Threshold near zero

Among the first cluster reactions studied were reactions of readily formed dimers. These are usually dimers of open-shell molecules, such as NO2. Wren and Menzinger studied the chemiluminescence resulting from the reaction of Ba( S) with NOj monomers and dimers. They concentrated on the effect of the collision energy on the reaction s cross section. The monomers in this case react with appreciable cross sections even at low collision energy, and their excitation function is bimodal. The cross section for the clusters, in contrast, rises monotonically from a threshold near zero collision energy. 

ZEKE (zero kinetic energy) photoelectron spectroscopy has also been applied to negative ions [M]. In ZEKE work, the laser wavelengdi is swept tlirough photodetachment thresholds and only electrons with near-zero kinetic energy are... 

Appearance potential methods all depend on detecting the threshold of ionization of a shallow core level and the fine structure near the threshold they differ only in the way in which detection is performed. In all of these methods the primary electron energy is ramped upward from near zero to whatever is appropriate for the sample material, while the primary current to the sample is kept constant. As the incident energy is increased, it passes through successive thresholds for ionization of core levels of atoms in the surface. An ionized core level, as discussed earlier, can recombine by emission either of a characteristic X-ray photon or of an Auger electron. 

The threshold energy or activation energy for the reaction of atomic fluorine with hydrocarbons (79, 80) or hydrogen (81) is near zero, and these reactions, in fact, produce a similar set of HF molecules in excited vibrational states. In a variety of studies by various techniques, the reactions of F and F2 with such species are generally reported to have activation energies of... 

Figure 4a shows the thickness of the photoresist layer. Below the threshold dose, nearly no thickness change is observed. When the threshold dose is reached, the layer thickness goes to near zero. Above the threshold dose, a small residual layer was detected that disappears at about 120% of the threshold dose. This behaviour leads to the conclusion that the sidewalls of processed photoresist structures are in a state comparable to that of a pro-... 

In an effort to simulate the theoretical behavior of neuron cells, researchers in the 1940 s and the 1950 s such as McCullogh, Pitts, and Rosenblatt developed functions that mimicked the threshold response of a synapse. Their theory of synapses held that the output of a neuron cell was at or near zero until the sum of all of the input potentials connected to it passed a certain threshold, at which point the cell s output would be at or near one. Mathematically, their neuron functions yielded a binary or a sigmoidal response to a linear combination of its inputs, and could be connected... 

Koplik et al. (1988) considered flow rates in percolation networks from zero (pure diffusion) to extremely high (the convective limit where the average transit time varies linearly with 1/v). The results obtained for many network realizations were averaged. In the case of 2 x 2 and 3x3 network lattices, all possible configurations could be evaluated and hence, the exact averaged transit time moments could be determined. These authors found that anomalous diffusion occurs on networks at the percolation threshold at zero flow. Hence, the CDE does not apply in this case. Koplik et al. (1988) demonstrate that the moments of the transit time distribution for transport near the percolation threshold scale universally. 

The assumption is here that deformation is localized and results in changes in aperture. A threshold value (e ) is considered. Therefore the changes in aperture start when deformation reaches this value. Obviously, deformation perpendicular to the fracture plane should be used when aperture changes have to be obtained. The threshold value (Eo) is associated with fracture initiation. It marks the initiation of the failure of the rock in tension. This parameter will be set to zero if the fracture already exists and has an initial aperture b . The initial aperture can be nearly zero when the fracture exists but is closed. 

Figure 18.10 shows a number of hypothetical dose-effect relations The "unmeasurable range" is indicated widiin the circle. The dashed-dotted line outside the circle indicates the uncertainty in the "measurable range". Line a is based on the ICRP recommendations and the message is clear the risk is zero only at zero radiation dose. Curve b indicates a threshold around SO mSv, below which their is no increase in cancer (or other radiation induced diseases) many radiologists support this hypothesis. Curve d assumes that there is a constant risk at the lowest doses. Curve c illustrates the "quadratic-linear" model, which presently seems to be favored by several radiation protection agencies (incl. ICRP), who assume that the slope near zero is one half of the slope at higher doses and dose rates. As this slope is unknown, it could as well be less. 

Typically in radioanalytical chemistry, the null hypothesis is the hypothesis that no analyte is in the sample. Even if no analyte is present, the net result of the measurement has uncertainty, and, if the measurement were repeated a number of times, a distribution of results about zero, including both positive and negative values, should be observed. Although results near zero are most likely, in principle there is no upper or lower bound for what the result might be. Observation of a positive result in a single measurement does not necessarily constitute strong evidence that the analyte is present. The result must exceed some positive threshold value, called the critical value, to lead one to conclude that the analyte is really present. The question is how to determine the critical value ... 

Rydberg states with a principle quantum number w> 100. These Rydberg states are formed by laser excitation and are located a few cm (or a fraction of meV) below the ionization threshold. Because the electrons ejected from these Rydberg states carry near zero electron kinetic energy, these states are known as ZEKE states and the ejected electrons are named as ZEKEs. The measured electron peak position is lower than that without the presence of the field by the Stark shift 6)... 

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