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Macaulay's method (the double integration method) is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams.Use of Macaulay's technique is very convenient for cases of discontinuous and/or discrete loading.
The goal of a power-flow study is to obtain complete voltage angles and magnitude information for each bus in a power system for specified load and generator real power and voltage conditions. [3] Once this information is known, real and reactive power flow on each branch as well as generator reactive power output can be analytically determined.
Fig. 1: Isoclines (blue), slope field (black), and some solution curves (red) of y' = xy. The solution curves are y = C e x 2 / 2 {\displaystyle y=Ce^{x^{2}/2}} . Given a family of curves , assumed to be differentiable , an isocline for that family is formed by the set of points at which some member of the family attains a given slope .
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.
the slope field is an array of slope marks in the phase space (in any number of dimensions depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (,,, …,) and is parallel to the vector
Here, is a free parameter encoding the slope at =, which must be greater than or equal to because any smaller value will result in a function with multiple inflection points, which is therefore not a true sigmoid.
The end of the holiday weekend added two fresh examples of a historic shift on Wall Street: More CEOs than ever are heading for the exits. Over the past 24 hours, the leaders of chipmaker Intel ...
Heun's Method addresses this problem by considering the interval spanned by the tangent line segment as a whole. Taking a concave-up example, the left tangent prediction line underestimates the slope of the curve for the entire width of the interval from the current point to the next predicted point.