Orthogonality measurement

Substituents on aromatic rings, where the objective is to obtain orthogonal measures which could be used for design of test set in QSAR modelling.[32]... 

To provide a method for the evaluation, or at least comparison between two analyzers probabilities of false alarms, a model for the prediction of FAR was devised, which is based on relating the total number of the analyzer s orthogonal measurement channels and the analyzer s signal-to-noise ratio (R, ) tio to the probability of analysis errors obtained imder specific test conditions, which also corresponds to errors predicted by ROC curves [8], as illustrated by the example in Fig. 9.3.14. The area above the ROC curve, 1-Az, represents the total instrumental error of the involved analyzer, and may be plotted by simply using the result of tests yielding values of FPF (False Positive Fraction) and FNF [16]. One set of specific test conditions assumed in early model computations consisted of a simple symmetry for FPF and FNF, leading to the symmetrical Decision Matrix and Proportions shown in Fig. 9.3.14. 

Figure 4 Orthogonality and peak capacity, p is estimated from orthogonality measures. Practical peak capacity available for separation is represented by the area marked A . Based on reference [48].

Afw is the area of the shear reinforcement arranged parallel to the shear force, with a pace Pf orthogonally measured along the direction of the shear force... 

This automatic velocity measurement method (AUTO-V) has also been suecessfijlly applied to other materials sueh as non-ferrous metals and even eeramics and plasties. The only requirement for this type of sequential velocity and thickness measurement is a certain isotropy of the material materials having anisotropie properties will lead to incorrect thickness readings due to the velocity difference in the two orthogonal directions. 

The last identity follows from the orthogonality property of eigenfunctions and the assumption of nomralization. The right-hand side in the final result is simply equal to the sum over all eigenvalues of the operator (possible results of the measurement) multiplied by the respective probabilities. Hence, an important corollary to the fiftli postulate is established ... 

These various techniques were recently applied to molecular simulations [11, 20]. Both of these articles used the rotation matrix formulation, together with either the explicit reduction-based integrator or the SHAKE method to preserve orthogonality directly. In numerical experiments with realistic model problems, both of these symplectic schemes were shown to exhibit vastly superior long term stability and accuracy (measured in terms of energy error) compared to quaternionic schemes. 

The term Q/TOF is used to describe a type of hybrid mass spectrometer system in which a quadrupole analyzer (Q) is used in conjunction with a time-of-flight analyzer (TOP). The use of two analyzers together (hybridized) provides distinct advantages that cannot be achieved by either analyzer individually. In the Q/TOF, the quadrupole is used in one of two modes to select the ions to be examined, and the TOF analyzer measures the actual mass spectrum. Hexapole assemblies are also used to help collimate the ion beams. The hybrid orthogonal Q/TOF instrument is illustrated in Figure 23.1. 

If, just before the ion beam reaches the ion detector, a pusher electrode is used alongside it to deflect the beam at right angles (orthogonal) to its original direction into the flight tube of a time-of-flight sector (TOP analyzer), the m/z values can be measured by the TOP section. 

Passive test The test object is mounted on the shake table and subjected to both horizontal (X and Pj movements or one cumulative orthogonal horizontal and one vertical ground movement simultaneously. Accelerometers are mounted on the shake table to measure its movements and also on the test object at its most vulnerable points. These points may be identified by the manufacturer or the user to monitor the behaviour of the object in such locations. 

Rather than using separate systems for horizontal and vertical wind measurements, a u-v-w anemometer system Fig. 19-9) sensing wind along three orthogonal axes, with proper processing to give average wind direction and (Tj, from the combination of the u and v components and w and o-, from the lO component may be used. 

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