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The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper ...
The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. [1] It has applications in geophysics, seismic imaging, photonics and more recently in neural networks. [2] The adjoint state space is chosen to simplify the physical interpretation of equation ...
For example, a typical gradient profile in reversed phase chromatography for might start at 5% acetonitrile (in water or aqueous buffer) and progress linearly to 95% acetonitrile over 5–25 minutes. Periods of constant mobile phase composition (plateau) may be also part of a gradient profile.
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.
Example: For a column of fresh water of 8.33 pounds per gallon (lb/U.S. gal) standing still hydrostatically in a 21,000 feet vertical cased wellbore from top to bottom (vertical hole), the pressure gradient would be grad(P) = pressure gradient = 8.33 / 19.25 = 0.43273 psi/ft. and the hydrostatic bottom hole pressure (BHP) is then
A calibration curve plot showing limit of detection (LOD), limit of quantification (LOQ), dynamic range, and limit of linearity (LOL).. In analytical chemistry, a calibration curve, also known as a standard curve, is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration. [1]
Rational Numbers Excel Add-In Proprietary: De novo identification tool for small molecules that works with Microsoft Excel (2010, 2013, 2016 and 2019). This software treats small molecules as mathematical partitions of the molecular mass and generates subfragment formulas with atoms that are sets of partitions comprising the molecular formula.
For avoidance of saddle points: For example, if the gradient of the cost function is Lipschitz continuous and one chooses standard GD with learning rate <1/L, then with a random choice of initial point (more precisely, outside a set of Lebesgue measure zero), the sequence constructed will not converge to a non-degenerate saddle point (proven in ...