Real equivalent

Optical parametric oscillator (OPO, see 20) is the real equivalent to the radio frequency shifter however OPO can be replaced by a simple addition of a local oscillator (e.g. laser) through a beam splitter. Multiplication takes place at the level of detectors. For sake of S5mimetry, detectors can be placed at both output of the beam splitter, the intermediate frequency is then the output of the differential amplifier. 

There is no real equivalent or economical replacement for a hot asphalt membrane system. 

Radial equation 155 Radial function 209 Raman spectroscopy 285 Rank 317 Reaction field 258 Reaction path 234 Real equivalent 156... 

In the case of a plate column the performance of a real plate is related to the performance of a theoretical one by the plate efficiency. In the case of a packed column the height equivalent to a theoretical plate HETP) gives a measure of the contacting efficiency of the packing. 

A second recent development has been the application 46 of the initial value representation 47 to semiclassically calculate A3.8.13 (and/or the equivalent time integral of the flux-flux correlation fiinction). While this approach has to date only been applied to problems with simplified hannonic baths, it shows considerable promise for applications to realistic systems, particularly those in which the real solvent bath may be adequately treated by a fiirther classical or quasiclassical approximation. 

From a mathematical point of view, conformations are special subsets of phase space a) invariant sets of MD systems, which correspond to infinite durations of stay (or relaxation times) and contain all subsets associated with different conformations, b) almost invariant sets, which correspond to finite relaxation times and consist of conformational subsets. In order to characterize the dynamics of a system, these subsets are the interesting objects. As already mentioned above, invariant measures are fixed points of the Frobenius-Perron operator or, equivalently, eigenmodes of the Frobenius-Perron operator associated with eigenvalue exactly 1. In view of this property, almost invariant sets will be understood to be connected with eigenmodes associated with (real) eigenvalues close (but not equal) to 1 - an idea recently developed in [6]. 

Most of the SpartanView models on the CD have been constructed using quantum mechanical calculations although some simplifications have been used to accelerate the calculations This means that the models although closely resembling real molecules never precisely duplicate the properties of real molecules Even so the models are suf ficiently similar to real molecules that they can usually be treated as equivalent This is important because models can contain more types of information and models can be constructed for molecules that cannot be studied m the laboratory Also models can be joined together to make animations that show how molecules move... 

It is equivalent, when an ftk spectrometer is used, to re-apodization of the data. Curve fitting is a method of modeling a real absorption band on the assumption that it consists of a series of overlapped peaks having a specific lineshape. Typically the user specifies the number of peaks to attempt to resolve and the type of lineshape. The program then varies the positions, sizes, and widths of the peaks to minimize the difference between the model and the spectmm. The largest difficulty is in knowing the correct number of peaks to resolve. Derivative spectra are often useful in determining the correct number (18,53,54). 

MaxweU-Boltzmaim particles are distinguishable, and a partition function, or distribution, of these particles can be derived from classical considerations. Real systems exist in which individual particles ate indistinguishable. Eor example, individual electrons in a soHd metal do not maintain positional proximity to specific atoms. These electrons obey Eermi-Ditac statistics (133). In contrast, the quantum effects observed for most normal gases can be correlated with Bose-Einstein statistics (117). The approach to statistical thermodynamics described thus far is referred to as wave mechanics. An equivalent quantum theory is referred to as matrix mechanics (134—136). 

Operations The QRA team will need specific data on how the system is actually operated. For example, are the bypass valves normally left open to increase throughput, what happens when the high level alarm sounds, or do operators bypass interlocks to continue production Human actions/errors are usually dominant contributors to the real-world risks, and truthful data on actual process operations are vital to credible QRA results. Expect to commit one full-time equivalent for the life of the project. 

The values in Fig. 23-5 have to be corrected in the case of differing resistivity values because of the dependence of mutual inductance on the soil resistivity. This is achieved by substituting an equivalent distance, a instead of the real distance, a, giving ... 

---