Probability limit

Free-Electron Lasers. The free-electron laser (EEL) directly converts the kinetic energy of a relativistic electron beam into light (45,46). Relativistic electron beams have velocities that approach the speed of light. The active medium is a beam of free electrons. The EEL, a specialized device having probably limited appHcations, is a novel type of laser with high tunabiHty and potentially high power and efficiency. 

There is Httie known chemistry of tetrakis-Cp thorium complexes. Pseudotetrahedral molecules, (rj-ring) Tb (15), where ring = Cp [1298-75-5] or Ind [11133-17-6], have a measurable dipole, resulting from deviation of symmetry (88). Difference of coordination environments, eg, v] in the indenyl system and in the Cp system, appears to indicate great steric crowding about the thorium center, which probably limits the reactivity and synthetic derivatization of these complexes. 

Two other deposition mechanisms, in addition to the six listed, may be in operation under particular circumstances. Some dust particles may be collected on filters by sieving when the pore diameter is less than the particle diameter. Except in small membrane filters, the sieving mechanism is probably limited to surface-type filters, in which a layer of collected dust is itself the principal filter medium. 

There are several environmentally significant mercury species. In the lithosphere, mercury is present primarily in the +II oxidation state as the very insoluble mineral cirmabar (HgS), as a minor constituent in other sulfide ores, bound to the surfaces of other minerals such as oxides, or bound to organic matter. In soil, biological reduction apparently is primarily responsible for the formation of mercury metal, which can then be volatilized. Metallic mercury is also thought to be the primary form emitted in high-temperature industrial processes. The insolubility of cinnabar probably limits the direct mobilization of mercury where this mineral occurs, but oxidation of the sulfide in oxygenated water can allow mercury to become available and participate in other reactions, including bacterial transformations. 

The LCA of Heyde and Kremer (a.6) gives an extensive review of emissions and resource use. However, by and large one could assume that the emissions by using plastics as reducing agent will be more or less equal to the emissions that would occur if another reducing agent were to be used. For a discussion on the (probably limited) relevance of dioxin emission see Section 3.5.3. 

In occupational settings, exposure to endosulfan is mainly via the dermal and inhalation routes. Although workers involved in the manufacture and formulation of pesticide products containing endosulfan are potentially exposed to high concentrations of the compound, actual exposure is probably limited by the use of engineering controls and personal protection equipment. The highest documented dermal and inhalation exposures have been reported for agricultural workers involved in the spray... 

As mentioned earlier, physiological concentrations of carotenoids in vivo are in the micromolar range, mainly because of limited bioavailabiUty. Also, the antioxidant efficiencies of carotenoids after absorption are probably limited. Concentrations before absorption are much higher and can justify possible antioxidant actions in vivo. To test this hypothesis, Vulcain et al. developed an in vitro system of lipid peroxidation in which the oxidative stress is of dietary origin (metmyoglobin from meat) and different types of antioxidants (carotenoids, phenols) are tested. 

The use of lightly crosslinked polymers did result in hydrophilic surfaces (contact angle 50°, c-PI, 0.2 M PhTD). However, the surfaces displayed severe cracking after 5 days. Although qualitatively they appeared to remain hydrophilic, reliable contact angle measurements on these surfaces were impossible. Also, the use of a styrene-butadiene-styrene triblock copolymer thermoplastic elastomer did not show improved permanence of the hydrophilicity over other polydienes treated with PhTD. The block copolymer film was cast from toluene, and transmission electron microscopy showed that the continuous phase was the polybutadiene portion of the copolymer. Both polystyrene and polybutadiene domains are present at the surface. This would probably limit the maximum hydrophilicity obtainable since the RTD reagents are not expected to modify the polystyrene domains. 

The antidotal action of the barbiturates is probably limited to the effects of chlordan on the nervous system. They most likely have no beneficial antagonistic action against the delayed parenchymatous degenerative changes produced by chlordan (4). Therefore, they are primarily only of possible value in acute poisoning in which severe stimulation of the central nervous system may be the primary cause of death. 

Laser evaporation of clusters will not be a popular technique, it is costly in equipment, demanding in know-how, and probably limited to a spectroscopic scale. Nevertheless, it has already shown itself... 

The mesoionic tetrazole dehydrodithizone is transformed by iron penta-carbonyl into 4-phenyl-2-phenylazo-A2-l,3,4-thiadiazolin-5-one, presumably by a mechanism of ring opening, complexation, carbonyl insertion and subsequent ring closure (Scheme 128).193 Unfortunately, analogous processes do not occur on other mesoionic compounds in the 1,2,3-oxadiazole, s-triazole or tetrazole series, and the scope of this unusual carbonylation is probably limited. 

AE does equal ((AA A/r/2)), as predicted by Equation 11.8 [18]. This strengthens Equation 11.9. The accuracy of AE is probably limited by Equation 11.5, which is based on an expansion in which AN is small. 

Condamin et al. 1976, Stern et al. 2000). Although Condamin et al. (1976) identified oil residues from Mediterranean amphorae, their claim of identifying olive oil is supported by archaeological evidence alone (similar to the case of wine discussed above), and not by the molecular evidence, which is probably limited to the identification of a generic plant oil. Fatty acids have also been found in preserved human soft tissues (Evershed and Connolly 1988, Evershed 1990) and bones (Evershed et al. 1995). 

In the latest experimental work131 not only the heat conductivities of ice and water, but also the latent heat of fusion were considered, but convection still disregarded. The importance of the refinements of the theory is clear from the comparison of the most recent value for the ysl of the ice - water interface, namely 29 erg/cm2, with the early result129) of 7si = 41 erg/cm2. The probable limits of error were given as 9 erg/cm2 in the early, and as 2 erg/cm2 in the later paper the former estimate appears to be too optimistic. For the interface of solid and liquid lead, 7S) = 76 erg/cm2 was calculated130). 

The standard tools of statistical inference, including the concept and approaches of constructing a null hypotheses and associated p values, are based on the frequentist view of probability. From a frequentist perspective, the probability of an event is defined as the fraction of times that the event occurs in a very large number of trials (known as a probability limit). Given a hypothesis and data addressing it, the classical procedure is to calculate from the data an appropriate statistic, which is typically... 

Thus in the N-silyl substituted series, 17 and 18, which rearrange thermally to the corresponding diazo compounds, the stability increases through the series R=Me, Ph, i-Pr. As discussed below, these compound undergo the usual cycloaddition and electrocyclization reactions of nitrile imines and are not simply overstabilized curiosities. The usefulness in synthesis of those with P—C bonds is probably limited since these bonds are not easily broken, but products derived from those with C—Si and C—B bonds (e.g., 21 and 22) should be capable of further... 

As mentioned above, it is reasonable to assume that this tetrahedral V species forms at defect sites (hydroxyl nests) in the zeolite framework, but is stabilized by this interaction in a well defined environment through V-O-Si bonds. As indicated by the characterization data, the local coordination of vanadium must be different from that found for well dispersed vanadium sites on silica. This stabilization probably limits the unselective metal-bonded propane or propylene adsorption, in agreement with the role of adsorbate bonding on the selection of partial and total oxidation pathways of ethane on vanadium supported on silica (76) and in agreement with IR evidence (Fig. 

Figure 4. Finemann-Ross plots of cis-Decalin-Tetralin co-oxidations in Table V. The symbol X indicates probable limits of experimental error for...

Gold s method has been used by a number of workers, including Siska (1973), who applied it to molecular-beam scattering data, MacNeil and Dixon (1977), who applied it to photoelectron spectra, and Jones et al. (1967), who restored infrared spectra of condensed-phase samples. The author is unaware of any experimental results with this method, however, that illustrate the full potential achievable by constrained methods to be described later in this chapter. In the work of Jones et al., the resulting resolution is probably limited by the inherent breadth of spectral lines observed with condensed-phase samples. 

Although nitrogen Is probably limiting to some extent In most natural systems. It Is not the major limiting nutrient In all of them, and Is not limiting to the same extent at all times of the year. In large areas of Australia for example, phosphorus Is the principle limiting element (24). 

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