Prime symbols

An alternative approach is to assume, in the light of the experimental evidence just mentioned, that the reactions of cations and neutral molecules have similar values of (or, equivalently, of log ( /l mol and to try to calculate the difference which would arise from the fact that the observed entropy of activation for a minority free base includes a contribution from the acidic dissociation of the conjugate acid in the medium in question (see (5) above). Consider the two following reaction schemes one (primed symbols) represents nitration via the free base, the other the normal nitration of a non-basic majority species (unprimed symbols) ... 

The numbering scheme used for nucleosides maintains the independence of the two structural units The pyrimidine or purine is numbered m the usual way So is the car bohydrate except that a prime symbol ( ) follows each locant Thus adenosine is a nude oside of D nbose and 2 deoxyadenosine is a nucleoside of 2 deoxy d ribose... 

For biochemical reactions in which hydrogen ions (H ) are consumed or produced, the usual definition of the standard state is awkward. Standard state for the ion is 1 M, which corresponds to pH 0. At this pH, nearly all enzymes would be denatured, and biological reactions could not occur. It makes more sense to use free energies and equilibrium constants determined at pH 7. Biochemists have thus adopted a modified standard state, designated with prime ( ) symbols, as in AG°, AH°, and so on. For values determined... 

The starting point for London s treatment is a partitioning of the N electrons and v nuclei of a composite Hamiltonian H into two subunits (distinguished by prime and double-prime symbols) associated with respective Hamiltonian operators H and H",... 

Note that the constants in Equation (2.4) are distinguishable from those in Equation (2.3) because they lack the prime symbol. For both Equations (2.3) and (2.4), the terms in brackets represents the molar compressibility Z. Table 2.5 lists a few virial coefficients. 

All the unprimed symbols are in the plus part of y[Pg.39]

Second, there must be enough different kinds of primed symbols to fill the first column of y, the unused ones plus those of which there are at least two must be enough to fill the second column, etc. Again, by reasoning analogous to the above, one concludes that this part of the T-condition is satisfied if and only if... 

Ify(r) m y — w+) — w(p-) w(r-) boxes remaining empty. Also, we can fill with primed symbols, no two like ones in the same column, with nrv symbols not being used. In general, this partial transfer... 

The mechanisms which underlie enzyme inhibition are described more fully in Chapter 3. Suffice to say here that reversible inhibitors which block the active site are called competitive whilst those which prevent release of the product of the reaction are non-competitive. By preventing the true substrate accessing the active site, competitive inhibitors increase Km (designated by or K PParent). A non-competitive inhibitor decreases V m[Pg.42]

Here the prime symbolizes the lighter isotope. Also upper case Greek A is used for the isotopic difference (primed — unprimed), and lower case Greek 8 for the phase difference (vapor — condensed). The sections which follow further develop Equation 5.1 in order to arrive at more practical expressions involving measurable quantities. 

If we designate the heat and work quantities for the reverse cycle by primed symbols, the reverse and forward relationships are... 

Every chemical reaction reaches after a time a state of equilibrium in which the forward and back reactions proceed at the same speed. The law of mass action describes the concentrations of the educts (A, B) and products (C, D) in equilibrium. The equilibrium constant K is directly related to the change in free enthalpy G involved in the reaction (see p.l6) under standard conditions (AG° = - R T In K). For any given concentrations, the lower equation applies. At AG < 0, the reaction proceeds spontaneously for as long as it takes for equilibrium to be reached (i.e., until AG = 0). At AG > 0, a spontaneous reaction is no longer possible (endergonic case see p.l6). In biochemistry, AG is usually related to pH 7, and this is indicated by the prime symbol (AG° or AG ). 

In the text, the force-mass-length-time system of units has been used, with exceptions noted. Primed symbols refer to actual average values, as distinct from superficial or apparent values. A double prime indicates a point value. 

Here the superscript prime symbol refers to the dispersed phase, // is the viscosity, vr and ve the radial and tangential velocity components, 0 and r are the polar coordinates, and a is the surface tension. In the case under consideration,... 

Note that in the following analyses, we will drop the prime symbol. It should still be clear that deviation variables are being used. Then this linear representation can easily be separated into the standard state-space form of Eq. (72) for any particular control configuration. Numerical simulation of the behavior of the reactor using this linearized model is significantly simpler than using the full nonlinear model. The first step in the solution is to solve the full, nonlinear model for the steady-state profiles. The steady-state profiles are then used to calculate the matrices A and W. Due to the linearity of the system, an analytical solution of the differential equations is possible ... 

In this equation the standard state corresponds to the state that results from letting fw - 1 and xw - 1, in which case = n°s w. Letting/ - 1 is equivalent to saying that the surfactant behaves ideally, and letting xw - 1 is equivalent to having pure surfactant possessing the kind of interactions it has when surrounded by water. Physically, this corresponds to an infinitely dilute solution of surfactant in water. Using the primed symbol to represent the chemical potential of surfactant in micelles per mole of micelles, we write... 

In this two-dimensional space, we can also describe the chosen basis intensities as complementary, and let the prime symbol on R denote the complement of Rh so that... 

Primed symbols represent the steady-state value of the variable (e.g. 0 ). 

The three independent rate constants /cqK, and kfc = kf + k, Kf fully determine the kinetic properties of Scheme 2, because the rate constants kf for enolization are related to those of the reverse reactions, Equation (9), where Kw is the ionization constant of water. We use primed symbols for the enolization of the neutral ketone K. In the rate equation for enolization, the terms k(f and k e ATW/AT are kinetically indistinguishable (see Equation (10) below). 

Here A2 symbolizes a pseudo-scalar of A2 symmetry, normalized to unity. The actual form of this pseudoscalar need not bother us. The only property we will have to use later on is that even powers of A2 are equal to +1. Now we can proceed by defining rotation generators f x, y,t 2 in the standard way, as indicated in Table 1 [10]. Note that primed symbols are used here to distinguish the pseudo-operators from their true counterparts in real coordinate space. Evidently the action of the true angular momentum operators t y, (z on the basis functions is ill defined since these functions contain small ligand terms. 

Note that we have chosen to use primed symbols to emphasize the shell-theoretical nature of these labels, as opposed to true spatial symmetry assignments. The corresponding tetragonal symmetries can easily be found from the standard D h j D4k subduction relations, keeping in mind that the results must be multiplied by the pseudoscalar Blg representation of D4h, One thus obtains ... 

One difficulty in characterizing the CD for a typical p turn has been the lack of well characterized model compounds and the variability of the p turn structure in terms of allowable backbone dihedral angles. Early classification schemes described three general classes of p turns, termed types I, n, and III (see Table I). Type III turns resemble a single turn of a 3jo helix (see below), while types I and II are the most common structures for chain reversal found in globular proteins. Types I and IT have also been identified, with the prime symbols indicating an approximate 180° rotation of the peptide group of the i+lth residue. 

Next, one should note that the same protocol that had been developed in the proposed nomenclature for "organic" compounds is readily applied to coordination compounds in inorganic chemistry namely, the monocyclic compound which I.U.P.A.C. calls dichloro[N,N-dimethyl-2,2 -thiobis(ethylamine) -S,N ]platinum (II) (Figure 20), may be named, without resorting to different prefixes for the number two (di- and bis-) and without the prime symbol, as ... 

In all cases, no use has been made of the prime symbol, nor is there any need to delve into why IUPAC chooses to use double primes with the oxygen atoms in these names vs. their use of single primes with the examples they showed using nitrogen atoms [50],... 

However, a better form of this relation, especially for the mathematical ideal of a polymer as an infinitely repeating moiety, is expressed using that congruence property of number theory referred to as "modulus" [10], In this form, a prime symbol is affixed to a repeating locant number in the next module, rather than including more numbers than exist in the monomer. (7) thus becomes ... 

Although there have been two different uses of the prime notation when dealing with polymers, because this usage is limited to the monomer part of the name there should not be confusion with the occasional use of the prime symbol as part of the initial end group... 

A 1,4 link. The anomeric carbon is bonded to the oxygen atom on C4 of the second sugar. The prime symbol ( ) in 1,4 indicates that C4 is on the second sugar. 

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