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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 ...
This analogy with mechanical equilibrium motivates the terminology of stability and instability. In mathematics, and especially algebraic geometry, stability is a notion which characterises when a geometric object, for example a point, an algebraic variety, a vector bundle, or a sheaf, has some desirable properties for the purpose of ...
Stability generally increases to the left of the diagram. [1] Some sink, source or node are equilibrium points. 2-dimensional case refers to Phase plane. In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable.
A surface shaped like this with two "low points" can act as a bistable system; a ball resting on the surface can only be stable at those two positions, such as balls marked "1" and "2". Between the two is a local maximum . A ball located at this point, ball 3, is in equilibrium but unstable; the slightest disturbance will cause it to move to ...
A group of finite Morley rank is an abstract group G such that the formula x = x has finite Morley rank for the model G.It follows from the definition that the theory of a group of finite Morley rank is ω-stable; therefore groups of finite Morley rank are stable groups.
Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale ...
Such stability conditions were introduced in a rudimentary form by Michael Douglas called -stability and used to study BPS B-branes in string theory. [1] This concept was made precise by Bridgeland, who phrased these stability conditions categorically, and initiated their study mathematically.
Limits Of Stability (LOS) Test: This is a more advanced tool compared to FRT and is used to measure balance under multi-directional conditions. In this test, the subject stands on force plates and intentionally shifts their body weight in the cued direction.