Internal parameter

Constrained optimization refers to optimizations in which one or more variables (usually some internal parameter such as a bond distance or angle) are kept fixed. The best way to deal with constraints is by elimination, i.e., simply remove the constrained variable from the optimization space. Internal constraints have typically been handled in quantum chemistry by using Z matrices if a Z matrix can be constructed which contains all the desired constraints as individual Z-matrix variables, then it is straightforward to carry out a constrained optimization by elunination. 

Internal parameters are generally optimized with respect to the geometries, vibrational spectra, and confonnational energetics of selected model compounds. The equilib-... 

Optimization of external parameters tends to be more difficult as the quantity of the target data is decreased relative to the number of parameters to be optimized compared to the internal parameters, leaving the solution more undetermined. This increases the... 

In our calculations we have used experimental values" for all internal parameters in the D8g structure. To otain the true theoretical equilibrium structure one should also relax the structure with respect to all its internal parameters. In D8g we have 2 coordinates and the c/a dependence of the total energy. 

In table 2 and 3 we present our results for the elastic constants and bulk moduli of the above metals and compare with experiment and first-principles calculations. The elastic constants are calculated by imposing an external strain on the crystal, relaxing any internal parameters (case of hep crystals) to obtain the energy as a function of the strain[8]. These calculations are also an output of onr TB approach, and especially for the hep materials, they would be very costly to be performed from first-principles. For the cubic materials the elastic constants are consistent with the LAPW values and are to within 1.5% of experiment. This is the accepted standard of comparison between first-principles calculations and experiment. An exception is Sr which has a very soft lattice and the accurate determination of elastic constants is problematic. For the hep materials our results are less accurate and specifically in Zr the is seriously underestimated. ... 

Rettig W (1980) External and internal parameters affecting the dual fluorescence of p-cyano-dialkylanilines. J Lumin 26 21 16... 

At the first level of detail, it is not necessary to know the internal parameters for all the units, since what is desired is just the overall performance. For example, in a heat exchanger design, it suffices to know the heat duty, the total area, and the temperatures of the output streams the details such as the percentage baffle cut, tube layout, or baffle spacing can be specified later when the details of the proposed plant are better defined. It is important to realize the level of detail modeled by a commercial computer program. For example, a chemical reactor could be modeled as an equilibrium reactor, in which the input stream is brought to a new temperature and pressure and the... 

The summations in Eq. (8) and (9) usually extend over all internal parameters, independent and dependent, i.e. the potential constants in these expressions are also not all independent. For example, the nonsymmetric tetrasubstituted methane CRXR2R3R4 possesses five independent force constants for angle deformations at the central carbon atom, whereas in our calculations we sum over the potential energy contributions of the six different angles (only five are independent ) at this atom using six different potential constants for angle deformations. The calculation of the independent force constants, which is necessary for the evaluation of the vibrational frequencies, will be dealt with in Section 2.3. 

The subscript e means that the second derivatives are taken for internal parameters of the known or assumed molecular geometry.) It then follows that, in principle, to every molecule a F-matrix is assigned with molecule-specific force constants Fd.Transferability can only be expected for molecules which contain qualitatively and quantitatively very similar internal coordinates For instance, a force field which reproduces very well frequencies of n-al-kanes (from which it was derived) gives significantly worse results for branched alkanes... 

FREG JENCIES U/C 0 AND RELATIVE EIGENVECTOR COMPONENTS (CHANGES IF INTERNAL PARAMETERS (LEFT COLUNN) IN A AND RAD/ RESPECTIVELV)... 

The NH3 molecule is generally agreed to have a trigonal pyramidal structure, characterized by three internal parameters d = 101 pm, z0 = 38 pm, a = 68°, and with nitrogen at the apex, over a trigonal array of hydrogen atoms. 

Thermal treatment, applied to honey, may destroy vitamins and bionutrients, and produce a simultaneous decrease in diastase activity and an increase in HMF content. Honey treatment temperature and time must be limited when pasteurising and stabilising it both diastase activity and HMF content are national and international parameters used as controls so as to limit thermal treatment application. HMF can be formed by hexose dehydration in acid media or by the Maillaid reaction [11,12]. According to Ibarz et al., HMF formation can be described by a second order kinetics (auto-catalytic), with the following equation as expression model [13] ... 

The results obtained from the experimental studies confirm that the information-processing functions predicted by the pertinent analytical models can be achieved experimentally. Moreover, these results support the view that artificial biochemical neurons can be implemented in practice for informationprocessing purposes. Furthermore, because of the very high dependence of the system function on the internal parameters and the relations between them, the analytical models developed are essential tools for the engineering design of such systems as well as for determination of the operational parameters required for these systems to perform the information-processing function desired. 

A sublattice phase can be envisaged as being composed of interlocking sublattices (Fig. 5.3) on which the various components can mix. It is usually crystalline in nature but the model can also be extended to consider ionic liquids where mixing on particular ionic sublattices is considered. The model is phenomenological in nature and does not define any crystal structure within its general mathematical formulation. It is possible to define internal parameter relationships which reflect structure with respect to different crystal types, but such conditions must be externally formulated and imposed on the model. Equally special relationships apply if the model is to be used to simulate order-disorder transformations. 

In a similar vein it was later shown that all the internal parameters [x for M(2) and x,y,z for 0] could be determined by maximising the volume subject to the constraint of all four M-0 distances being kept equal and constant. Finally, taking the M-O distance from tables , the lattice parameter could be calculated. Table 5 lists parameters for the real, the maximum volume, and the ideal [metal atoms as in CusAu, O centering the... 

TABLE 19. Analysis of the normal modes of cyclopropane using, as internal parameter modes, adiabatic modes from Reference 163 ... 

All frequencies in cm HF/6-31G(d,p) calculations. Each normal mode is dissected into internal parameter associated vibrations according to Reference 162. Compare with Figure 20. 

In the broadest sense, stability of emulsions should be defined as maintenance of an initial state that was attained after homogenization of the two (or more) liquids (Sjoblom, 1996). The initial state of the emulsion can be defined by a set of internal parameters. The primary parameters used to describe the state of an emulsion are droplet size distribution and concentration, since the bulk properties of emulsions such as color, texture, and taste are primarily a function of these two colloidal parameters (McClements, 1999). In selected cases it may be necessary to include additional parameters such as pH and microbial load to further define the initial state of the emulsion. 

Support Vector Machine (SVM) is a classification and regression method developed by Vapnik.30 In support vector regression (SVR), the input variables are first mapped into a higher dimensional feature space by the use of a kernel function, and then a linear model is constructed in this feature space. The kernel functions often used in SVM include linear, polynomial, radial basis function (RBF), and sigmoid function. The generalization performance of SVM depends on the selection of several internal parameters of the algorithm (C and e), the type of kernel, and the parameters of the kernel.31... 

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