Rigorous Study

Describing the titration curve by the three different Eqs. (17.9) [or (17.8)], (17.12), and (17.10) [or (17.11)] is not fully satisfactory. Indeed they implicate that both antagonistic couples do not play a part simultaneously in the fixation of the equilibrium potential values (except at the equivalence point). This is a kind of negation of the very existence of the titration. Moreover, such a methodology also implicates that the titration curve is discontinuous, since three different equations are used. Finally, with this description, it is not possible to study the slope of the curve dEld( about the equivalent point. This is a drawback because it is this slope that governs the success of a titration, as we saw when we considered acid-base titrations. This is the basis for the sharpness index concept. 

A general equation exists that applies itself to any stage of the titration. It can be easily deduced from Eqs. (17.3)-(17.7). It is the following  

Equation (17.13) is explicit in 9, but not in E. It is very easy to check that relation (17.9) describing the first part of the curve is equivalent to Eq. (17.13) in which 

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Clearly there was no lack of devoted adversaries (perhaps a more proper term than enemies) on both sides of the norbornyl ion controversy. It is to their credit that we today probably know more about the structure of carbocations, such as the norbornyl cation, than about most other chemical species. Their efforts also resulted not only in rigorous studies but also in the development or improvement of many techniques. Although many believe that too much effort was expended... 

The core curriculum provides a background in some of the basic sciences, including mathematics, physics, and chemistry. This backgronnd is needed to undertake a rigorous study of the topics central to chemical engineering, including ... 

In each of the composition diagrams in Fig. 14.2, the numbers represent a series of reactions run at a defined composition and temperature. These are isometric sulfur slices through three-dimensional K/P/RE/S quaternary phase diagrams. As just one example of what we have studied. Table 14.1 identifies the compositions at each point and the resulting phase(s). We have rigorously studied how phase formation is dependent upon the compositions of reactions for the rare-earth elements Y, Eu, and La and we have also discovered key structural relationships between the rare-earth elements, indicating a significant dependence on rare-earth and alkali-metal size for sulfides and selenides. 

We are now ready to consider some soUd state reactions that relate more directly to the real world. These include the tarnishing reaction and Pick s Laws of Diffusion. Both of these scientific areas have been rigorously studied because of their importcmce in revealing how diffusion mechanisms are related to everyday solid state reactions which occur on a daily basis. 

The cautious approach to drug approval, as overseen by the federal Food and Drug Administration (FDA), has been described in detail elsewhere (Findlay, 1999). The risks and benefits of a new drug submitted for FDA approval are rigorously studied through randomized, controlled clinical trials. Despite the enormous effort put forth to study new drugs, and the huge financial investment required to support clinical trials, many questions are often left unanswered by the relatively small-scale preapproval studies that may fail to detect, or fully describe, low-incidence adverse effects. These adverse effects may become evident within the months or years immediately... 

Part of this program was realized at the Survey. Between 1901 and 1907, the chemist Allen, the physicist Day, and the petrographer, Iddings, completed a rigorous study of the thermal properties of the plagioclase feldspars, the most abundant rockforming minerals. This study was important in several respects. 

One of the more methodologically rigorous studies on the utility of TCA/antipsychotic combinations in treating PMD was completed by Spiker et al. [1985). In this study, 54 patients who met criteria for depression with psychotic features on the Schedule for Affective Disorders and Schizophrenia [Endicott and Spitzer 1978) and by Research Diagnostic Criteria [Spitzer et al. 1985) were randomly selected to treatment with amitriptyline alone, perphenazine alone, or the combination of two drugs. After a 7-day placebo washout, patients were treated for 35 days with doses averaging approximately 50 mg/day of perphenazine and approximately 200 mg/day of ami-... 

As with other drugs, a methodologically rigorous study addressing this issue has not been done with venlafaxine. Nevertheless, there are data from an open-label trial of venlafaxine that warrant comment (149). In this study, high-dose venlafaxine produced an acute response in more than 30% of patients who had historically not adequately benefited from adequate trials of at least three antidepressants from different classes or two antidepressants plus ECT. Until more definitive data are available, this study does support a trial of high-dose venlafaxine in such patients. 

The system has a specific capability for the resolution of very complex mixtures in which large energy peaks tend to mask small adjacent ones. It is therefore particularly suitable for rigorous studies of the slow incorporation of low levels of radionuclides into biological or environmental systems. It should encourage investigation in these areas, where up to now the accumulation of data has been slow, laborious, and expensive. 

Detailed and rigorous study of the most important problems is done mainly in subsequent articles in the second part of this book, and in a series of monographs and papers (see the bibliography at the end of this volume). However, this does not diminish the significance of the monograph included here, which presents the main aspects in the clearest and most concise form. 

Any rigorous study of the oxidation of polymeric organolithium compounds should consider these products and their variation in yield with reaction conditions. To date, few of these reaction products have been considered, let alone identified and analyzed. However, the presence of the macroperoxide has been identified recently among the products of the oxidation of poly(styryl)lithium 352). Lithium aluminium hydride reduction followed by SEC analysis of the dimer fraction before and after reduction... 

One of the most significant results from the advent of these surface science studies on oxides relevant for the present catalytic applications is the fact that oxides can be multiply terminated and that they are not terminated [154, 180, 186-190] in cuts through the bulk structure. This is not unexpected in general [98,156,179] but it is of great value to know this in attempts to understand the mechanisms that activate oxides for catalysis. These rigorous studies must be differentiated from more empirical studies carried out on termination issue with qualitative methods and without predictive power but with the still invaluable advantage that they can be applied [97,191-193] to complex MMO catalyst systems. Such studies can be used to probe the surface reactivity, to address the issue of segregation of, for example, vanadium out of an MMO system and to compare different qualities of the nominally same material with speculative assumptions about the influence of defects. 

Preformulation should include rigorous studies to determine the number of polymorphs that exist, relative degree of stability of the various polymorphs, solubilities, method of preparation of each form, effect of micronization and tableting, and interaction with formulation ingredients. 

Ginseng. The dried roots of this plant, which is native to China, are believed to increase stamina and concentration. Few well-designed, rigorous studies of ginseng have been conducted, and those that have been done found no evidence for ginseng s effectiveness. 

As researchers have pointed out, well-controlled, rigorous studies of the neuroleptics have been rare. One analysis of seven studies showed improvement of behavioral symptoms in 59% of patients, but there was also improvement in 41% of those taking placebo (sugar pill). Patients with psychosis but without signs of movement disorder are often started on 0.5-1 mg of haloperidol (Haldol), with a subsequent increase in the dosage, trading off between adverse side effects and benefits. 

Ideally, reference ranges consist of biomonitoring values developed according to scientifically rigorous study design and quality-control procedures (see Chapter 4). The utility of reference ranges depends on attention to reference populations and data quality. 

Most biomolecules, such as polysaccharides, simple sugars, lipids, and proteins, are crystalline (International Centre for Diffraction Data, 2006). If HS consist merely of associations of biological residues, they should have characteristic crystal structures that can be rigorously studied and identified by X-ray diffraction analysis. However, the research evidence clearly shows that environmental organic matter has to be considered as highly amorphous material, which additionally contains microcrystalline regions like polymethylene crystallite (Hu et al., 2000 Schaumann, 2006b). 

The elegant evaluations of Co—C BDEs from the Halpem and the Finke laboratories require exhaustive and extensive experimental studies. The rates of decomposition of many alkyl Cbls have been evaluated in earlier, less rigorous studies in Schrauzer s and Pratt s laboratories [77], The general features appear to be correct and the effects of steric factors on Co—C bond cleavage have been reviewed [77], An abbreviated series relevant to our discussion is CH3 < 5 -deoxyadenosyl < C2H5 < /-C3H7, CH2CMe3. 

Experimental design and analysis have become essential because of the greater detail in modem biological theories and the complexities in treatments of disease. The clinician is usually interested in small, but biologically important, treatment effects that can be obscured by uncontrolled natural variation and bias in non-rigorous studies. This places well-performed clinical trials at the very center of clinical research today (pp. 9-10). 

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