Measurement discrete data

For longer boreholes the data may need to be synchronized by comparing the return temperature not with the current time step but with the time step— n, where n is the travel time. The error minimized is the sum square error of the difference between the calculated and measured borehole heat exchanger return temperature. We have set up the analyses procedure in such a way that it is easy to select discrete data-windows for the calibration. 

The strategy depends on the situation and how we measure the concentration. If we can rely on pH or absorbance (UV, visible, or Infrared spectrometer), the sensor response time can be reasonably fast, and we can make our decision based on the actual process dynamics. Most likely we would be thinking along the lines of PI or PID controllers. If we can only use gas chromatography (GC) or other slow analytical methods to measure concentration, we must consider discrete data sampling control. Indeed, prevalent time delay makes chemical process control unique and, in a sense, more difficult than many mechanical or electrical systems. 

These measures, t and cr, are directly linked by theory to D and D/wL. The mean, for continuous or discrete data, is defined as... 

Malvern (Insitec) ECPS2 is designed to monitor and control particle size distributions from 0.5 to 1,500 pm, at concentrations up to 10,000 ppm, directly in pneumatic powder flow streams. Up to one thousand size distribution measurements per second are carried out at flow velocities from static to ultrasonic. Discrete data point, extracted from the log file, can be viewed. The data can also be viewed in tabular form and as a size distribution curve. Data can also be integrated over any selected range. A Statistical Process Control (SPC) option enables the file data to be viewed in standard control chart format either as an X or R chart. Various interface arrangements have been described, [203] ... 

Discrete Data. Generally, the computational methods used for the discrete data were the same as those used for the continuous data. The discrete computations of the components of the carbonate system, however, were an exception. In this case, the observables were titration alkalinity (TA) and the total CO2 (TCO2) rather than pH and calculated alkalinity (CTA). Both TA and TCO2 were measured with the GEOSECS titrators... 

Situations may arise, where the boundary conditions are unknown and only some experimental data in certain locations are known. In this case, the problem is defined as an inverse one. This situation often occurs in many branches of science and mathematics where only the values of some model parameters can be obtained from observed data or measured data. Data on electric potential can be obtained in galvanic corrosion as a set of discrete data with one free parameter due to measuring potential differences. This situation, where measurements on electric potential can be provided as a set of discrete data within simply connected domain Q imposes the problem to be inverse. 

The problem is to recover the current density, based on experimental data on electric potential. Let us consider a domain 1, to be a simply connected domain or a subdomain of a bigger domain which is not necessarily simply connected and bounded. Let potential measurements be known at some discrete points (j=l,...,N), located within Q. The general problem is formulated as follows given the discrete data on electric potential (f>] =1. ..N find field of current... 

It is necessary to calculate the real coefficient of diffusion D (x) of Equations (2.30M2.37) on the basis of the discrete data in the space of measurement Zj (x) (/ = 1,. .., M), which causes the minimum to the quadratic function ... 

A battery of tests developed by Dutka et al. 1986 to test the sediments of near-shore sites of Lake Ontario (Canadian part) is used to exemplify the definitions and some results of HDT. In Lake Ontario 55 sediment samples were tested, thus, the set E contains 55 objects. Dutka et al. classified their results and used discrete scores instead of the measured (raw) data. For our analysis we have adopted their classification. Thus, s, denotes the score of the i-th test of the battery. Five specific tests form the actual battery (1) Fecal Coliforms FC , as an indicator designed to control the health state of the sediments, (2) Coprostanol CP and (3) Cholesterol CH both being indicators of loadings by fecals, (4) Microtox tests MT and (5) Genotoxicity tests GT disclosing some kind of acute toxicity and the potential for carcinogenicity, respectively (see Table 3). 

Fig. 2.8 Porosity logs determined by resistivity measurements on three gravity cores from the South Atlantic (see also Fig. 2.7 and Table 2.1). Gray curve Boyce s (1968) values were used for the constants (a) and (m). Black curve (a) and (m) were derived from the slope and intercept of a linear least square fit. These values are given at the top of each log. Superimposed are porosities determined on discrete samples by weight and volume measurements (unpublished data from P. Muller, University Bremen, Germany).

Centrifugal analysers, discussed In Chapter 4, are discrete In nature. Sample collection and reagent dispensation take place In an automated dosing module. However, the transfer disc containing the radially arranged samples and reagents Is transferred manually to the analyser module, where reaction, signal measurement and data acquisition and treatment, all completely automated,... 

This section considers the response measurement of a single-degree-of-freedom system or a single-channel measurement of a multi-degree-of-freedom system. Discrete data is sampled with a time step Ar and y denotes the measured response at time t = nAt. The measurement is different from the model response ... 

Discrete data with a time step Af are collected in the experiment. Let y be the measured surface fluctuation at time t = nAt. There is a difference between the measured response y and the actual response x nAt) due to measurement noise and this is modeled here by a discrete white noise process e with zero mean and variance... 

Assume that discrete data at times f = nht, n = 1,2,..., A, are available at No < Nj) measured DOFs. Also, due to measurement noise and modeling error, there is prediction error, i.e., a difference between the measured response y e and the model response at time t = nAt corresponding to the measured degrees of freedom. The latter is given by LoX( Ar), where Lo e is an observation matrix. In the case of measuring the displacement time... 

The observational process in the network gives for each element h t) a subset of discrete data (results of measurements) ... 

Create the functional sample. The curves are created based on discrete data, recording each function based on an expansion of basic functions [7]. In this way, there is a functional sample, where each function represents the measurement already within a complete time unit. 

To help resolve potential ambiguities these measurements and data may be certified as accurate by the representative of the inspected State Party, at the discretion of the inspected State Party, immediately after they are gathered. In case of discrepancies both Parties shall make efforts to resolve discrepancies as soon as possible before the end of the inspection period. If necessary, the representative of the inspected State Party and the inspector shall each record the method(s) used and the final result(s). Such measurements shall be recorded in the document on preliminary findings. 

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