Intensive form

The main idea of stage decomposition (see Figure 9.10) is to remove the ties between the scenario subproblems of the 2S-MILP by fixing the first-stage variables. The 2S-MILP is written in its intensive form [9], where the resulting master problem is... 

This relationship is expressed in extensive properties that depend on the extent of the system, as opposed to intensive properties that describe conditions at a point in the system. For example, extensive properties are made intensive by expressing them on a per unit mass basis, e.g. s = S/m density, p 1 /v, v V/m. For a pure system (one species), Equation (1.2) in intensive form allows a definition of thermodynamic temperature and pressure in terms of the intensive properties as... 

Unstable radionuclei result on subjecting the nuclei of some elements to neutron bombardment. During the decay process, in which the radionuclei return to more stable forms, characteristic radiation is emitted. The energy of the radiation is characteristic of the element, and its intensity forms the basis for quantitative elemental analysis. The advantages of NAA for trace analysis include low detection limits, good sensitivity, multi-element capability and relative freedom from matrix effects. However, for successful application of this technique skilled personel are required and because of the low sample throughput the amount of work involved in the analysis of column fractions, for example, is prohibitively high. In addition, it may take up to several weeks before the results are available. Further, only few laboratories have easy access to a neutron source. 

It is up to the implementation of the REACH system to make sure, that this intensive form of cooperation will mobilise synergies, which - contrary to... 

I experienced in a most intense form vivid color and tex-... 

Next to hydropower, wind energy is generally believed to be the most cost-effective, least capital-intensive form of alternative primary energy. 

The decrease of the polarization with increasing field is in strong contrast to normal NMR, where the Boltzmann population differences increase linearly with Bq. The approximate proportionality between h)q5erfine coupling constant and polarization intensity forms the basis of identifying paramagnetic... 

Some discussion should be devoted to the conditions under which two-strand helices can be formed. As has been shown, the configuration results in a circular dichroic spectrum differing markedly in intensity, form, and position on the wavelength scale from that of the single-chain helix. 

Before proceeding, we note again that the equations thus far have been entirely in their extensive form. Each can be converted to the intensive form by dividing each... 

In iS Relaxation, the static magnetic field is applied parallel to the initial spin direction (x axis of Fig. 3). Where there are no magnetic interactions, the hf relaxation of Mu and of pseudo- Mu wiU be the only source of spin relaxation, and p spin in any other chemical states wiU not evolve. Where there are electric or nuclear spins that interact with p" spin, the latter will start to evolve at a rate depending on the magnetic field intensity formed by the electric or nuclear spins. The experiments are performed using positron counters placed at the upstream and/or downstream positions of the p" beam (Dj and Dj in Fig. 3). The count rates of the counters, Rj(t) and R ft), are described using Eq. 3 as. 

Since the definition (4.2.1) is a linear combination of thermodynamic properties, all relations among extensive properties, such as those in Chapter 3, can be expressed in terms of residual properties. Examples of such relations include the four forms of the fundamental equation and the Maxwell relations. Moreover, using the expressions developed in 4.1.4 for ideal-gas mixtures, the following intensive forms for residual properties are obtained ... 

We now relate the two kinds of residual properties introduced in 4.2.1 and 4.2.2. First write the intensive form of the definition (4.2.1) for isobaric residual properties,... 

Using the intensive form of (3.3.38) for the volume derivative of u, we find... 

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