Discrete quantities

Tracer Type. A discrete quantity of a foreign substance is injected momentarily into the flow stream and the time interval for this substance to reach a detection point, or pass between detection points, is measured. From this time, the average velocity can be computed. Among the tracers that have historically been used are salt, anhydrous ammonia, nitrous oxide, dyes, and radioactive isotopes. The most common appHcation area for tracer methods is in gas pipelines where tracers are used to check existing metered sections and to spot-check unmetered sections. 

The results of the theory of quantum mechanics require that nuclear states have discrete energies. This is in contrast to classical mechanical systems, which can have any of a continuous range of energies. This difference is a critical fact in the appHcations of radioactivity measurements, where the specific energies of radiations are generally used to identify the origin of the radiation. Quantum mechanics also shows that other quantities have only specific discrete values, and the whole understanding of atomic and nuclear systems depends on these discrete quantities. 

Since discrete quantities are trapped and transferred, the delivery pressure and flow varies, as shown in Figure 32.21, which also illustrates how increasing the number of cylinders in a reciprocating pump reduces fluctuations. In the case of lobe and gear pumps the fluctuations are minimized by speed of rotation and increasing tooth number, but where, for control or process reasons, the ripple in pressure is still excessive, means of damping pulsations has to be fitted. Often a damper to cope with this and pressure pulses due to valve closure is fitted, and two types are shown in Figure 32.22. 

A quant is a discrete quantity of any material (e.g. final product, raw material). This discrete quantity is called the quant size. The quant size may be chosen as needed. 

There was another clue, too. In 1901 the German physicist Max Planck had propounded his quantum theory and shown that atoms emit light in certain discrete quantities, or quanta. An atom could emit one quantum of light, or two, or six, or any other whole number. But it couldn t emit one and a half quanta, or three and a third, or any fractional number. Bohr realized that Planck s result could be explained if the electron in a hydrogen atom could revolve around the nucleus only in certain prescribed orbits with definite energies. It could follow these orbits, but not any in between. An atom emitted light when an electron suddenly made a jump from one orbit to another. 

Lot discrete quantity of coal for which the overall quality to a particular precision needs to be determined (ASTM D-2234). 

Moreover, the troubles for Aristotle s scheme do not end with this list of highest kinds—Kant s criticism extends to Aristodes intra-categorial divisions of quantity and quality as well. Aristode divides each of these categories into several distinct species quantity divides into continuous and discrete quantities, the former of which divides into body, line, surface, time and place, the latter of which divides into... 

Despite the fact that time s definitional posteriority to number allows one to focus attention on number itself, one complication does at this point emerge. In the Categories, time and number occur in distinct non-subordinate genera. Time, according to Aristode, is continuous, but number is discrete—so the definition from the Physics, which would make rime a kind of number and hence a discrete quantity, does not seem to fit with the Categories differentiation. 

The identification of quantity with unlimited extension thus allows for a derivation of the species in quantity. The main divisions in the category of quantity have already been derived. Continuous quantity and measurable quantity are convertible—and they arise from the limiting of extension by form-m. Discrete quantity and numerable quantity are likewise convertible—and they arise from the limiting of form matter composites by forms-c. And because number, owing to the elimination of Xoyog, is the only species under numerable quantity, we can suppose that numbers (of F s) just are limited pluralities of a certain sort. The divisions among the types of continuous quantity, then, flow from the dimensionality of extension itself. Body is limited measurable quantity in three dimensions surface, limited measurable quantity in two dimensions and line, limited measurable quantity in one dimension.9... 

The new media that are commercially available possess many distinct characteristics some are completely free of animal-derived components, others are serum-free, sometimes requiring addition of some protein fraction or containing a discrete quantity of proteins. Another class is protein-free media, which can include components derived from animals, plants, or yeast hydrolysates. In some cases, the development of novel media is unnecessary, as it is sufficient to supplement basal medium with a few known specific components. It is emphasized that the final osmolality of the formulated medium should be compatible with cellular tolerance, as discussed in Chapter 2. 

A probability distribution is a mathematical description of a function that relates probabilities with specified intervals of a continuous quantity, or values of a discrete quantity, for a random variable. Probability distribution models can be non-parametric or parametric. A non-parametric probability distribution can be described by rank ordering continuous values and estimating the empirical cumulative probability associated with each. Parametric probability distribution models can be fit to data sets by estimating their parameter values based upon the data. The adequacy of the parametric probability distribution models as descriptors of the data can be evaluated using goodness-of-fit techniques. Distributions such as normal, lognormal and others are examples of parametric probability distribution models. 

Those forms of acute viral hepatitis that have a normal clinical course also present discrete quantities of bile to be found as intraepithelial drops and intercellular cylinders or deposits in the stellate cells. These findings cannot be confirmed biochemically. A cholestatic course of disease is occasionally witnessed with a marked increase in alkaline phosphatase, particularly in older patients and in women. It is mostly accompanied by jaundice. The... 

In general terms, discrete quantities of matter possess thermodynamic properties that render this matter as hot or cold in relation to one another. Heat transfer describes the... 

When the parameter is a discrete quantity, Eq. 6.2 should be consistently rewritten for summation ... 

Design studies had shown that to recover the high heat content in the reactor effluent stream efficiently, it is desirable to split the effluent streams from each reactor into two parts, with the major part going to preheat the recycle gas to that reactor. A small fuel-fired heater is provided in each reactor train to trim the temperature of the recycle gas to that reactor. The excess hot effluent streams from all the reactors are combined and used to preheat and vaporize the methanol feed to the dehydration reactor. Although the process design is nearly in heat balance, a discrete quantity of... 

The new era in physics started in 1900 with a young German physicist named Max Planck. While analyzing the data on radiation emitted by solids heated to various temperatures, Planck discovered that atoms and molecules emit energy only in certain discrete quantities, or quanta. Physicists had always assumed that energy is continuous and that any amount of energy could be released in a radiation process. Planck s quantum theory turned physics upside down. Indeed, the flurry of research that ensued altered our concept of nature forever. 

English granunar, even though this is a math book you can only have less of a continuous quantity (e.g., less money) hut fewer of a discrete quantity (e.g., fewer dollars)—despite colloquial usage. Fortunately, however, you can have more of both ... 

The continuous variables are chosen to equal the discrete quantities when x = /= for k = 0,1,..., . Although the time dependence is not shown explicitly, A. (x) and g(x) can vary slightly with time because of the dependence of the global average free volume (/) on time. 

On p. 556, one can find the following historical sentence on the total energy denoted as Un which translates as Therefore, it is necessary to assume that Uat does not represent any continuous quantity that can be divided without any restriction. Instead, one has to understand that it as a discrete quantity composed of a finite number of equal parts. ... 

The magnitude and number of zones is given by the task and by all input quantities (both variable and discrete quantities) that enter the calculation of the failure probability. 

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