Definition of times

The choice of capacity is sometimes a problem, and may change according to the particular circumstance. Sometimes using a definition of time constant, based on the above equations, is not very helpful and other means must be employed. For example, mixing time is a very important time constant relating to liquid mixing, and this is best obtained directly from empirical correlations of experimental data. 

Time is a fundamental property of the physical world. Because time encompasses the antinomic qualities of transience and duration, the definition of time poses a dilemma for the formulation of a comprehensive physical theory. The partial elimination of time is a common solution to this dilemma. In his mechanical philosophy, Newton appears to resort to the elimination of the transient quality of time by identifying time with duration. It is suggested, however, that the transient quality of time may be identified as the active component of the Newtonian concept of inertia, a quasi occult quality of matter that is correlated with change, and that is essential to defining duration. The assignment of the transient quality of time to matter is a necessary consequence of Newton s attempt to render a world system of divine mathematical order. Newton s interest in alchemy reflects this view that matter is active and mutable in nature... 

Relativity theory, with its rigorous operational definitions of time and space, led to many unexpected results that are contrary to common experience. One result was that the measured length of a body depends on the speed with which the body moves with respect to the observer. These new theorems from relativity theory removed apparent contradictions that had perplexed physicists in their measurements of the speed of light, and they also allowed prediction of a variety of new phenomena that since have been verified abundantly. 

What does time to steady-state mean Why is there no unique definition of time to steady-state for a linear first-order differential equation ... 

Aristode s definition of place, like his definition of time, makes place derivative upon another more fundamental quantity, in this instance surface. Unlike the definition of rime, however, the definition of place does not make immediately apparent the connection. But with only a litde interpretive work, such a connection does emerge. 

Aristotle s linking of numerical oneness with the having of unified matter, however, though it satisfies a common sense intuition about numerical identity, would seem to restrict the sort of entities that can be numbered to those entities that have matter. But, Aristode dearly thinks that there are entities that can be numbered that do not in any obvious way have. Motions, for instance, as Aristode s definition of time makes clear, can be numbered.6 So too can tones (Meta. 1016b24), categories, and unmoved movers (Meta. 1074al5). So it would seem that a fundamental tension exists in Aristode s account of number. 

The final section examines the biogeochemistry of selected chemical elements. Each of these chapters builds on earlier sections. Thus, the description of carbon will make use of the characteristics of biological systems, definitions of time-scales, and properties of the oceans described in earlier chapters. Five groups of substances are considered in Chapters 11 through 15. Chapter 16 brings us back to some of the questions important to society. 

The rate of a reaction is time dependent. It is therefore important that we know how to measure the period of time during which the observed change in concentration has taken place. Time may look like the easiest parameter to record, but this is not so. In foct the definition of time in kinetic studies deserves to be re-examined in much more detail. 

All circuits which contain inductive reactance and resistance have an X-to-R ratio, in practice between 2.0 and 100.00. In short-circuit analysis it is usually necessary to relate the asymmetrical current to the symmetrical current. This can only be done if the short-circuit power factor of the circuit and hence the X-to-R ratio is known. Table 8.1 shows the relationship between these parameters and currents. Normally the short-circuit power factor is low, between 0.01 and 0.45. It is customary in short-circuit analysis to assume that one of the phases has the worst-case situation of fully asymmetrical current. Figure 8.1 shows an example, together with the various definitions of times and currents. 

A dynamic programming model should distinguish between the decisions made at different points in time. The major reason for this is that the information available to the decision maker is different at different points in time—typically more information is available at later points in time (in fact, many people hold this to be the definition of time). 

Classically, this law is written with a time derivation and corresponds in that case to Faraday s law of induction. Here, one has written a generalized law valid independently of any definition of time. This law is also customarily written with a minus sign because of the choice of the generator convention for orienting current and potential difference. For harmonization, it is preferable to use the receptor convention used in most domains. (This point will be made clearer when a solenoid will be associated to other different dipoles as in Chapter 9.)... 

This illustrates the link between time, symmetry, and energy conservation, which is a great principle in classical physics. It also outlines the importance of defining the validity domain of any invariance rule or principle and that the notion of reversibility depends on the definition of time. 

The definition of time as a variable following (or controlling) the extent of an energy conversion is a local definition, valid in the considered system, even if the same variable is used for all conversions whatever the involved subvarieties. This opens to other conceptions of time, as for instance in Einstein s theory of spacetime, in which time depends on the localization in space. Also, the Formal (jraph theory allows considering some possible discontinuity or a granular structure of time through the use of evolution operators that may differ from temporal derivations. 

Figure 7.4 Definition of time response characteristics of an electron multiplier detector. The initiating event is here assumed to be an effectively instantaneous ( delta function ) flash of light, but could equally well be a single charged particle. Reproduced from Photomultiplier Tubes Basics and Applications (3rd Edn), Hamamatsu Corporation, with permission.

Table 4.1 Selected examples of studies using different ion sources/interfaces that fall under the broad definition of time-resolved mass spectrometry. Please refer to the text in this and the following chapters for discussion of representative interfaces and their applications. A large portion of the examples refer to the early-stage demonstrations of the newly developed techniques however, several examples of mechanistic and routine analyses have also been included...

We will briefly introduce examples of applications of microfluidic devices which enable rapid analysis of small volumes of dynamic samples with mass spectrometric detection. Please note that some of the discussed approaches are covered by the broad definition of time-resolved mass spectrometry (TRMS) (cf. Section 1.3), while others lay the foundations for possible TRMS measurements following further technical developments. 

Besides the commonly applied perturbative evaluation of spectroscopic signals, recently also nonperturbative descriptions have been considered. d08-iio Assuming, as usual, an optically thin sample, the only formal difference between the two formulations is whether the electric polarization P(t) is evaluated in a perturbative or nonperturbative manner. As a consequence, the definitions of time- and frequency-resolved PP signals are completely equivalent in both formulations. Besides the obvious point that one needs to propagate the wave function with a time-dependent Hamiltonian instead of an time-independent one, the calculation of PP signals appears to be rather similar in both formulations. 

Note that in most cases we can set r = L/V. Using the above definitions of time-space normalization we can introduce the following normalized pressure p, concentration c and temperature T ... 

Studies evaluating the possibility to use SBA in the diagnostic approach of liver disease have been performed in the last few years, in concomitance with the improving knowledge of their determinants in health and disease. The definition of timing of the measurement (fasting or postprandial or both) and the evaluation of its accuracy have been the main problems to be overcome. 

---