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Graphs of cumulative percent passing versus the logarithmic sieve size. The results are presented in a graph of percent passing versus the sieve size. On the graph the sieve size scale is logarithmic. To find the percent of aggregate passing through each sieve, first find the percent retained in each sieve. To do so, the following equation is used,
Step-growth polymerization is a random process so we can use statistics to calculate the probability of finding a chain with x-structural units ("x-mer") as a function of time or conversion. Probability that an 'A' functional group has reacted. Probability of finding an 'A' unreacted.
Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time ...
P–P plot. In statistics, a P–P plot ( probability–probability plot or percent–percent plot or P value plot) is a probability plot for assessing how closely two data sets agree, or for assessing how closely a dataset fits a particular model. It works by plotting the two cumulative distribution functions against each other; if they are ...
The greedy algorithm, which builds up a set by incrementally adding the element which increases the most at each step, produces as output a set that is at least (/) (). That is, greedy performs within a constant factor of ( 1 − 1 / e ) ≈ 0.63 {\displaystyle (1-1/e)\approx 0.63} as good as the optimal solution.
Ammonium sulfate precipitation is a useful technique as an initial step in protein purification because it enables quick, bulk precipitation of cellular proteins. [4] It is also often employed during the later stages of purification to concentrate protein from dilute solution following procedures such as gel filtration.
The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from zero to one in a very short time.
Logarithmic scale. A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences between the magnitudes of the numbers involved. Unlike a linear scale where each unit of distance corresponds to the same increment, on a logarithmic scale each ...