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A Poincaré plot, named after Henri Poincaré, is a graphical representation used to visualize the relationship between consecutive data points in time series to detect patterns and irregularities in the time series, revealing information about the stability of dynamical systems, providing insights into periodic orbits, chaotic motions, and bifurcations.
Pile weave is a form of textile created by weaving. This type of fabric is characterized by a pile —a looped or tufted surface that extends above the initial foundation, or 'ground' weave. The pile is formed by supplemental yarn running in the direction of the length of the fabric ( warp pile weave ) or the width of the fabric ( weft or ...
Q dy = ultimate dynamic bearing capacity of driven pile; α = pile driving hammer efficiency; W H = weight of hammer; H = hammer drop; S = inelastic set of piles, in distance pr. hammer blow; S e = elastic set of piles, in distance pr. hammer blow; L = pile length; A = pile end area; E = modulus of elasticity of pile material
Symmetry breaking in pitchfork bifurcation as the parameter ε is varied. ε = 0 is the case of symmetric pitchfork bifurcation.. In a dynamical system such as ¨ + (;) + =, which is structurally stable when , if a bifurcation diagram is plotted, treating as the bifurcation parameter, but for different values of , the case = is the symmetric pitchfork bifurcation.
The normal distribution is NOT assumed nor required in the calculation of control limits. Thus making the IndX/mR chart a very robust tool. This is demonstrated by Wheeler using real-world data [4], [5] and for a number of highly non-normal probability distributions. [6]
For diagrams that do not possess grid lines, the easiest way to determine the values is to determine the shortest (i.e. perpendicular) distances from the point of interest to each of the three sides. By Viviani's theorem , the distances (or the ratios of the distances to the triangle height ) give the value of each component.
The plot is occasionally attributed to Augustinsson [5] and referred to the Woolf–Augustinsson–Hofstee plot [6] [7] [8] or simply the Augustinsson plot. [9] However, although Haldane, Woolf or Eadie were not explicitly cited when Augustinsson introduced the versus / equation, both the work of Haldane [10] and of Eadie [3] are cited at other places of his work and are listed in his ...
In particular "pile length" or "pile depth" refer to the length of the yarn strands (half-length of the loops). Pile length affects and is affected by knot density: "The greater the knot density, the thinner the weft and warp yarns and the more weakly are they twisted; the smaller the density, the coarser are the foundation yarns."