Defined, 210 estimate values

The reduction potentials for the actinide elements ate shown in Figure 5 (12—14,17,20). These ate formal potentials, defined as the measured potentials corrected to unit concentration of the substances entering into the reactions they ate based on the hydrogen-ion-hydrogen couple taken as zero volts no corrections ate made for activity coefficients. The measured potentials were estabhshed by cell, equihbrium, and heat of reaction determinations. The potentials for acid solution were generally measured in 1 Af perchloric acid and for alkaline solution in 1 Af sodium hydroxide. Estimated values ate given in parentheses. 

Probabilistic techniques of estimation provide some Insights Into the potential error of estimation. In the case of krlglng, the variable pCic) spread over the site A is first elevated to the status of a random function PC c). An estimator P (2c) is then built to minimize the estimation variance E [P(2c)-P (2c) ], defined as the expected squared error ( ). The krlglng process not only provides the estimated values pCiyc) from which a kriged map can be produced, but also the corresponding minimum estimation variances 0 (39 ) ... 

Referring to Fig. 1.4, the solution begins with the initial concentration conditions Aq, Bq, Cq and Dq, defined at time t = 0. Knowing the magnitudes of the kinetic rate constants k], k2, k3 and k4, thus enables the initial rates of change dCA/dt, dCfi/dt, dCc/dt and dCo/dt, to be determined. Extrapolating these rates over a short period of time At, from the initial conditions, Aq, Bq, Cq and Do, enables new values for A, B, C and D to be estimated at the new time, t = t -I- At. If the incremental time step At is sufficiently small, it is assumed that the error in the new estimated values of the concentration. A, B, C and D, will also be small. This procedure is then repeated for further small increments of time until the entire concentration versus time curves have been determined. 

Below-ground biomass is typically estimated from the root to shoot ratio (Johnson et al. 2006 Bolinder et al. 2007). Extreme care must be used when using published root to shoot ratios because different scientists define root to shoot ratios differently. For example, Johnson et al. (2006) defined root to shoot ratios for com (Zea mays) as the ratio between root biomass and total above-ground biomass (grain, stover, and cob), whereas Amos and Walters (2006) defined this value as the ratio between root biomass and com stover. In addition, a standardized root to shoot ratio has not been used in maintenance calculations. For example, Barber (1978) used a value of 0.17 for com, Huggins et al. (1998) used a value of 0.53, and Larson et al. (1972) did not consider roots. 

The value of the proportionality constant /3 can be determined experimentally. In the absence of any other experimental data, an acceptable model would be based on any combination of the adjustable parameters C, K, and Ns that yields the correct value of /3, according to Equation 29. Since three adjustable parameters are available to define the value of one experimentally observable quantity, covariability among these parameters is expected. In reality an independent estimate of Ng might be available, and curvature of the <7q vs. log a + plot might reduce some of the covariability, but Equation 29 provides an initial step in understanding the relationship between covarying adjustable parameters. 

In the work described earlier, the applicability of the Weibull model was further tested by assessing the precision of estimation [expressed by the CV defined as the standard error of estimates divided by the estimated value] and the relative accuracy of estimation of the model parameters (based on the difference of the estimates from the actual value, divided by the actual value). Regarding the precision of estimates, for data with SD = 2 the maximum CV value for Wo, b, and c was 13%, 52%, and 16%, respectively, whereas the corresponding numbers for data with SD = 4 were 33%, 151%, and 34%, respectively. As expected, the precision of the estimates decreases as the SD of the data increases, with the poorest precision for the b estimates and the best for the Wo estimates. Additionally, the maximum CV values were associated with low c values (c = 0.5). 

Let us define the time variable r] f) = (3. R xi t),X2 t)) toward obtain-ment of estimated value of heat generation term. Such a variable describes the generation heat due to reaction along the solution of the dynamical model (3). 

The estimated value of -67 nm (no lattice strains) [6] is at the border of nanocrystallinity if one defines it as the grain size smaller than 100 nm [7]. Our result correlates very well with the grain size of 78 nm reported very recently by Kojima et al. [8] for their commercial MgH. Both resnlts suggest that certain commercial varieties of MgH could be subjected to either ball milling or other type of postdeformation in the proprietary mannfactnring process, which results in the final nearly nanosize grains (crystallites). 

The modulus defined by eqn. (10) then has the advantage that the asymptotes to t (0) are approximately coincident for a variety of particle shapes and reaction orders, with the specific exception of a zero-order reaction (n = 0), for which t = 1 when 0 < 1 and 77 = 1/0 when 0 > 1. The curve of 77 as a function of 0 is thus quite general for practical catalyst pellets. Figure 2 illustrates the form of For 0 > 3, it is found that 77 = 1/0 to an accuracy within 0.5%, while the approximation is within 3.5% for 0 > 2. The errors involved in using the generalised curve to estimate 77 are probably no greater than the errors perpetrated by estimating values of parameters in the Thiele modulus. 

For estimating the contribution of volatile compounds to bread aroma Rothe and coworkers (S) defined "aroma value" as the ratio of the concentration of some volatile compounds to the taste threshold value of the aroma. This concept was further developed by Weurman and coworkers (9) by introducing "odor value", in which aroma solutions were replaced by synthetic mixtures of volatile compounds in water. These mixtures showed the complexity of the volatile fractions of wheat bread, because none of them resembled the aroma of bread. Recently two variations of GC-sniffing were presented (10-11), in which the aroma extract is stepwise diluted with a solvent until no odor is perceived for each volatile compound separately in the GC effluent. The dilution factors obtained indicate the potency of a compound as a contributor to the total aroma. 

The enthalpies of formation of aqueous ions may be estimated in the manner described, but they are all dependent on the assumption of the reference zero that the enthalpy of formation of the hydrated proton is zero. In order to study the effects of the interactions between water and ions, it is helpful to estimate values for the enthalpies of hydration of individual ions, and to compare the results with ionic radii and ionic charges. The standard molar enthalpy of hydration of an ion is defined as the enthalpy change occurring when one mole of the gaseous ion at 100 kPa (1 bar) pressure is hydrated and forms a standard 1 mol dm-3 aqueous solution, i.e. the enthalpy changes for the reactions Mr + (g) — M + (aq) for cations, X (g) — Xr-(aq) for monatomic anions, and XOj (g) —< XO (aq) for oxoanions. M represents an atom of an electropositive element, e.g. Cs or Ca, and X represents an atom of an electronegative element, e.g. Cl or S. 

This chapter describes several properties of dry gases which commonly are normally used by tire petroleum engineer. We will define each property and then give correlations useful for estimating values of the property using normally available information about the gas. 

The preceding estimated values compare well with those experimental values. The percent errors as defined in Example. 1 are -1.4 percent for the power consumption, 15 percent for the gas holdup, and -21.7 percent for the volumetric mass-transfer coefficient. 

The analyzed approach to finding the optimum indicates that the model must have a possibility to estimate the direction of further design points with associated precision. Since we are unaware of the direction of movement towards the optimum before defining the model, the accuracy of estimation of the mathematical model must be the same in all directions. This is to say that estimated values in experiment region may differ from the real, measured response values for the previously given magnitude. The model which fulfills this requirement is called adequate, to be discussed in a separate section. 

Solubility constraints define the maximum concentrations of radionuclides at the point of release from the waste. In the second section, radionuclide solubilities in natural waters are reported as measured values and estimated values from thermodynamic data. In addition, information is given concerning the chemical species of radionuclides that could be present in natural waters. 

Least squares is used to determine the model parameters for concentration prediction of unknown samples. This is achieved by minimizing the usual sum of the squared errors, (y-y)T(y-y). As stated before, the errors in y are assumed to be much larger than the errors in X for these models. Because the regression parameters are determined from measured data, measurement errors propagate into the estimated coefficients of the regression vector b and the estimated values in y. In fact, we can only estimate the residuals, e, in the y measurements, as shown in Equation 5.12 through Equation 5.14. Summarizing previous discussions and equations, the model is defined in Equation 5.11 as... 

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