order to quantify the area at risk and burden of ischaemia, both ST-segment elevations and depressions should be assessed. The latter are not the expression of subendocardium injury, but the real expression ofsubepicardium (transmural) injury in a distant area. Therefore, in LAD occlusion, an ST-segment depression detected in II, III and VF, more significant compared with an ST-segment elevation in the same leads, represents more ischaemia (compare Figures 4.21 and 4.23). 

Each of the terms in Eq. [Al] to [A3] will be separated into its real and imaginary parts. Equation [A4] is already a real expression so it needs no attention. 

In the simple classical theory of the vibrational Raman effect [1] the electric vector is taken as the real expression... 

Since the original expression Equation A10.19 is linear with respect to the parameter kA, this method is called linear regression. Many computer programs exist for the automatic fitting of linear models y = kx and y = ko + k X, and the real expressions for least-square models, such as Equation A10.21, thus remain unknown for the program user. 

Equation (13.5.8), which represents the generalization of the Hellmann-Feynman theorem to coupled-cluster wave functions, is shown in Exercise 13.1 to give size-extensive first-order properties. For variational wave functions, the Hellmann-Feynman theorem contains the real average value of the operator V (4.2.51) rather than a transition expectation value as in (13.5.8). Likewise, to ensure teal properties, we may in coupled-cluster theory work in terms of the manifestly real expression... 

A disadvantage of the multipole method presented so far is that it is exfaessed in terms of complex multipole moments and interaction tensors. Since the Coulomb interactions are real, it is more natural (and, it turns out, more efficient) to express the expansions in terms of real moments and interaction tensors. In the remainder of this section, we shall see how the transformation to real expressions may be accomplished. 

Let us finally consider the real expression for the interaction matrix. We proceed in the same maimer as for the translation matrix, beginning with (9.13.19), which we write as... 

For real gases, density is expressed by the following relationship ... 

The adaptive estimation of the pseudo-inverse parameters a n) consists of the blocks C and E (Fig. 1) if the transformed noise ( ) has unknown properties. Bloek C performes the restoration of the posterior PDD function w a,n) from the data a (n) + (n). It includes methods and algorithms for the PDD function restoration from empirical data [8] which are based on empirical averaging. Beeause the noise is assumed to be a stationary process with zero mean value and the image parameters are constant, the PDD function w(a,n) converges, at least, to the real distribution. The posterior PDD funetion is used to built a back loop to block B and as a direct input for the estimator E. For the given estimation criteria f(a,d) an optimal estimation a (n) can be found from the expression... 

It is possible to use the quantum states to predict the electronic properties of the melt. A typical procedure is to implement molecular dynamics simulations for the liquid, which pemiit the wavefiinctions to be detemiined at each time step of the simulation. As an example, one can use the eigenpairs for a given atomic configuration to calculate the optical conductivity. The real part of tire conductivity can be expressed as... 

Real gases follow the ideal-gas equation (A2.1.17) only in the limit of zero pressure, so it is important to be able to handle the tliemiodynamics of real gases at non-zero pressures. There are many semi-empirical equations with parameters that purport to represent the physical interactions between gas molecules, the simplest of which is the van der Waals equation (A2.1.50). However, a completely general fonn for expressing gas non-ideality is the series expansion first suggested by Kamerlingh Onnes (1901) and known as the virial equation of state ... 

It is detemrined experimentally an early study was the work of Andrews on carbon dioxide [1], The exact fonn of the equation of state is unknown for most substances except in rather simple cases, e.g. a ID gas of hard rods. However, the ideal gas law P = pkT, where /r is Boltzmaim s constant, is obeyed even by real fluids at high temperature and low densities, and systematic deviations from this are expressed in tenns of the virial series ... 

A quite different approach was adopted by Robinson and Stokes [8], who emphasized, as above, that if the solute dissociated into ions, and a total of h molecules of water are required to solvate these ions, then the real concentration of the ions should be corrected to reflect only the bulk solvent. Robinson and Stokes derive, with these ideas, the following expression for the activity coefficient ... 

Of course, real molecules are not hamronic oscillators, and the energy level expression can be expanded in powers of (v + 1/2). For a single mode we have... 

A teclmique that employs principles similar to those of isomorphous replacement is multiple-wavelength anomalous diffraction (MAD) [27]. The expression for the atomic scattering factor in equation (B1.8.2h) is strictly accurate only if the x-ray wavelength is well away from any characteristic absorption edge of the element, in which case the atomic scattering factor is real and Filiki) = Fthkl V- Since the diffracted... 

This expression holds true only in the large g region in reciprocal space (or small r in real space). Since... 

This gives the total energy, which is also the kinetic energy in this case because the potential energy is zero within the box , m tenns of the electron density p x,y,z) = (NIL ). It therefore may be plausible to express kinetic energies in tenns of electron densities p(r), but it is by no means clear how to do so for real atoms and molecules with electron-nuclear and electron-electron interactions operative. 

Let us express the displacement coordinates as linear combinations of a set of new coordinates y >q= Uy then AE = y U HUy. U can be an arbitrary non-singular matrix, and thus can be chosen to diagonalize the synmietric matrix H U HU = A, where the diagonal matrix A contains the (real) eigenvalues of H. In this fomi, the energy change from the stationary point is simply AF. = t Uj A 7- h is clear now that a sufBcient... 

The derivation of the D matrix for a given contour is based on first deriving the adiabatic-to-diabatic transformation matrix, A, as a function of s and then obtaining its value at the end of the arbitrary closed contours (when s becomes io). Since A is a real unitary matrix it can be expressed in terms of cosine and sine functions of given angles. First, we shall consider briefly the two special cases with M = 2 and 3. 

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