Natural function

Properties can be computed by finding the expectation value of the property operator with the natural orbitals weighted by the occupation number of each orbital. This is a much faster way to compute properties than trying to use the expectation value of a multiple-determinant wave function. Natural orbitals are not equivalent to HF or Kohn-Sham orbitals, although the same symmetry properties are present. 

Lange PF, Wartosch L, Jentsch TJ et al (2006) C1C-7 requires Ostml as a p-subunit to support bone resorption and lysosomal function. Nature 440 220-223... 

C.G. Vayenas, S. Bebelis, and S. Ladas, Dependence of Catalytic Rates on Catalyst Work Function, Nature 343, 625-627 (1990). 

Lindenbach BD, Rice CM (2005) Unravelling hepatitis C virus replication from genome to function. Nature 436 933-938... 

Sallusto F, Lenig D, Forster R, Lipp M, Lanzavecchia A. Two subsets of memory T lymphocytes with distinct homing potentials and effector functions. Nature 1999 401 708-712. 

Because a hyperplane corresponds to a boundary between pattern classes, such a discriminant function naturally forms a decision rule. The global nature of this approach is apparent in Fig. 19. An infinitely long decision line is drawn based on the given data. Regardless of how closely or distantly related an arbitrary pattern is to the data used to generate the discriminant, the pattern will be classified as either o>i or <02. When the arbitrary pattern is far removed from the data used to generate the discriminant, the approach is extremely prone to extrapolation errors. 

Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371 683... 

The presence of serum-binding proteins. Some biopharmaceuticals (including insulin-like growth factor (IGF), GH and certain cytokines) are notable in that the blood contains proteins that specifically bind them. Such binding proteins can function naturally as transporters or activators, and binding can affect characteristics such as serum elimination rates. 

Step functions, pulses, and square waves can be generated with a low volume, chromatographic-type 4-way valve. We have found that the desired two gas mixtures are best made up and stored in cylinders rather than made continuously by blending two streams. At the time of the switch, there is a momentary stopping of the flow, and this usually results in a change in composition if the mixture is made by the continuous blending of two streams. By this method one or more spurious peaks are added to the desired step function. Naturally these are trivial for slow responses, but important for fast ones. 

OLIVER, S.G., From DNA sequence to biological function, Nature, 1996,379, 597-600. 

Rockman, H. A., Koch, W. J., and Lefkowitz, R. J. (2002) Seven-transmembrane-spanning receptors and heart function. Nature 415, 206-212. 

Jordan, B. A. and Devi, L. A. (1999) G protein-coupled receptor heterodimerization modulates receptor function. Nature 399, 697-700. 

Notice that how the shape function naturally enters this discussion. Because the number of electrons is fixed, the variational procedure for the electron density is actually a variational procedure for the shape function. So it is simpler to restate the equations associated with the variational principle in terms of the shape function. Parr and Bartolotti have done this, and note that because the normalization of the shape function is fixed,... 

Figure 8. Structures and functionalization nature of poly(styrene) derivatives reacted with TiClj.

It is convenient to categorize 7V-[(acyloxyjinelhy 11 derivatives according to the simple or complex (i. e., functionalized) nature of the COR " acyl group. Simple N-[(acyloxy)methyl] derivatives of amides are treated first. 

Davies PA, Pistis M, Hanna MC, Peters JA, Lambert JJ, et al. 1999. The 5-HT3B subunit is a major determinant of serotonin-receptor function. Nature 397 (6717) 359. 

Hazucha, M., and D. V. Bates. Combined effect of ozone and sulphur dioxide on human pulmonary function. Nature 257 50-51, 1975. 

Lange, P.F., Wartosch, L., Jentsch, T.J., and Fnhrmann, J.C. (2006) ClC-7 Requires Ostml as a p Subunit to Support Bone Resorption and Lysosomal Function. Nature 440, 220-223. 

The definition of what constitutes reactive or unstable functionality naturally varies somewhat, but there is also a good deal of consensus (aldehydes, alkyl halides, vinyl ketones, and so forth) [14,16-18]. 

Much of the focus of the following work was aimed at the previously mentioned Chemlok adhesive system. This was because it had been used extensively in a familiar marine application, we were acquainted with its long term performance so it could be used as a baseline for comparison with other commercial adhesive formulations. All of the commercial adhesives used, including Chemlok 205/220, are proprietary formulations, thus the exact functional nature of each adhesive is not available. 

The functional nature of some rate equations requires that rate constants occasionally can be of a mixed order, (i.e., they can have nonintegral dimensions with respect to reactant molarity). Whether the reaction order is an integer or a fractional value, its value n is obtained from the slope of a plot of reaction rate versus logio [Reactant]. 

Goodman CM, Choi S, Shandler S, DeGrado WF. Foldamers as versatile frameworks for the design and evolution of function. Nature Chem Biol 2007 3 252-262. 

---