Discrete versus continuous

The arguments generally adopted for choosing a continuous time variable are that  

The idea that time has no objective existence but depends on events led some scientists to abandon the assumption that it is a continuous variable. Following the establishment of the Planck-Einstein quantum theory, it was suggested by Poincare and others that time is quantized one calculation gave the value 10 s to the chronon . 

Perhaps the best argument for time quantization (at least in the empirical spirit of quantum mechanics) is that we perceive temporal intervals of finite duration rather than durationless instants and it is dangerous to assume that the world has properties that can never be observed. But this psychological argument, as developed for example by Bergson, provides no quantitative justification for a division of physical time into chronons of the order of lO s. (Brush, 1982) 

Weaker arguments could have been made for adopting continuous time analogue computers operate in continuous time, and certain physicochemical quantities can be transduced continuously. However, it is important to note that in most applications the real time is transformed to state-time (e.g. number of generations). 

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Discrete versus continuous drug regulation development... 

DISCRETE VERSUS CONTINUOUS APPROACHES TO ULTRASOUND-ASSISTED SAMPLE PREPARATION... 

DISCRETE VERSUS CONTINUOUS ULTRASOUND-ASSISTED LEACHING... 

Long- and short-term memoiy Frequency and repetitiveness Continuity (discrete versus continuous)... 

Dinger DR, Punk JE. Particle packing III - Discrete versus continuous particle size. Interceram 1992 41(5) 41-6. 

Table 3.3 summarizes the history of the development of wave-profile measurement devices as they have developed since the early period. The devices are categorized in terms of the kinetic or kinematic parameter actually measured. From the table it should be noted that the earliest devices provided measurements of displacement versus time in either a discrete or continuous mode. The data from such measurements require differentiation to relate them to shock-conservation relations, and, unless constant pressures or particle velocities are involved, considerable accuracy can be lost in data processing. 

Optical devices or optical systems have provided most of the available strong shock data and were the primary tools used in the early shock-compression investigations. They are still the most widely used systems in fundamental studies of high explosives. The earliest systems, the flash gap and mirror systems on samples, provided discrete or continuous measurements of displacement versus time. 

In Figure 4.3, the major milestones in dmg regulatory development in the 10 countries are presented as a time-scale, to illustrate discrete development versus continuous development of dmg regulation. 

Note that if Bn is zero, then T13 and T23 are also zero, so Equation (5.81) reduces to the specially orthotropic plate solution. Equation (5.65), if D11 =D22- Because Tn, T12, and T22 are functions of both m and n, no simple conclusion can be drawn about the value of n at buckling as could be done for specially orthotropic laminated plates where n was determined to be one. Instead, Equation (5.81) is a complicated function of both m and n. At this point, recall the discussion in Section 3.5.3 about the difference between finding a minimum of a function of discrete variables versus a function of continuous variables. We have already seen that plates buckle with a small number of buckles. Consequently, the lowest buckling load must be found in Equation (5.81) by a searching procedure due to Jones involving integer values of m and n [5-20] and not by equating to zero the first partial derivatives of N with respect to m and n. 

Continuous-time versus discrete-time approaches for scheduling of chemical... 

Floudas, C.A. and Lin, X. (2004) Continuous-time versus discrete-time approaches for scheduling of chemical processes a review. Computers and Chemical Engineering, 28, 2109-2129. 

Obtaining Eft), t, and of from experimental tracer data involves determining areas under curves defined continuously or by discrete data. The most sophisticated approach involves die use of E-Z Solve or equivalent software to estimate parameters by nonlinear regression. In this case, standard techniques are required to transform experimental concentration versus time data into Eft) or F(t) data the subsequent parameter estimation is based on nonlinear regression of these data using known expressions for Eft) and F t) (developed in Section 19.4). In the least sophisticated approach, discrete data, generated directly from experiment or obtained from a continuous response curve, are... 

Medication resistance. Sackeim et al. (1990) conducted a prospective, naturalistic study of relapse rates in 58 patients who were followed up to 1 year after ECT. The investigators used methods similar to those of Prudic et al. (1990) the patients were rated for their degree of medication resistance during the index episode before ECT. In most cases, continuation pharmacotherapy was at the discretion of the patient s private physician. Relapse following ECT was twice as common in patients who were medication resistant before ECT than in nonresistant patients (64% versus 32%). Eurther-more, among medication-resistant patients, the adequacy of continuation pharmacotherapy had no effect on relapse rates. In a lithium continuation trial post-ECT, Shapira et al. (1995) also found that patients who were medication-resistant were more likely to relapse than were patients who were not known to be medication-resistant before ECT. 

Continuous versus Discrete Models The preceding discussion has focused on systems where variables change continuously with... 

The depletion layer profile contains information about the density of states distribution and the built-in potential. The depletion layer width reduces to zero at a forward bias equal to and increases in reverse bias. The voltage dependence of the jimction capacitance is a common method of measuring W V). Eq. (9.9) applies to a semiconductor with a discrete donor level, and 1 is obtained from the intercept of a plot of 1/C versus voltage. The 1/C plot is not linear for a-Si H because of the continuous distribution of gap states-an example is shown in Fig. 4.16. The alternative expression, Eq. (9.10), is also not an accurate fit, but nevertheless the data can be extrapolated reasonably well to give the built-in potential. The main limitation of the capacitance measurement is that the bulk of the sample must be conducting, so that the measurement is difficult for undoped a-Si H. 

The integral we are trying to evaluate (/ of Equation A.3-1) equals the area under the continuous curve of y versus x, but this curve is not available—we only know the function values at the discrete data points. The procedure generally followed is to fit approximating functions to the data points, and then to integrate these function analytically. 

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