Range Approximations

In the case where nuclear stopping predominates, the range can be estimated by ignoring the contributions from electronic stopping  

A power law-based estimate of the nuclear stopping cross-section, Sn(E), given in (5.7), results in an approximate expression for R, which is given by 

A rather useful rule-of-thumb equation for predicting heavy-ion ranges (m = 1/2), usually with an accuracy of -30-40%. is given by 

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In general, FAB and LSIMS will give excellent molecular mass information in the range (approximately) of m/z 100-2000. Above this value, the abundance of molecular ions tends to diminish until, in the region of m/z 4000-5000, they become either nonexistent or very difficult to... 

Effect of Feed Rate The effect of feed rate on hydrodesulfiirization of vacuum gas oil is shown in Figure 3. Halving the feed rate in this range approximately halves the product sulfur. 

In Europe, synthesis gas is mainly produced by steam reforming naphtha. Because naphtha is a mixture of hydrocarbons ranging approximately from C5-C10, the steam reforming reaction may be represented using n-heptane ... 

The stability of tin over the middle pH range (approximately 3-5-9), its solubility in acids or alkalis (modified by the high hydrogen overpotential), and the formation of complex ions are the basis of its general corrosion behaviour. Other properties which have influenced the selection of tin for particular purposes are the non-toxicity of tin salts and the absence of catalytic promotion of oxidation processes that may cause changes in oils or other neutral media affecting their quality or producing corrosive acids. 

From the sensitivity diagrams it would appear that the influence of parameter Vq is small at the beginning, peaks over the range approximately between 8 and 12 days, and slowly fades, being still evident at 20 days conversely, the MCCC study would indicate its maximal effect at the very beginning of the experiment, with a subsequent fast monotonic decrease to essentially zero within 5 days. 

Elevated serum creatinine concentration (normal range approximately 0.6 to 1.2 mg/dL [53 to 106 pmol/L])... 

The pH optimum of an enzyme will often vary from one substrate to another and must be determined for each substrate. The buffer system used will often affect the overall activity of an enzyme and may alter its pH optimum. In general, the amino buffers such as glycylglycine and tricine, etc. (Table 8.2) result in a greater enzyme activity than do the simple inorganic buffers such as phosphate and carbonate. Buffers are most effective over a narrow pH range (approximately two units) which centres on their pK, value. Those buffers with pKa values similar to the known optimum pH of the enzyme should be tested for their effect on the activity of the enzyme over a limited pH range. 

Diesel fuel fnel nsed for internal combnstion in diesel engines usually, that fraction which distills within the temperature range approximately 200 to 370°C. A general term covering oils used as fuel in diesel and other compression ignition engines. 

Light Cycle Oil (LCO) is composed of liquid products boiling in the range approximately 430°-700°F (494-644 K). The best linear regression model to predict LCO yield for catalyst A has the form ... 

Numerically the polarizability contribution to the deuterium IK energy shift in the zero range approximation is equal to [39]... 

Experimental data on the deuterium-hydrogen isotope shift (see Table 12.4 below) have an accuracy of about 0.1 kHz and, hence, a more accurate theoretical result for the polarizability contribution is required. In order to obtain such a result it is necessary to go beyond the zero range approximation, and take the deuteron structure into account in more detail. Fortunately, there exist a number of phenomenological potentials which describe the properties of the deuteron in all details. Some calculations with realistic proton-neutron potentials were performed [40, 41, 42, 43]. The most precise results were obtained in [43]... 

A breakthrough was achieved a few years ago when it was realized that an anal dic calculation of the deuterium recoil, structure and polarizability corrections is possible in the zero range approximation [76, 77]. An analytic result for the difference in (12.29), obtained as a result of a nice calculation in [77], is numerically equal 44 kHz, and within the accuracy of the zero range approximation perfectly explains the difference between the experimental result and the sum of the nonrecoil corrections. More accurate calculations of the nuclear effects in the deuterium hyperfine structure beyond the zero range approximation are feasible, and the theory of recoil and nuclear corrections was later improved in a number of papers [78, 79, 80, 81, 82]. Comparison of the results of these works with the experimental data on the deuterium hyperfine splitting may be used as a test of the deuteron models and state of the art of the nuclear calculations. 

Mass transfer coefficient range (approximate values). 

Molecular Weight Molecular Weight Range Approximate Number Class (kDa) of P Chains... 

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