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In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation , for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature ...
One of the common tasks of numerical analysis is to try to select algorithms which are robust – that is to say, do not produce a wildly different result for very small change in the input data. An opposite phenomenon is instability. Typically, an algorithm involves an approximative method, and in some cases one could prove that the algorithm ...
Complex eigenvalues of an arbitrary map (dots). In case of the Hopf bifurcation, two complex conjugate eigenvalues cross the imaginary axis. In the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where, as a parameter changes, a system's stability switches and a periodic solution arises. [1]
Numerical stability, a property of numerical algorithms which describes how errors in the input data propagate through the algorithm; Stability radius, a property of continuous polynomial functions; Stable theory, concerned with the notion of stability in model theory; Stability, a property of points in geometric invariant theory
That is because what enters the analytic formula for the class number is not h, the class number, on its own — but h log ε, where ε is a fundamental unit. This extra factor is hard to control. It may well be the case that class number 1 for real quadratic fields occurs infinitely often.
Health education aims to immediately impact an individual's knowledge, behavior, or attitude about a health-related topic with the ultimate aim of improving quality of life or health status for an individual. [17] Health education utilizes several different intervention strategies in its practices to improve quality of life and health status.
A new House bill would ban health insurers from imposing arbitrary time limits on patients under anesthesia — days after Anthem Blue Cross Blue Shield only backed off the move amid outcry.
A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8 / 3 An animation of a double-rod pendulum at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory.