Counting function

Counting functions are most often used as a convenient means of representing such phenomena as the arrival times of electrons at the plate of a vacuum tube, the times at which customers receive service in a waiting line or the times at which the atoms of a radioactive substance emit radiation. 

The Poisson process represents only one possible way of assigning joint distribution functions to the increments of counting functions however, in many problems, one can argue that the Poisson process is the most reasonable choice that can be made. For example, let us consider the stream of electrons flowing from cathode to plate in a vacuum tube, and let us further assume that the plate current is low enough so that the electrons do not interact with one another in the... 

In other words, if we assume that the counting function N(t) has statistically independent increments (Eq. (3-237)), and has the property that the probability of a single jump occurring in a small interval of length h is approximately nh but the probability of more than one jump is zero to within terms of order h, (Eq. (3-238)), then it can be shown 51 that its probability density functions must be given by Eq. (3-231). It is the existence of theorems of this type that accounts for the great... 

Co-representation matrices explicit forms, 733 multiplication of, 731 of the nonunitary group, 732 Corliss, L. M., 757 Corson, E. M., 498 Coulomb field Dirac equation in, 637 Coulomb gauge, 643,657,664 Counting functions, 165 Covariance matrix, 160 Covariant amplitude of one-particle system, 511 of one, two, etc. particle systems, 511... 

Figure 2. Potency vs. carbon count functions. (A) DICARB and ESCARB functions for Phase I mite (Eq. 3) and egg (Eq. 4) (B) Schematic illustration of underprediction for Phase I DICARB quadratic functions outside Phase I range in DICARB (C) Phase II DICARB functions vs. Phase I DICARB functions.

The potential association between the immune system and mood disorders has become a major topic of interest in biological psychiatry in the past decade. In general, three immune measures have been examined, namely white blood cell counts, functional measures of cellular immunity such as natural killer cell activity and immune cell markers as exemplified by human lymphoctye antigen (HLA). The cumulative data from these studies suggests that depressed patients have a decreased number of lymphocytes, reduced mitogen-induced lymphocyte proliferation and a reduction in the number of natural killer cells. However, this does not apply to all depressed patients. Furthermore, not all aspects of immune function... 

Assume that we have a set of energy levels Ej, j = 1,2,..., M, where M can be finite or infinite. The first and most elementary thing we can do with a set of energy levels is to count them. We introduce the counting function... 

Use the Excel help facility to look up the use of the COUNT function. Use the function to determine the number of data in each column of the spreadsheet of Figure 3-7. The count function is quite useful for determining the number of data entered into a given area of a spreadsheet. 

The COUNT function counts the number of nonzero cells in the range B2.B7 and displays the result in cell B12. Since we have found the sum of the values and the number N of data points, we can find the mean x by typing the following formula in cell B13. 

This can be viewed as a counting function, i.e., for any specific configuration XN, this quantity counts the number of pairs of particles occupying the elements dX and dX". Hence, the integral (2.31) is the average number of pairs occupying dX and dX". The normalization of pl2)(X, X") follows directly from (2.31) ... 

Each term in (2.92) contributes unity whenever Rj — Ri < Rc, i.e., whenever the center of particle j falls within the first coordination sphere of particle i. Hence, Q(R1 ) is the number of particles (j i) that falls in the coordination sphere of a particle i for a given configuration RN. Next, we define the counting function for this property by... 

Chemiluminescence at ambient temperature in this study was obtained from circular samples 1.0" in diameter (average wt. 0.5g), irradiated to 5MR only, which were placed in the sample well of an apparatus with automated counting function (Turner Designs, Inc. Model 20 Luminometer). The light emission was measured for several time periods of 120 seconds each. Average values and standard deviations were then obtained with pocket calculators. 

It is, of course, open to an NRP theorist to respond by claiming that we should broaden Lewis s notion of distinctness beyond the idea of events that enter into implication relations, figure in part-whole relations, and share parts and that we should count functional events and their realizers as nondistinct events, as well, and so the counterfactual dependence between them as noncausal. But NRP theorists are under a dialectical obligation to make a non-question-be ing case that such complications to the theory are needed. They must make a case that there are functional events — events with functional properties as their constitutive properties or essences. 

One way of generating new distribution functions from previous ones is by combining properties. For instance, the counting function for BE and the volume of the VP is... 

The corresponding counting function [in the following equations the subscript H stands for hydrogen bonds]... 

Since a digital controller necessarily includes a very accurate electronic clock, both pulse coimtmg and conversion to velocity can be implemented in software (i.e., made a part of the controller program). Hardware implementation of pulse counting may be necessary if time-intensive counting would divert the controller from other necessary control functions. A special-purpose 1C, known as a quadrature decoder/counter interface, can perform the decoding and counting functions and transmit the count to the controller as a data word. 

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