Unknowns

In each of these problems, there are m unknowns either the pressure or the temperature is unknown and there are m - 1 unknown mole fractions. 

An apparent systematic error may be due to an erroneous value of one or both of the pure-component vapor pressures as discussed by several authors (Van Ness et al., 1973 Fabries and Renon, 1975 Abbott and Van Ness, 1977). In some cases, highly inaccurate estimates of binary parameters may occur. Fabries and Renon recommend that when no pure-component vapor-pressure data are given, or if the given values appear to be of doubtful validity, then the unknown vapor pressure should be included as one of the adjustable parameters. If, after making these corrections, the residuals again display a nonrandom pattern, then it is likely that there is systematic error present in the measurements. ... 

The bubble and dew-point temperature calculations have been implemented by the FORTRAN IV subroutine BUDET and the pressure calculations by subroutine BUDEP, which are described and listed in Appendix F. These subroutines calculate the unknown temperature or pressure, given feed composition and the fixed pressure or temperature. They provide for input of initial estimates of the temperature or pressure sought, but converge quickly from any estimates within the range of validity of the thermodynamic framework. Standard initial estimates are provided by the subroutines. 

As stated previously, the source of capital is often not known, and hence it is not known whether or not Eq. (A. 10) is appropiiate to represent the cost of capital. Equation (A. 10) is, strictly speaking, only appropriate if the money for capital expenditure is to be borrowed over a fixed period at a fixed rate of interest. Moreover, if Eq. (A. 10) is accepted, then the number of years over which the capital is to be annualized is unknown, as is the rate of interest. However, the most important thing is that even if the source of capital is not known, etc., and uncertain assumptions are necessary, Eq. (A. 10) provides a common basis for the comparison of competing projects. 

C2H4N2O3, NH2CONHCOOH. Unknown in the free state as it breaks down immediately to urea and COi- The NH4, Ba, Ca, K and Na salts are known and are prepared by treating ethyl allophanate with the appropriate hydroxide. The esters with alcohols and phenols are crystalline solids, sparingly soluble in water and alcohol. They are formed by passing cyanic acid into alcohols or a solution of an alcohol or phenol in benzene. The amide of allophanic acid is biuret. Alcohols are sometimes isolated and identified by means of their allophanates. 

Nitroxylic acid, HiNO . Yellow NajNOa formed by electrolysis NaN02 in NHj. Structure unknown free acid unknown. Nitramide, H2NNO2. A weak acid. 

To obtain the different values of p, it is only hecessary to produce as many independent equations as there are components in the mixture and, if the mixture has n components, to solve a system of n equations having n unknowns. Individual analysis is now possible for mixtures having a few components but even gasoline has more than 200 It soon becomes unrealistic to have ail the sensitivity coefficients necessary for analysis in this case, 200. ... 

A static bottom hole pressure survey (SBHP) is useful for determining the reservoir pressure near the well, undisturbed by the effects of production. This often cannot be achieved by simply correcting a surface pressure measurement, because the tubing contents may be unknown, or the tubing contains a compressible fluid whose density varies with pressure (which itself has an unknown profile). 

The recognition ratios achieved by CBR systems developed as part of this project could not be bettered by either neural-network classifiers or rule-based expert system classifiers. In addition, CBR systems should be mote reliable than simple classifiers as they are programmed to recognise unknown data. The knowledge acquisition necessary to build CBR systems is less expensive than for expert systems, because it is simpler to describe the knowledge how to distinguish between certain types of data than to describe the whole data contents. 

During the inspection of an unknown object its surface is scanned by the probe and ultrasonic spectra are acquired for many discrete points. Disbond detection is performed by the operator looking at some simple features of the acquired spectra, such as center frequency and amplitude of the highest peak in a pre-selected frequency range. This means that the operator has to perform spectrum classification based on primitive features extracted by the instrument. 

Classifier structures resulting from the training were verified in a blind test. To evaluate the reliability and performance of the NSC it was subjected to a blind test using unknown data containing spectra measured for various sizes and locations of the disbonds (from 50% to over 100% of the probe size). 

The Index n = k- ) - M + m is the current variable that indicates the sequence for the beam projections. Exploiting the current measurings y fn) one has to estimate the unknown image parameters a, with undefined conditions about their distribution and the noise FDD function. 

The adaptive estimation of the pseudo-inverse parameters a n) consists of the blocks C and E (Fig. 1) if the transformed noise ( ) has unknown properties. Bloek C performes the restoration of the posterior PDD function w a,n) from the data a (n) + (n). It includes methods and algorithms for the PDD function restoration from empirical data [8] which are based on empirical averaging. Beeause the noise is assumed to be a stationary process with zero mean value and the image parameters are constant, the PDD function w(a,n) converges, at least, to the real distribution. The posterior PDD funetion is used to built a back loop to block B and as a direct input for the estimator E. For the given estimation criteria f(a,d) an optimal estimation a (n) can be found from the expression... 

Consider the reflection of a normally incident time-harmonic electromagnetic wave from an inhomogeneous layered medium of unknown refractive index n(x). The complex reflection coefficient r(k,x) satisfies the Riccati nonlinear differential equation [2] ... 

The linear integral equation (5) is solved by a standard technique, including expansion of the unknown An z) by some basis functions and transformation of (5) into a matrix equation to... 

The reconstruction algorithm proposed in this work is based on a special choice of basis flinctions to expand the unknown refractive index profile. The following set of functions is used here ... 

No a priori information about the unknown profile is used in this algorithm, and the initial profile to start the iterative process is chosen as (z) = 1. Moreover, the solution of the forward problem at each iteration can be obtained with the use of the scattering matrices concept [8] instead of a numerical solution of the Riccati equation (4). This allows to perform reconstruction in a few seconds of a microcomputer time. The whole algorithm can be summarized as follows ... 

The -error is caused by interference of signals from the defect reflecting points. In general the expressions of Equations (2) and (3) describe a set of 2m equations in 3i unknowns. 

The first equation (1) is the equation of state and the second equation (2) is derived from the measurement process. Finally, G5 (r,r ) is a row-vector that takes the three components of the anomalous ciurent density vector Je (r) = normal component of the induced magnetic field. This system is non hnear (bilinear) because the product of the two unknowns /(r) and E(r) is present. 

We suppose that a measurement signal is a mix of r (unknown) independent sources Sj with variance cf. A detector give p> r measurement signals /W/t obtained with several frequencies. The relations between sources and measurement signals are supposed to be linear, but the transfer matrix T is unknown. If we get n >p>r samples m i) of measurement signals, mix of n... 

So, a comparison of different types of magnetic field sensors is possible by using the impulse response function. High amplitude and small width of this bell-formed function represent a high local resolution and a high signal-to-noise-characteristic of a sensor system. On the other hand the impulse response can be used for calculation of an unknown output. In a next step it will be shown a solution of an inverse eddy-current testing problem. 

Many applications of infrared thermograph are still unknown and the potential of this method is still growing. 

The exact values of E and 5E / 5n are in general unknown and the Kirchhoff or physical optics method consists in approximating the values of these two quantities on the surface and then evaluating the Helmholtz integral. We shall approximate the field at any point of the surface by the field that would be present on a tangent plane at the point. With this approximation, the field on the surface and its normal derivative are... 

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