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The restriction of applying equation (5.47) to an isolated system seems to seriously limit the usefulness of this equation since we seldom work with isolated systems. But this is not so the pre-eminent example of an isolated system is the universe, since neither mass nor energy can flow in or out of the universe. Thus, the isolated system shown in Figure 5,6 can be made the universe, with A the system of interest, and B the surroundings. When we designate the combined system as the universe, we can drop the subscript A in... 

To put this in words, when heat flows at constant temperature, the entropy change is equal to the heat transferred (Jt) divided by the temperature in kelvins (T). The units of A S are energy/temperature, or J/K. The subscript T in Equation is a reminder that the quantity of heat transferred depends on the conditions. This equation is restricted to processes that occur at constant temperature. 

Subscripts 1 and 2 refer to the positions before and after the restriction, respectively. Combining the continuity equation and Eq. (3-147) yields the total pressure change,... 

The characteristic ratio, C, is evaluated by RIS theory for polyethylene chains that contain randomly placed short branches. The size of the short branches ranges from methyl to octyl. Calculations are restricted to chains with few branches, where C is nearly a linear function of branch content. The calculations provide numerical values for (3 In C / d Pb)0, where P/, is the probability that a repeat unit has a short branch and zero as a subscript denotes the initial slope. 

A restriction enzyme is named according to the organism from which it was isolated. The first letter of the name is from the genus of the bacterium. The next two letters are from the name of the species. An additional subscript letter indicates the type or strain, and a final number is appended to indicate the order in which the enzyme was discovered in that particular organism. For example, Haelll is the third restriction endonuclease isolated from the bacterium Haemophilus aeqyptius. 

Instead of Je Lodge (46) derived another quantity called constrained shear recovery sIn this case a shear recovery is considered, where the liquid is constrained by boundary planes which are rigid and do not change their mutual distance during recovery of the liquid. Subscript oo means that the recovery is measured after an infinite time, reckoned from the moment that the shear stress is made zero. According to Lodge, a quite different type of recovery occurs, when the mentioned restrictions are released. This fact has already been noted in the first paragraph of this section. In the definition of Je, however, the mentioned restrictions are tacitly made. 

We have obtained the expression given in GT, p. 225 for the spectral function of free rotors moving in a homogeneous potential in the interval between strong collisions see also VIG, Eqs. (7.12) and (7.13). So, the subscript F means free. The subscript R in Eq. (74c) is used as an initial letter of restriction. Indeed, as it follows from the comparison of Eq. (77) with Eq. (74a), the second term of the last equation expresses the steric-restriction effect arising for free rotation due to a potential wall. If we set, for example, p = 7t, what corresponds to a complete rotation (without restriction) of a dipole-moment vector p, then we find from Eqs. (74a)-(74c) that LR z) = 0 and L(z) = Lj,(z). This result confirms our statement about restriction. ... 

However, for many of these species, some peculiarities strongly limit the number of published data. From the actinide list above, Np(VI) luminescence has been observed and characterized only in solid matrix (Dewey and Hopkins, 2000). Bk, Cf and Es are hardly available in large quantities and few papers have appeared on Am(III), due to its very short luminescence lifetime, so that in practice, actinide luminescence studies are more or less restricted to U(VI) and Cm(III). Similarly, the extensive lanthanide list above is restricted mostly to Eu(III), Gd(III) and Tb(III), with fewer papers devoted to the other lanthanides. Note that Eu(II), although luminescent, is not stable in solution under normal conditions which limits the number of studies. As a consequence, this chapter reflects the tendencies described above by presenting examples mostly from Eu(III), Gd(III), Tb(III) and from U(VI) and Cm(III) studies. In solution, these ions are solvated so that either the subscript aq or solv will be used, depending on the solvent of interest. 

The subscript on the wavefunction identifies it as the one with some particular value of n. n = 0 would force the wavefunction to vanish everywhere, so there would be no probability of finding the particle anywhere. Hence we are restricted to n > 0. 

The coefficient at A describes the linear response of the quantity A to the perturbation W. It can be given a rather more symmetric form. Indeed the amplitude of the j-th unperturbed state in the correction to the fc-th state is proportional to some skew Hermitian operator (the perturbation matrix W is Hermitian, but the denominator changes its sign when the order of the subscripts changes). With this notion and assuming that Wkk = 0 (see above) we can remove the restriction in the summation and write ... 

Based on the above discussion, the physics of the ion acceleration process can be theoretically modeled under the following assumptions, leading to the formulation of a relatively simple system of equations which can be investigated analytically and numerically. First of all, let us restrict our analysis to a one-dimensional geometry. The electron population can be described as a two-temperature Boltzmann distribution, where the subscripts c and h refer to the cold and hot electron components, respectively,... 

The subscript, specific surface area, unit mass that would be observed if the adsorbate were removed. GJ is defined as in Equation 9, except that it is now necessary to include the restriction that both n2 and [Pg.357]

We have included the double-primed subscripts in (2.68) to emphasise that the differentiation is performed with space-fixed nuclear centre-of-mass electronic coordinates held constant. Equation (2.68) can be appreciated when we realise that the total Hamiltonian is independent of / so that we can take the eigenfunctions PYlK to be independent of x also. This relationship provides a crucial restriction on the redundant coordinates its form is such that we could, if we wished, write down the inverses of equations (2.59), (2.60) and (2.61). 

As discussed earlier, the future of journals is clearly electronic. However, there are many reasons why journal articles are problematic in comparison to other documents such as web pages and databases. First, most chemistry journals (with the notable exception of Chemistry Central Journal, www.journal.chemistrycentral. com) are not open access, and thus the content of articles is restricted by the publishers. Although most universities and large organizations have institutional subscriptions to the popular journals, access usually requires validation on computer IP addresses or the use of private login credentials. Thus, automated access to this information by a computer is difficult. Further, it is unclear whether the terms under which journal articles are made available permit automated processing of the content... 

Most of the mass spectrometry journal sites contain tables of contents and abstracts. Many of these sites offer on-line access to the full articles although it is typically restricted to subscribers only. General information such as aims and scope, editorial board, instructions to authors, contact and subscription information are also found on these sites ... 

This general notation is deceptively simple. The bra is an excited determinant. There is an equation for each excited determinant, and each level of excitation leads to a different type of equation. Furthermore, the equations are all coupled, and they are non-linear in the amplitudes. However, they may be formulated in a quasilinear manner [27], and they have been solved for a wide range of CC schemes. The operator HN is the Hamiltonian written in second-quantized form minus the energy of the reference determinant, i.e. HN = H— < 0 /7 0 >. The subscript C restricts the operator product of HN and eT to connected terms. Once the CC equations have been solved, the CC correlation energy can be calculated from... 

For the sake of simplicity, consideration will be restricted to systems in which only one intermediary exists this will be denoted by the subscript r, and the other species will be denoted by the subscripts j(j = 1,..., iV — 1). The discussion and results are applicable qualitatively for a given chain carrier in flames containing any number of chain carriers. 

In the remainder of the chapter, attention will be restricted to steady-state, one-dimensional, consiant-area flows in which all particles travel at the same velocity and have the same chemical composition. Hence, djdt = 0, Vjj d/dx, d/dv, M = 1 (and the subscript j will usually be omitted), and... 

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