Connection natural

The reconstruction functionals may be understood as substantially renormalized many-body perturbation expansions. When exact lower RDMs are employed in the functionals, contributions from all orders of perturbation theory are contained in the reconstructed RDMs. As mentioned previously, the reconstruction exactly accounts for configurations in which at least one particle is statistically isolated from the others. Since we know the unconnected p-RDM exactly, all of the error arises from our imprecise knowledge of the connected p-RDM. The connected nature of the connected p-RDM will allow us to estimate the size of its error. For a Hamiltonian with no more than two-particle interactions, the connected p-RDM will have its first nonvanishing term in the (p — 1) order of many-body perturbation theory (MBPT) with a Hartree-Fock reference. This assertion may be understood by noticing that the minimum number of pairwise potentials V required to connectp particles completely is (p — 1). It follows from this that as the number of particles p in the reconstmcted RDM increases, the accuracy of the functional approximation improves. The reconstmction formula in Table I for the 2-RDM is equivalent to the Hartree-Fock approximation since it assumes that the two particles are statistically independent. Correlation corrections first appear in the 3-RDM functional, which with A = 0 is correct through first order of MBPT, and the 4-RDM functional with A = 0 is correct through second order of MBPT. 

R. M. Sharpe, Reproductive Biology. Another DDT Connection, Nature (1995) 538-39. 

It has been shown in /69/ (see also /123/) that the operator 0-1H 0 is explicitly connected, so that, invoking the same arguments as those used in proving the connected nature of the S operators in an ordinary exponential, the connectedness of S operator can be proved. The blocks representing the matrix—elements of eq.(7.2.14) will now have diagrams in which S-S contractions do not appear, and as a result a complete decoupling of the various m-valence... 

The ability to connect natural products to the genes that produce them has had two important consequences. The first consequence was stimulating genetic and biochemical studies into natural product biosynthesis, which increased our knowledge of the inner workings of these pathways dramatically and set the stage for the modification of existing pathways and the construction of new pathways. 

Boeke J.D. (1997). LINEs and Alus-the polyA connection. Nature Genet. 6 6-7. 

Some anaerobic organisms have developed only parts of the citric acid cycle, which they use exclusively to make the important precursors. These simple yet important reactions emphasize the truly connected nature of what we often artificially separate into pathways. They also illustrate the convergence of evolution to a few key molecules and metabolic steps. 

Chemical modification is known to be capable to change substantially sorption properties of silica surface [72]. Due to identity of support for a hydroxylated and chemically modified silica changes in sorption properties of different samples are to be connected naturally with corresponding peculiarities of p within the surrounding of functional groups. Thus in case of chlorinated silica (Figure 28.7) it should be noticed that p has substantially... 

Our group has found it most advantageous computationally to take advantage of the highly connected nature of the bond networks for the systems we simulate [8-11]. For example, in a diamondoid bond network one bond stretch can be part of as many as... 

Like the waste tips, the settling ponds must also be incorporated into the restored landscape. The choice of location for these features can be an important factor in this connection. Natural depressions in the ground, hollows or old quarry workings can suitably be used for the purpose. 

Pamiske, M. (2005) Plant-fungal associations cue for the branching connection. Nature 435 750-751. 

Pamiske, M. (2005) Cue for the branching connection. Nature, 435, 750-751 Pamiske, M. (2008) Arbuscular mycorrhiza the mother of plant root endosymbioses. Nature Review 6, 763-775... 

Nevertheless, the thermally connected nature of the monolith supports provides, in principle, an alternative mechanism of radial and axial heat transport, namely heat conduction, which is essentially not available for the random packing of catalyst pellets. The conduction within the solid phase of the pellets is, in fact, almost negligible, since only point contacts exist between the pellets, and convection in the gas phase dominates as the primary mechanism for heat exchange. Accordingly, the... 

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Word processing on a computer allows for rapid "quick-fix" control of letters, words, sentences, and paragraphs. Computer users also can walk to a printer and obtain a typed, "hard copy" of their document for study, revision, or dissemination. All these soon, certain, positive consequences are connected naturally to word-processing behavior. No wonder... 

Figure 1 Diagrammatic representation of NMR spectra illustrating carbon-carbon coupling. (A) The spectrum of two connected natural abundance carbon atoms. (B) The spectrum of two directly connected atoms. The separation between each doublet is equal to the carbon-carbon coupling constant (Jcc)- (C) The spectrum of three directly connected atoms.

DePinho R (1998) Transcriptional repression. The cancer-chromatin connection. Nature 391 535-536... 

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