Methods derivative

The isotopic derivative method may help where other methods fail because too little material is available for analysis or the concentration of the component to be determined is too low in the sample. The procedure is useful even where the isotope dilution technique cannot be employed because the substance to be determined is not available in radioactive form. 

The method is based on the reaction of an inactive element, radical or molecule with a radioactive reagent, yielding a hot derivative, which can be detected and determined with radiometric measuring methods. 

---

Manolopoulos D E 1986 An improved log derivative method for inelastic scattering J. Chem. Phys. 85 6425-9... 

Pulay P 1987 Analytioal derivative methods in quantum ohemistry Advances in Chemical Physics vol LXIX, ed K P Lawley (New York Wiley-Intersoienoe) pp 241-86... 

Pulay P 1987 Analytical derivative methods in quantum chemistry Adv. Chem. Phys. 69 241... 

When discussing derivative methods it is useful to write the function as a Taylor series expansion about the point jc. ... 

Second Derivative Methods The Newton-Raphson Method... 

Derivative methods are particularly well suited for locating end points in multi-protic and multicomponent systems, in which the use of separate visual indicators for each end point is impractical. The precision with which the end point may be located also makes derivative methods attractive for the analysis of samples with poorly defined normal titration curves. 

Derivative methods work well only when sufficient data are recorded during the sharp rise in plT occurring near the equivalence point. This is usually not a problem when the titration is conducted with an automatic titrator, particularly when operated under computer control. Manual titrations, however, often contain only a few data points in the equivalence point region, due to the limited range of volumes over which the transition in plT occurs. Manual titrations are, however, information-rich during the more gently rising portions of the titration curve before and after the equivalence point. 

Solubihties of 1,3-butadiene and many other organic compounds in water have been extensively studied to gauge the impact of discharge of these materials into aquatic systems. Estimates have been advanced by using the UNIFAC derived method (19,20). Similarly, a mathematical model has been developed to calculate the vapor—Hquid equiUbrium (VLE) for 1,3-butadiene in the presence of steam (21). 

A more sophisticated version of the sequential univariate search, the Fletcher-Powell, is actually a derivative method where elements of the gradient vector g and the Hessian matrix H are estimated numerically. 

When unpleasant odors resulting from manufacturing processes or waste-disposal operations give rise to public complaints they should be identified and quantified prior to deriving methods of abatement. Such work is often innovative, requiring the design and fabrication of new equipment for the sampling and analysis of pollutants. 

Prepare 250 mL of 0.02 M potassium dichromate solution and an equal volume of ca 0.1 M ammonium iron(II) sulphate solution the latter must contain sufficient dilute sulphuric acid to produce a clear solution, and the exact weight of ammonium iron(II) sulphate employed should be noted. Place 25 mL of the ammonium iron(II) sulphate solution in the beaker, add 25 mL of ca 2.5M sulphuric acid and 50 mL of water. Charge the burette with the 0.02 M potassium dichromate solution, and add a capillary extension tube. Use a bright platinum electrode as indicator electrode and an S.C.E. reference electrode. Set the stirrer in motion. Proceed with the titration as directed in Experiment 1. After each addition of the dichromate solution measure the e.m.f. of the cell. Determine the end point (1) from the potential-volume curve and (2) by the derivative method. Calculate the molarity of the ammonium iron(II) sulphate solution, and compare this with the value calculated from the actual weight of solid employed in preparing the solution. 

A F Fell and G Smith, Higher derivative methods in ultraviolet, visible and infrared spectrophotometry, Anal. Proc., 1982, 19, 28... 

Saver JL. Number needed to treat estimates incorporating effects over the entire range of clinical outcomes novel derivation method and application to thrombolytic therapy for acute stroke. Arch Neurol 2004 61 1066-1070. 

The %HIA, on a scale between 0 and 100%, for the same dataset was modeled by Deconinck et al. with multivariate adaptive regression splines (MARS) and a derived method two-step MARS (TMARS) [38]. Among other Dragon descriptors, the TMARS model included the Tig E-state topological parameter [25], and MARS included the maximal E-state negative variation. The average prediction error, which is 15.4% for MARS and 20.03% for TMARS, shows that the MARS model is more robust in modeling %H1A. 

The derivation method of the model equations for extraction columns with backmixing are explained in Sec. 4.4.3. Here the balances are easier to formulate because concentrations are used. The form of the component balance equations in terms of concentrations are as follows. 

As described in Section 7.3.1 when the derivative method is used, the specific MAb production rate at any time t during the batch start-up period is determined by... 

During the continuous operation of the bioreactor the specific MAb production rate at time t is determined by the derivative method as... 

Another problem that should be considered carefully is the fact that the evaluated phase shift data set is discrete, so that conventional numerical derivation methods... 

Both the Chen and Gross [48] and the Gallo et al. [49] methods have been applied to eliminating compartments. Both derivation methods are based on the specific mass balance equations for the given model structure. Monte Carlo investigations have demonstrated that both methods provide reasonably accurate and precise estimates of partition coefficients from concentration-time data sets containing error, data one is likely to encounter from in vivo studies. 

Galego and Arroyo [14] described a simultaneous spectrophotometric determination of OTC, hydrocortisone, and nystatin in the pharmaceutical preparations by using ratio spectrum-zero crossing derivate method. The calculation was performed by using multivariate methods such as partial least squares (PLS)-l, PLS-2, and principal component regression (PCR). This method can be used to resolve accurately overlapped absorption spectra of those mixtures. 

The various response tensors are identified as terms in these series and are calculated using numerical derivatives of the energy. This method is easily implemented at any level of theory. Analytic derivative methods have been implemented using self-consistent-field (SCF) methods for a, ft and y, using multiconfiguration SCF (MCSCF) methods for ft and using second-order perturbation theory (MP2) for y". The response properties can also be determined in terms of sum-over-states formulation, which is derived from a perturbation theory treatment of the field operator — [iE, which in the static limit is equivalent to the results obtained by SCF finite field or analytic derivative methods. 

In the considered value chain planning problem, the uncertainty of spot sales prices impacts the profitability of the overall value chain plan, since volume decisions can lead to profit-suboptimal plans, if the average sales price cannot be realized as planned. Therefore, price volatility is considered as an external (stochastic) influence in the considered value chain planning problem. The following model extensions account for this uncertainty and try to derive methods to achieve more robust plans with respect to profit results with contributions from Habla (2006). The objective of the proposed modeling approach is to maximize profit for the entire value chain network. It is assumed that the company behaves risk-averse in face of the price uncertainty. 

---