Most probable object

Contaminants can be deposited on the surface of or can permeate PPE and other equipment. The longer a contaminant stays in contact with an object, the greater the probability and extent of permeation. Minimizing contact time is one of the most important objectives of a decontamination program. This is why contact time with hazardous material should be taken into consideration when considering different methodologies in the actual performance of the task itself... 

The task now is to select the linear combinations that will most probably correspond to independent parts of the reaction network with easily interpretable stoichiometry. A simplification of the data in the matrix can be achieved by such a rotation that the axes go through the points in Fig. A-2 (this is equivalent to some zero-stoichiometric coefficients) and that the points of Fig. A-3 are in the first quadrant (this corresponds to positive reaction extents) if possible. Rotations of the abscissa through 220° and the ordinate through 240° lead to attaining both objectives. The associated rotation matrix is ... 

It is reasonable to assume that the most probable values of the parameters have normal distributions with means equal to the values that were obtained from well test and core data analyses. These are the prior estimates. Each one of these most probable parameter values (kBj, j=l,...,p) also has a corresponding standard deviation parameter estimate. As already discussed in Chapter 8 (Section 8.5) using maximum likelihood arguments the prior information is introduced by augmenting the LS objective function to include... 

The proper setting for variographic analysis is a set of 60 representative increments (this is a minimnm requirement, 100 samples is always preferable if possible, the minimum number of increments ever snc-cessfnlly snpporting an interpretable variogram is 42), in order to cover well the specific process variations to be characterized. It is important to select a 0niin that is smaller than the most probable sampling frequency likely to be used in rontine process monitoring and QC. It will be the objective of the data analysis to... 

The deconvolved or restored object that we seek is the most probable number-count set nm. This is called the maximum-likelihood (ML) estimate of the object. It obeys simply... 

One of the more important factors affecting the isolation of radioactive waste is the rate of release of the radioactivity from the solid waste form to the environment. The most probable mechanism for release and transport of radioactivity from a solid waste form is by leaching of radioactive isotopes with groundwater. The objective of leach-testing various waste forms is to evaluate the rate at which specific hazardous radionuclides migrate from waste if and when the waste form comes in contact with groundwater. In this paper, measurement of leach rates of radioactive waste by a method which incorporates neutron activation is described. 

The analytical chemist will choose the appropriate analytical technique (e.g., chromatography, spectroscopy, or titration) to satisfy the technical objective based upon his or her expertise and past experiences with similar analytical problems. Often, however, the analyte itself dictates the kind of analysis method to be used. For example, a residual volatile solvent would most probably be analyzed by gas chromatography (GC), while a residual catalyst, such as palladium, would best be analyzed by atomic absorption or emission spectroscopy. 

Evidence for the presence of a black hole at the center of our galaxy comes from studies of the motion of stars in orbit around the center. The speeds of these stars decrease from the center as the inverse square root of the radius, which is the primary indication for the existence of a point mass at the center. The mass of the central object is measured to be 4 x 106 solar masses, which are contained within a sphere of less than 0.05 pc Eckart Genzel (1997) Ghez, Klein, Morris Becklin (1998) Ghez et al.(2003). No stellar or gas system can be so dense, indicating that the central object is most probably a black hole. The position of the black hole happens to coincide with the position of a strong radio source called Sagittarius A, which is thus identified with the central black hole. 

As investigators create files on enrolled (and excluded) patients, CRAs are probably making periodic checks of the completeness and internal consistency of these notations of patients visits, checking also for protocol violations. This is the first step in what should be an ongoing effort to ensure adherence to the protocol and accurate and complete documentation of all selected variables. Visual and computerized reviews by data managers are the next checks. Records are gathered from the various clinicians and checked again in these interim reviews of the raw data, the most important objectives are as follows ... 

New comets approaching the Sun for the first time are probably the most pristine objects of the solar system. Their relation to the C I carbonaceous chondrites and the similarity of their compositions suggest that they have come from the same source, the presolar nebula, from which also the Sun and the planets originated. It is, therefore, anticipated that a better quantitative picture of their... 

The most probable internal exposure pathway for the workers in a radiation controlled area is inhalation of radioactivities in air. The objectives of an air monitoring program in a radiation controlled area are as follows ... 

Maximum likelihood (ML) estimation can be performed if the statistics of the measurement noise Ej are known. This estimate is the value of the parameters for which the observation of the vector, yj, is the most probable. If we assume the probability density function (pdf) of to be normal, with zero mean and uniform variance, ML estimation reduces to ordinary least squares estimation. An estimate, 0, of the true yth individual parameters (pj can be obtained through optimization of some objective function, 0 (0 ). ModeP is assumed to be a natural choice if each measurement is assumed to be equally precise for all values of yj. This is usually the case in concentration-effect modeling. Considering the multiplicative log-normal error model, the observed concentration y is given by ... 

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