Functions meaning

The localized natme of the nucleai functions means that these reduce to classical equations of motion... 

A potential advantage of methods based on a series expansion of the free energy is that the convergence of the series is determined by the A dependence of the potential energy function meaning that the efficiency of the approach could be enhanced by a judicious choice of coupling scheme. 

A table giving the characteristic function, mean, and variance of some important probability distributions appears in Fig. 3-6. 

Distribution Probability Density Function Characteristic Function Mean Variance... 

Fig. 3-6. Some Typical Characteristic Functions, Means, and Variances.

Other thermodynamic quantities such as chemical potential and entropy also follow directly from the partition function, as we demonstrate later on. However, to illustrate what a partition function means, we will first discuss two relatively simple but instructive examples. 

Figure 9.9. Infinite functions in a periodic world. Using a function (black line) as an orientation function means to wrap it around the orientation sphere. Only one branch of a LORENTZ distribution at the right side of the equator is sketched. Shape change occurs... 

Prosite is perhaps the best known of the domain databases (Hofmann et al., 1999). The Prosite database is a good source of high quality annotation for protein domain families. Prosite documentation includes a section on the functional meaning of a match to the entry and a list of example members of the family. Prosite documentation also includes literature references and cross links to other databases such as the PDB collection of protein structures (Bernstein et al., 1977). For each Prosite document, there is a Prosite pattern, profile, or both to detect the domain family. The profiles are the most sensitive detection method in Prosite. The Prosite profiles provide Zscores for matches allowing statistical evaluation of the match to a new protein. Profiles are now available for many of the common protein domains. Prosite profiles use the generalized profile software (Bucher et al., 1996). 

The amine function means that local anesthetics exist either as the neutral amine or positively charged ammonium cation, depending upon their dissociation constant (pKa value) and the actual pH value. The pKa of typical local anesthetics Ues between 7.5 and 9.0. The pka indicates the pH value at which 50% of molecules carry a proton. In its protonated form, the molecule possesses both a polar hydrophilic moiety (protonated nitrogen) and an apolar lipophilic moiety (ring system)—it is amphiphilic. 

Pregabalin is eliminated from the systemic circulation primarily by renal excretion as unchanged drug, with a mean elimination half-life of 6.3 hours in subjects with normal renal function. Mean renal clearance was estimated to be 67 to 80.9 mL/min in young healthy subjects. Because pregabalin is not bound to plasma proteins, this clearance rate indicates that renal tubular reabsorption is involved. Pregabalin elimination is nearly proportional to Ccr. 

Like E, P, and V, His estate function, meaning that its value has only to do with the state of the system and nothing to do with how the system got to that state. Heat (q) is not a state function it s simply a form of energy that flows from warmer objects to cooler objects. 

The p-function means take the log of a number, and then change the sign. ... 

TABLE 7.3 NPD Functions, Means, Variances, and Moment of Some Model Batch and Flow Systems with Recirculation... 

Table 1 Known properties of the exact density functional. (+- means some, ++ means most)...

We see that, for atoms or molecules more complex than beryllium, the use of correlated basis sets of Hylleraas type rapidly becomes infeasible and the Cl method and its variants become more attractive. For a correlated basis, the number of terms required to reach a particular metric order can become hopelessly large. In a 10-electron problem like neon, 1596 terms are needed to construct a wave function complete through u = 2. If instead the wave function is limited to a single rfj factor per term, this number is reduced to 561 terms, still a sizeable number for such a low metric order. It must also be kept in mind that antisymmetrizing the wave function means that each term... 

The second assumption is the unique functionality [72] of the bridge function, meaning that B = B [y] is a simple function of the indirect correlation function, as expressed in the majority of the approximations for the bridge function. Changing the integration variable from X to y, and integrating by parts yields... 

NMDA dysfunction. Although, the functional meaning of this upregulation is subject to speculation, it has potential therapeutic implications that we will discuss here. 

This process assumes advance knowledge of how many basis functions (or data clusters) will be required to appropriately partition the data space. There are numerous heuristic methods of addressing this issue. Since training radial basis function networks is rapid, it is easy to start with a small number of centers and iteratively increase the number until no further benefit is noticed. Note that the dimension of the basis function means is the same as the dimension of the input data vectors. 

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