Indicator variables, defined

Glaser and Lichtenstein (G3) measured the liquid residence-time distribution for cocurrent downward flow of gas and liquid in columns of -in., 2-in., and 1-ft diameter packed with porous or nonporous -pg-in. or -in. cylindrical packings. The fluid media were an aqueous calcium chloride solution and air in one series of experiments and kerosene and hydrogen in another. Pulses of radioactive tracer (carbon-12, phosphorous-32, or rubi-dium-86) were injected outside the column, and the effluent concentration measured by Geiger counter. Axial dispersion was characterized by variability (defined as the standard deviation of residence time divided by the average residence time), and corrections for end effects were included in the analysis. The experiments indicate no effect of bed diameter upon variability. For a packed bed of porous particles, variability was found to consist of three components (1) Variability due to bulk flow through the bed... 

Table 37.3 shows the complete table of eight indicator variables for 10 triply substituted tetracyclines [31 ] that have been tested for bacteriostatic activity (1/Z), which is defined here as the ratio of the number of colonies grown with a substituted and with the unsubstituted tetracycline. In this application we have three substitution positions, labelled U, V and W. The number of substituents at the three sites equals 2,3 and 3, respectively. Arbitrarily, we chose the compound with substituents H, NOj and NO2 at the sites U, V and W as the reference compound. This leads to a reduction of the number of indicator variables from eight to five, as shown in Table 37.4. The solution of the Free-Wilson model can be obtained directly by means of multiple regression ...

In this section, the numerical solutions of the MINLP-model and of the MILP-model as presented in Sections 7.4 and 7.5 are compared with respect to their solution quality (measured by the objective values) and the required solution effort (measured by the computing time). In order to compare the MILP-solution with the MINLP-solution, the optimized values for the start times of polymerizations tn, the recipe assignments W, and the total holdups Mnr are inserted into the MINLP-model and the objective is calculated. To guarantee comparability of the results, the models were stated with identical initial conditions, namely t° = 0, = 2 Vk, pf = 0 Vs, and ra = 0.4 Vs (i.e., the variables defined at the beginning of the corresponding time axes are fixed to the indicated values). For the algorithmic solution procedure, all variables were initialized by 1 (i.e., the search for optimal values starts at values of 1 ), and none of the solvers was specifically customized. 

The selection of variables is of central importance for the outcome of a system comparison on environmental and resource use impacts. The ideal variable or set of variables respectively provides information and describes the state of environmental phenomena with certain significance. Thus, applying a set of variables should make it possible to monitor and assess the state of the environment, to identify changes and trends, to transmit scientific data to become relevant for policy, and to evaluate already implemented policy measures. The concept of environmental indicators is broadly accepted as an adequate tool. Accordingly, an indicator is defined as a parameter or a value derived from parameters, which indicates the state of the environment with significance extending beyond that which is directly associated with a parameter value. A parameter s definition in this context is a property that is measured or observed (OECD 1994). Fieri et al. (1996) states that the purposes of indicators are as follows ... 

Let Bl, B2, and B3 be codes that represent batches 1,2, and 3, respectively. The indicator variables are used to indicate at which batch (level of factor) is assigned the response variable. For instance, a response variable associated with Bl is represented by Mi = 1 and m2 = 0. Similarly, a response variable from B2 is represented by Mi = 0 and m2 = 1. Also a response variable from B3 is represented by = 0 and m2 = 0. Thus, the values of Mi and u2 define in a unique manner the factor combination. The indicator variables for this model are summarized in Table 20. 

Both the Yasuda et al. and Schnitzer theories indicate that the key variables defining permeability in a gel are the swelling degree of the gel and the average dimension of the solute. Thus the dependence of permeability on swelling degree for a responsive gel inert to solutes can be predicted using the theory of Yasuda et al. to obtain the ratio D/Dc (the ratio of the diffusion coefficient of a solute in the gel to its value in free solution) and the theory of Schnitzer for ideal size exclusion to obtain K. A dimensionless permeability can be defined as the... 

Equation (5.18) tells us, at last, how to obtain p(pc,y,z). We need merely to construct a Fourier series from the structure factors. The structure factors describe diffracted rays that produce the measured reflections. A full description of a diffracted ray, like any description of a wave, must include three parameters amplitude, frequency, and phase. In discussing data collection, however, I mentioned only two measurements the indices of each reflection and its intensity. Looking again at Eq. (5.18), you see that the indices of a reflection play the role of the three frequencies in one Fourier term. The only measurable variable remaining in the equation is Fhkf Does the measured intensity of a reflection, the only measurement we can make in addition to the indices, completely define Fhkp Unfortunately, the answer is "no."... 

Five variables are critical to the EtO process. They are EtO concentration, relative humidity, temperature, time, and pressure/vacuum. Temperature is the easiest variable to measure and monitor, therefore temperature is used as the indicator of the worst-case location within the loaded EtO sterilizer. Once the worst-case location is identified the validation studies are conducted with the goal of inactivating a known concentration of indicator micro-organisms in the worst-case location using a specific loading pattern with a specific EtO cycle with all variables defined and controlled. 

Simulate the kinetic behavior by combining the P (t) probability functions for the pseudocompartments to obtain the state probabilities P ( ) of a particle belonging to the phenomenological compartments at time t. That is defined by means of appropriate matrices Bi and E 2 with indicator variables, i.e., 0 s or l s ... 

Bodor and Huang correlated the octanol/water partition coefficient, Po/w (unitless) at 298 K for a set of 302 compounds with a set of 58 descriptors to obtain Eq. [49]. These parameters include seven QM based descriptors that were calculated with the AMI method. The dipole moment is p(D) Qo and Qn are the square roots of the sum of the squares of charges on the O and N atoms, respectively. The parameter Qon is the sum of absolute values of charges on the O and N atoms, and ABSQ is the sum of the absolute values of the charges on all atoms. In addition to these QM descriptors, the surface area, A (A ), and the ovality, O, were calculated from the QM-optimized geometry. The ovality is defined by actual area/area as a sphere, O = A/[4ti(3V/ 4ti) ]. The molecular mass, M, and two indicator variables, Ngik and Nq, for alkanes and carbon atoms, respectively, were also employed. 

In these equations the indicator variable I4" has been defined for the 4"-substituent of the 3-(pyridin-2-yl) moiety (zero for hydrogen and one otherwise) of thiazolidinones (Fig. 26). Also, in these compounds the HIV-1 RT inhibitory activity has been finked to their ability to assume a butterfly-like shape in the receptor. Collectively, the substituents of 2- and 3-aryl moieties of these compounds promote this molecular shape. In this connection, the indicator parameter 12,3 has been introduced to address the collective steric features of the 2- and 3-aryl moieties of these compoimds. In this, 12,3 has been defined to take a value of one if any one substituent at 1 - or 6 - of the 2-phenyl moiety or at the 3"- or 5"- positions of the 3-(pyridin-2yl) moiety is larger than hydrogen and zero otherwise. These equations, while favor-... 

To derive these equations, log P (hydrophobic parameter), MR (molar refrac-tivity index), and MV (molar volume) were calculated using software freely available on the internet (wwwlogP.com, www.daylight.com). The first-order valence molecular connectivity index of substituents was calculated as suggested by Kier and Hall [46,47]. In these equations, is cross-vahdated obtained by the leave-one-out jackknife procedure. Its value higher than 0.6 defines the good predictive ability of the equation. The different indicator variables in these equations were defined as follows. 

The most well-known approaches based on substituent descriptors are the Hansch analysis and - Free-Wilson analysis in the latter technique, the substituents are defined by - indicator variables representing their presence/absence in the substitution sites of the parent molecule. 

The upper Emit of the normal reference interval for urinary 5-HIAA excretion is variably defined and may be as low as 6mg/day (30p,mol/day) if dietary and medicinal intake are controlled, or as high as 15mg/day (80p,mol/day) to reduce false-positive results. At an intermediate value of 10.7mg/day (56llmol/day), urinary 5-HIAA has a reported 77% sensitivity and 97% specificity for carcinoid disease. " To exclude the presence of a carcinoid tumor, lower cutoff values may be preferred (higher sensitivity) to confirm the presence of a carcinoid tumor, higher cutoff values (higher specificity) would be indicated. 

These two indices were proposed by Gini [Gini, 1909] to derive the —> Gini concentration ratio. Range. A simple dispersion measure of the x variable, defined as... 

Like other random effects, the residual error can be dependent on subject-specific covariates and as such, covariates can be included in the residual variance model. The classic example is when some blood samples were assayed with one analytical assay, while others were assayed with another type of assay. If an indicator variable, ASY, is defined such that every sample is assigned either a 0 or 1, depending on the reference assay, the residual error could then be modeled as... 

Of course, Eq. (1) is only a mathematical formalism. Whereas biological activities can easily be defined by a certain endpoint (e.g., an effective dose, a 50% inhibition constant, a 100% lethal dose, etc.), it was and still is impossible to describe chemical structures in an absolute manner. Only changes in biological activities A

chemical structures AC (Eq. (2)). Such chemical changes can be quantified either by structural terms (indicator variables, dummy variables, Free-Wilson parameters) or by the resulting change in various physicochemical or other properties ... 

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