Statistics chance

Based on the flame-hole dynamics [59], dynamic evolutions of flame holes were simulated to yield the statistical chance to determine the reacting or quenched flame surface under the randomly fluctuating 2D strain-rate field. The flame-hole d5mamics have also been applied to turbulent flame stabilization by considering the realistic turbulence effects by introducing fluctuating 2D strain-rate field [22] and adopting the level-set method [60]. 

Some of the mathematical basis for the equations is due to the geneticist Moto Kimura, who is considered a resolute proponent of the neutral theory of evolution , which states that statistical, chance fluctuations are more important in the formation of new species than is Darwinian natural selection. Evolution via such chance fluctuations is referred to as genetic drift . Dyson considers that both forms of evolution are important (Dyson, 1999). 

The enzyme would not be useful. The probability of finding a particular unique restriction site of length 10 is 1/(4 °) = 1/1,048,576, i.e., about once per million base pairs of DNA. Therefore most viral genomes that contain only 50,000 base pairs have little statistical chance of having a site that would be recognized by this enzyme. 

Water, hydroxyl, and hydrogen ions have very special electrical properties. Water is strongly polar, but it is also to a small extent an electrolyte in itself. From Table 2.2, we see that the intrinsic conductivity is low, but it is not zero. The small rest conductivity is due to a protonic self-ionizing process. There is a small statistical chance that a water molecule transfers one of its protons to another water molecule in the following way ... 

The appearance of the fatigue fractures in specimens tested at both 75 and -300 F are quite typical of those stressed in reversed bending (Fig. 16). All fractures disclosed the characteristic mother-of-pearl" or "oyster shell" appearance. The nucleus of the fracture almost invariably is at die surface. The bead-on specimens fractured invariably at the plate, weld bead interface at both test temperatures. This is expected, since there is a geometrical or mechanical notch created by the bead. TTie bead-off specimens fractured either in the weld deposit or heat-affected zone when tested at 75 F. The location of the fracture appears unrelated to stress level and may merely represent the statistical chance of failing in either one of those two locations. At -300 F, the bead-off specimens fractured in the weld, indicating that the metallurgical notch, created by the weld deposit and heat-affected zone, has become relatively unimportant at this low temperature. 

Mathematical probability deals with the random or chance variation of numerical data. When the probability or statistical chance is expressed numerically (percentage or decimal), it is a specific likelihood representing the ratio of chances in favor to total chances available. In the usual probability-distribution graphs probability is represented by an area under the frequency curve. 

Elementary steps are described as unimolecular if only one chemical species (atom, ion, radical or molecule) is involved, and bimolecular if two chemical species are involved. True termolecular steps in the gas phase, which would involve the simultaneous collision of three chemical species, are virtually impossible, since the statistical chance of three species colliding is considerably less than that of two particles colliding. 

Of course, provision of accident data is not a panacea for removing incentives for cheating. Reductions in maintenance can occur long before they are reflected in accident rates. A purely informational response to a market failure due to myopia would therefore need to provide information on safety inputs such as maintenance activities, training and the age and condition of capital equipment. These are much more difflcult metrics to measure and to convey to customers than are accident data. For smaller railroads, information on accidents in a given year is unlikely to provide useful information on whether the safety precautions undertaken by that railroad are deteriorating. Accidents are rare events and it my be difflcult to determine from year to year whether the occurrence of an accident is due to myopic behavior or simply due to statistical chance. 

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