N-equivalent sites

We suppose that we have a gas of n electrons moving between N equivalent sites, and N>n. Then we have to ask whether or not such a material will conduct at low temperatures. There are several possibilities. 

The Hill s interaction coefficient, h, is a measure of the strength of interaction among n-sites. If the n-equivalent sites are noninteracting, then h = 1, whereas h approaches n (number of equivalent sites) for the strongly interacting n-equivalent sites. 

The first case of multiple-site bindings involves a biomacromolecule with n equivalent sites (each of the n sites has the same affinity, K for the ligand) and the binding is non-cooperative (each of the n sites is noninteracting/independent). Consideration of the stereochemistry of the bounded A for n equivalent sites suggests that there are... 

Rotation of whole, rigid molecules on lattice sites in crystals Rotation about an n-fold axis, or hopping between n equivalent sites, produces an averaged tensor, one of whose principal axes, r, lies along the rotation axis. The location of the other two principal axes, s and will be in the plane orthogonal to r, and they are fixed with respect to the lattice and not the molecules. Thus,... 

Consider a system with more than one equivalent exchangeable site, each of which contributes a factor of this form in the numerator for such sites on the transition state and in the denominator for those on the reactant. That is, for n such sites the factor is (l - d + xni)"/(1 - d + d< r) Then, if there are other sites inequivalent to these, corresponding factors for them also appear. The final expression, referred to as the Gross-Butler equation,23 is... 

The compounds described herein were prepared by three methods. The first route involves deprotonation/substitution at the N-H sites of 1, the second consists of a cleavage reaction of an Si-N derivative of 1 with PhBCI2, and the third route is a transamination reaction between a bis(dimethylamino)boryl derivative of 1 and an aliphatic diamine. In the first approach, compound 1 is deprotonated by treatment with one equivalent of n-BuLi. Quenching of the resulting anion with various electrophiles produces the monosubstituted products 2-4 (eq 3). 

The soil was collected from the Mezquital Valley, located near Pachuca in the State of Hidalgo (Mexico). The irrigation water used was slightly alkaline with a pH of 8.4. The experiment was carried out under greenhouse conditions. Soil collected from three sub sites was placed into cylindrical pots. Five treatments were established in order to study the effect of wastewater and urea on the cultivation of maize (Zen mays L.). The treatments were a) SMWW, maize plant plus wastewater b) SMUREA, maize plant plus urea as fertilizer c) SUREA, uncultivated soil and urea as fertilizer d) SWW, uncultivated soil plus wastewater and e) SCONTROL treatment, soil plus tap water. Soils from the SMWW and SWW treatments were irrigated with 1000 mL of wastewater every 7 days from the first day onwards, making a total of 13 times overall. This means that a total amount of mineral N equivalent to 120 kg N ha-1 was added to each maize plant, i.e. the recommended amount of N fertilizer for maize. 

The equivalent of the tryptic fragment of human transferrin receptor has been expressed in Chinese hamster ovary cells and its structure determined at a resolution of 0.32 nm (Lawrence et ah, 1999). The asymmetric unit of the crystals contains four transferrin receptor dimers. Interpretable electron density is found for the entire tryptic fragment except for Arg-121 at the amino terminus, and density is also seen for the first N-acetylglucosamine residue at each of the N-glycosylation sites. The transferrin receptor monomer is made up of three distinct domains, organized such that the dimer is butterfly shaped (Figure 5.10, Plate 7). The likely orientation of the dimer with respect to the plasma membrane has been assigned on the basis of the... 

This result is related to probability and arises for the same reason that if you reach into a barrel containing 50% white balls and 50% black balls, you will pull out one of each just twice as often as you will pull out a pair of white or a pair of black. In the general case of n equivalent binding sites, the microscopic formation constants K are related1213 to the stepwise constants Kt as follows ... 

The original derivation of the Langmuir equation (Langmuir, 1916) is a kinetic one. The adsorbent surface is pictured as an array of N equivalent and independent sites for localized adsorption (one molecule per site). The fraction of sites occupied by N molecules is 8 = N /Ns. 

N is the number density of molecule, and Ng is the number of equivalent sites (in a crystal). They are related by N = Ng/V, where V is the unit cell volume. The angle Sjf expresses the relation between the crystallographic (or laboratory) axis I and molecular a s for a particular constituent of the unit cell. The local field factors fi (ot)., etc., are related to the appropriate laboratory axis and frequency. For disordered materials, Ng=l. 

Consider an enzyme with n equivalent substrate binding sites. If the cooperativity in substrate binding is very marked (i.e., the factors a, b, c, etc., are very small numbers), then the concentrations of all enzyme-substrate complexes containing less than n molecules of substrate will be negligible at any [S] that is appreciable compared to Kb. Under this condition, the velocity equation will be dominated by the [S]" term. 

This theorem provides a connection between a degenerate irrep of dimension n — 1 and the existence of an orbit of n equivalent and equidistant sites. We will... 

Aniline has four different (nonequivalent) sites for possible substitution the two equivalent sites on nitrogen, the two equivalent ortho positions, the two equivalent meta positions and the unique para position. An alkylated aniline results from the replacement of one or more of these either N—H and/or C—H atoms with a group attached by a saturated carbon. 

If we consider that N molecules are adsorbed on a set of M equivalent sites (N < M) and that there are no interactions between adsorbed molecules, the grand partition function is [18]... 

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