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The Universal Soil Loss Equation (USLE) is a widely used mathematical model that describes soil erosion processes. [1]Erosion models play critical roles in soil and water resource conservation and nonpoint source pollution assessments, including: sediment load assessment and inventory, conservation planning and design for sediment control, and for the advancement of scientific understanding.
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
Stream power is the rate of energy dissipation against the bed and banks of a river or stream per unit downstream length. It is given by the equation: = where Ω is the stream power, ρ is the density of water (1000 kg/m 3), g is acceleration due to gravity (9.8 m/s 2), Q is discharge (m 3 /s), and S is the channel slope.
It has also been called Sen's slope estimator, [1] [2] slope selection, [3] [4] the single median method, [5] the Kendall robust line-fit method, [6] and the Kendall–Theil robust line. [7] It is named after Henri Theil and Pranab K. Sen , who published papers on this method in 1950 and 1968 respectively, [ 8 ] and after Maurice Kendall ...
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
In other words, it assumes that the electrode mass transfer rate is much greater than the reaction rate, and that the reaction is dominated by the slower chemical reaction rate ". [7] [circular reference] Also, at a given electrode the Tafel equation assumes that the reverse half reaction rate is negligible compared to the forward reaction rate.
For example, if the MRS xy = 2, the consumer will give up 2 units of Y to obtain 1 additional unit of X. As one moves down a (standardly convex) indifference curve, the marginal rate of substitution decreases (as measured by the absolute value of the slope of the indifference curve, which decreases).
The definition of strain rate was first introduced in 1867 by American metallurgist Jade LeCocq, who defined it as "the rate at which strain occurs. It is the time rate of change of strain." In physics the strain rate is generally defined as the derivative of the strain with respect to time. Its precise definition depends on how strain is measured.
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