Multiplier

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

According to Equation (14), the fugacity of component i becomes equal to the mole fraction multiplied by the standard-... 

The total enthalpy correction due to chemical reactions is the sum of all the enthalpies of dimerization for each i-j pair multiplied by the mole fraction of dimer i-j. Since this gives the enthalpy correction for one mole of true species, we multiply this quantity by the ratio of the true number of moles to the stoichiometric number of moles. This gives... 

Multiplying both sides of this equation by (1 + i) gives... 

See chemical equivalent, equivalent conductivity The specific conductance multiplied by the volume (ml) which contains 1 g equivalent of the electrolyte. 

Fuller s equation, applied for the estimation of the coefficient of diffusion of a binary gas mixture, at a pressure greater than 10 bar, predicts values that are too high. As a first approximation, the value of the coefficient of diffusion can be corrected by multiplying it by the compressibility of the gas /... 

The values of common hydrocarbon solubility parameters vary between 300 and 600 (kJ/m3) /2 Several tables are available where the solubility parameters are shown as (cal/cm ) / Jq convert these values, it is necessary to multiply by 64.69. Thus a solubility parameter value of 10 (cal/cm ) / jg equal to 646.9 (kJ/m ) / ... 

Cases 3 and 4 are both exploration prospects, since the volumes of potential oil present are multiplied by a chance factor which represents the probability of there being oil there at all. For example, case 3 has an estimated probability of oil present of 65%, i.e. low risk of failure fo find oil (35%). However, even if there is oil present, the volume is small no greater than 130 MMstb. This would be a low risk, low reward prospect. 

When an explorationist constructs an expectation curve, the above approach for the volumetries of an accumulation is taken, but one important additional parameter must be taken into account the probability of there being hydrocarbons present at all. This probability is termed the Probability of Success" (POS), and is estimated by multiplying together the probability of there being ... 

The estimated probabilities of each of these events occurring are multiplied together to estimate the POS, since they must a//occur simultaneously if a hydrocarbon accumulation is to be formed. If the POS is estimated at say 30%, then the probability of failure must be 70%, and the expectation curve for an exploration prospect may look as shown in figure 6.9. 

This is the method used by the commercial software packages Crystal Ball and RISK . The method is ideally suited to computers as the description of the method will reveal. Suppose we are trying to combine two independent variables, say gross reservoir thickness and net-to-gross ratio (the ratio of the net sand thickness to the gross thickness of the reservoir section) which need to be multiplied to produce a net sand thickness. We have described the two variables as follows ... 

A random number (between 0 and 1) is picked, and the associated value of gross reservoir thickness (T) is read from within the range described by the above distribution. The value of T close to the mean will be randomly sampled more frequently than those values away from the mean. The same process is repeated (using a different random number) for the net-to-gross ratio (N/G). The two values are multiplied to obtain one value of net sand thickness. This is repeated some 1,000-10,000 times, with each outcome being equally likely. The outcomes are used to generate a distribution of values of net sand thickness. This can be performed simultaneously for more than two variables. 

The method allows variables to be added or multiplied using basic statistical rules, and can be applied to dependent as well as independent variables. If input distributions can be represented by a mean, and standard deviation then the following rules are applicable for independent variables ... 

To estimate the product of the two variables below, a short cut method is to multiply the low, medium and high values in a matrix (in which numbers have been selected). 

The volume fraction would typically be used to represent the make up of a gas at a particular stage in a process line and describes gas composition e.g. 70% methane and 30% Ethane (also known as mol fractions) at a particular temperature and pressure. Gas composition may also be expressed in mass terms by multiplying the fractions by the corresponding molecular weight. 

The actual flowrate of each component of the gas (in for example cubic mefres), would be determined by multiplying the volume fraction of that component by the total flowrate. 

For the case of a double-D coil we multiply each matrix element with an element shifted by a constant distance of the same line. This is done in x- and y-direction. The distance between the two elements is the correlation length X for filtering in x-direction and a second correlation length for the movement in y-direction. Thus one gets two new matrices Ax and Ax for the filtering from the left to the right (positiv x-direction) and vice versa (negativ x-direction). 

To demodulate the signal, it is then necessary to multiply the carrier by itself. Of eourse, the carrier of the driver must be exactly the same as the demodulator one. But, as it is modified to be demodulated, we nevertheless need a common frequency reference for the driver and for the DSP. This reference is delivered by a quartz oscillator. 

The demodulation algorithm is very simple the DSP multiplies the received signal by each carrier, and then filters the result using a FIR filter. This kind of digital filter is phase linear, (constant group delay important for the EC combinations). Other filters may be programmed, other demodulation algorithms may be used. 

The resistance R is given by the relation. Here, the second term with the amplitude of very little flux in the tube cannot be neglected because it is multiplied by the pulsation (n=27tf. 

Use now this equation to describe liquid film flow in conical capillary. Let us pass to spherical coordinate system with the origin coinciding with conical channel s top (fig. 3). It means that instead of longitudinal coordinate z we shall use radial one r. Using (6) we can derive the total flow rate Q, multiplying specific flow rate by the length of cross section ... 

In general a thickness measurement using ultrasound is done by measuring the time of flight of the ultrasonic pulse and calculating the thickness of the objeet multiplying the time and the known constant sound velocity in the material. 

Figure 3 Feature relevance. The weight parameters for every component in the input vector multiplied with the standard deviation for that component are plotted. This is a measure of the significance of this feature (in this case, the logarithm of the power in a small frequency region.)...

This is exact—see Problem 11-8. Notice that Eq. 11-14 is exactly what one would write, assuming the meniscus to be hanging from the wall of the capillary and its weight to be supported by the vertical component of the surface tension, 7 cos 6, multiplied by the circumference of the capillary cross section, 2ar. Thus, once again, the mathematical identity of the concepts of surface tension and surface free energy is observed. 

A method that has been rather widely used involves the determination of the force to detach a ring or loop of wire from the surface of a liquid. It is generally attributed to du Noiiy [42]. As with all detachment methods, one supposes that a first approximation to the detachment force is given by the surface tension multiplied by the periphery of the surface detached. Thus, for a ring, as illustrated in Fig. II-ll,... 

Fig. IV-25. The evaporation resistance multiplied by the square root of temperature versus area per molecule for monolayers of octadecanol on water illustrating agreement with the accessible area model. (From Ref. 290.)...

Returning to the complete calculation, is then given by u multiplied by the number of atoms per unit area in the particular crystal plane. 

The last identity follows from the orthogonality property of eigenfunctions and the assumption of nomralization. The right-hand side in the final result is simply equal to the sum over all eigenvalues of the operator (possible results of the measurement) multiplied by the respective probabilities. Hence, an important corollary to the fiftli postulate is established ... 

If the structure factor vanishes, the corresponding fonn factor is irrelevant as it is multiplied by a zero... 

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